text: ///////////////////////////////////////////////////////////////////////
  // File:        colpartition.cpp
  // Description: Class to hold partitions of the page that correspond
  //              roughly to text lines.
  // Author:      Ray Smith
  //
  // (C) Copyright 2008, Google Inc.
  // Licensed under the Apache License, Version 2.0 (the "License");
  // you may not use this file except in compliance with the License.
  // You may obtain a copy of the License at
  // http://www.apache.org/licenses/LICENSE-2.0
  // Unless required by applicable law or agreed to in writing, software
  // distributed under the License is distributed on an "AS IS" BASIS,
  // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  // See the License for the specific language governing permissions and
  // limitations under the License.
  //
  ///////////////////////////////////////////////////////////////////////
  
  #ifdef HAVE_CONFIG_H
  #  include "config_auto.h"
  #endif
  
  #include "colpartition.h"
  #include "colpartitiongrid.h"
  #include "colpartitionset.h"
  #include "detlinefit.h"
  #include "helpers.h" // for UpdateRange
  #include "dppoint.h"
  #include "host.h" // for NearlyEqual
  #include "imagefind.h"
  #include "workingpartset.h"
  
  #include <algorithm>
  
  namespace tesseract {
  
  //////////////// ColPartition Implementation ////////////////
  
  // enum to refer to the entries in a neighbourhood of lines.
  // Used by SmoothSpacings to test for blips with OKSpacingBlip.
  enum SpacingNeighbourhood {
    PN_ABOVE2,
    PN_ABOVE1,
    PN_UPPER,
    PN_LOWER,
    PN_BELOW1,
    PN_BELOW2,
    PN_COUNT
  };
  
  // Maximum change in spacing (in inches) to ignore.
  const double kMaxSpacingDrift = 1.0 / 72; // 1/72 is one point.
  // Maximum fraction of line height used as an additional allowance
  // for top spacing.
  const double kMaxTopSpacingFraction = 0.25;
  // What multiple of the largest line height should be used as an upper bound
  // for whether lines are in the same text block?
  const double kMaxSameBlockLineSpacing = 3;
  // Maximum ratio of sizes for lines to be considered the same size.
  const double kMaxSizeRatio = 1.5;
  // Fraction of max of leader width and gap for max IQR of gaps.
  const double kMaxLeaderGapFractionOfMax = 0.25;
  // Fraction of min of leader width and gap for max IQR of gaps.
  const double kMaxLeaderGapFractionOfMin = 0.5;
  // Minimum number of blobs to be considered a leader.
  const int kMinLeaderCount = 5;
  // Minimum score for a STRONG_CHAIN textline.
  const int kMinStrongTextValue = 6;
  // Minimum score for a CHAIN textline.
  const int kMinChainTextValue = 3;
  // Minimum number of blobs for strong horizontal text lines.
  const int kHorzStrongTextlineCount = 8;
  // Minimum height (in image pixels) for strong horizontal text lines.
  const int kHorzStrongTextlineHeight = 10;
  // Minimum aspect ratio for strong horizontal text lines.
  const int kHorzStrongTextlineAspect = 5;
  // Maximum upper quartile error allowed on a baseline fit as a fraction
  // of height.
  const double kMaxBaselineError = 0.4375;
  // Min coverage for a good baseline between vectors
  const double kMinBaselineCoverage = 0.5;
  // Max RMS color noise to compare colors.
  const int kMaxRMSColorNoise = 128;
  // Maximum distance to allow a partition color to be to use that partition
  // in smoothing neighbouring types. This is a squared distance.
  const int kMaxColorDistance = 900;
  
  // blob_type is the blob_region_type_ of the blobs in this partition.
  // Vertical is the direction of logical vertical on the possibly skewed image.
  ColPartition::ColPartition(BlobRegionType blob_type, const ICOORD &vertical)
      : left_margin_(-INT32_MAX)
      , right_margin_(INT32_MAX)
      , median_bottom_(INT32_MAX)
      , median_top_(-INT32_MAX)
      , median_left_(INT32_MAX)
      , median_right_(-INT32_MAX)
      , blob_type_(blob_type)
      , vertical_(vertical) {
    memset(special_blobs_densities_, 0, sizeof(special_blobs_densities_));
  }
  
  // Constructs a fake ColPartition with a single fake BLOBNBOX, all made
  // from a single TBOX.
  // WARNING: Despite being on C_LISTs, the BLOBNBOX owns the C_BLOB and
  // the ColPartition owns the BLOBNBOX!!!
  // Call DeleteBoxes before deleting the ColPartition.
  ColPartition *ColPartition::FakePartition(const TBOX &box, PolyBlockType block_type,
                                            BlobRegionType blob_type, BlobTextFlowType flow) {
    auto *part = new ColPartition(blob_type, ICOORD(0, 1));
    part->set_type(block_type);
    part->set_flow(flow);
    part->AddBox(new BLOBNBOX(C_BLOB::FakeBlob(box)));
    part->set_left_margin(box.left());
    part->set_right_margin(box.right());
    part->SetBlobTypes();
    part->ComputeLimits();
    part->ClaimBoxes();
    return part;
  }
  
  // Constructs and returns a ColPartition with the given real BLOBNBOX,
  // and sets it up to be a "big" partition (single-blob partition bigger
  // than the surrounding text that may be a dropcap, two or more vertically
  // touching characters, or some graphic element.
  // If the given list is not nullptr, the partition is also added to the list.
  ColPartition *ColPartition::MakeBigPartition(BLOBNBOX *box, ColPartition_LIST *big_part_list) {
    box->set_owner(nullptr);
    auto *single = new ColPartition(BRT_UNKNOWN, ICOORD(0, 1));
    single->set_flow(BTFT_NONE);
    single->AddBox(box);
    single->ComputeLimits();
    single->ClaimBoxes();
    single->SetBlobTypes();
    single->set_block_owned(true);
    if (big_part_list != nullptr) {
      ColPartition_IT part_it(big_part_list);
      part_it.add_to_end(single);
    }
    return single;
  }
  
  ColPartition::~ColPartition() {
    // Remove this as a partner of all partners, as we don't want them
    // referring to a deleted object.
    ColPartition_C_IT it(&upper_partners_);
    for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
      it.data()->RemovePartner(false, this);
    }
    it.set_to_list(&lower_partners_);
    for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
      it.data()->RemovePartner(true, this);
    }
  }
  
  // Constructs a fake ColPartition with no BLOBNBOXes to represent a
  // horizontal or vertical line, given a type and a bounding box.
  ColPartition *ColPartition::MakeLinePartition(BlobRegionType blob_type, const ICOORD &vertical,
                                                int left, int bottom, int right, int top) {
    auto *part = new ColPartition(blob_type, vertical);
    part->bounding_box_ = TBOX(left, bottom, right, top);
    part->median_bottom_ = bottom;
    part->median_top_ = top;
    part->median_height_ = top - bottom;
    part->median_left_ = left;
    part->median_right_ = right;
    part->median_width_ = right - left;
    part->left_key_ = part->BoxLeftKey();
    part->right_key_ = part->BoxRightKey();
    return part;
  }
  
  // Adds the given box to the partition, updating the partition bounds.
  // The list of boxes in the partition is updated, ensuring that no box is
  // recorded twice, and the boxes are kept in increasing left position.
  void ColPartition::AddBox(BLOBNBOX *bbox) {
    TBOX box = bbox->bounding_box();
    // Update the partition limits.
    if (boxes_.empty()) {
      bounding_box_ = box;
    } else {
      bounding_box_ += box;
    }
  
    if (IsVerticalType()) {
      if (!last_add_was_vertical_) {
        boxes_.sort(SortByBoxBottom<BLOBNBOX>);
        last_add_was_vertical_ = true;
      }
      boxes_.add_sorted(SortByBoxBottom<BLOBNBOX>, true, bbox);
    } else {
      if (last_add_was_vertical_) {
        boxes_.sort(SortByBoxLeft<BLOBNBOX>);
        last_add_was_vertical_ = false;
      }
      boxes_.add_sorted(SortByBoxLeft<BLOBNBOX>, true, bbox);
    }
    if (!left_key_tab_) {
      left_key_ = BoxLeftKey();
    }
    if (!right_key_tab_) {
      right_key_ = BoxRightKey();
    }
    if (TabFind::WithinTestRegion(2, box.left(), box.bottom())) {
      tprintf("Added box (%d,%d)->(%d,%d) left_blob_x_=%d, right_blob_x_ = %d\n", box.left(),
              box.bottom(), box.right(), box.top(), bounding_box_.left(), bounding_box_.right());
    }
  }
  
  // Removes the given box from the partition, updating the bounds.
  void ColPartition::RemoveBox(BLOBNBOX *box) {
    BLOBNBOX_C_IT bb_it(&boxes_);
    for (bb_it.mark_cycle_pt(); !bb_it.cycled_list(); bb_it.forward()) {
      if (box == bb_it.data()) {
        bb_it.extract();
        ComputeLimits();
        return;
      }
    }
  }
  
  // Returns the tallest box in the partition, as measured perpendicular to the
  // presumed flow of text.
  BLOBNBOX *ColPartition::BiggestBox() {
    BLOBNBOX *biggest = nullptr;
    BLOBNBOX_C_IT bb_it(&boxes_);
    for (bb_it.mark_cycle_pt(); !bb_it.cycled_list(); bb_it.forward()) {
      BLOBNBOX *bbox = bb_it.data();
      if (IsVerticalType()) {
        if (biggest == nullptr || bbox->bounding_box().width() > biggest->bounding_box().width()) {
          biggest = bbox;
        }
      } else {
        if (biggest == nullptr || bbox->bounding_box().height() > biggest->bounding_box().height()) {
          biggest = bbox;
        }
      }
    }
    return biggest;
  }
  
  // Returns the bounding box excluding the given box.
  TBOX ColPartition::BoundsWithoutBox(BLOBNBOX *box) {
    TBOX result;
    BLOBNBOX_C_IT bb_it(&boxes_);
    for (bb_it.mark_cycle_pt(); !bb_it.cycled_list(); bb_it.forward()) {
      if (box != bb_it.data()) {
        result += bb_it.data()->bounding_box();
      }
    }
    return result;
  }
  
  // Claims the boxes in the boxes_list by marking them with a this owner
  // pointer. If a box is already owned, then it must be owned by this.
  void ColPartition::ClaimBoxes() {
    BLOBNBOX_C_IT bb_it(&boxes_);
    for (bb_it.mark_cycle_pt(); !bb_it.cycled_list(); bb_it.forward()) {
      BLOBNBOX *bblob = bb_it.data();
      ColPartition *other = bblob->owner();
      if (other == nullptr) {
        // Normal case: ownership is available.
        bblob->set_owner(this);
      } else {
        ASSERT_HOST(other == this);
      }
    }
  }
  
  // nullptr the owner of the blobs in this partition, so they can be deleted
  // independently of the ColPartition.
  void ColPartition::DisownBoxes() {
    BLOBNBOX_C_IT bb_it(&boxes_);
    for (bb_it.mark_cycle_pt(); !bb_it.cycled_list(); bb_it.forward()) {
      BLOBNBOX *bblob = bb_it.data();
      ASSERT_HOST(bblob->owner() == this || bblob->owner() == nullptr);
      bblob->set_owner(nullptr);
    }
  }
  
  // nullptr the owner of the blobs in this partition that are owned by this
  // partition, so they can be deleted independently of the ColPartition.
  // Any blobs that are not owned by this partition get to keep their owner
  // without an assert failure.
  void ColPartition::DisownBoxesNoAssert() {
    BLOBNBOX_C_IT bb_it(&boxes_);
    for (bb_it.mark_cycle_pt(); !bb_it.cycled_list(); bb_it.forward()) {
      BLOBNBOX *bblob = bb_it.data();
      if (bblob->owner() == this) {
        bblob->set_owner(nullptr);
      }
    }
  }
  
  // Nulls the owner of the blobs in this partition that are owned by this
  // partition and not leader blobs, removing them from the boxes_ list, thus
  // turning this partition back to a leader partition if it contains a leader,
  // or otherwise leaving it empty. Returns true if any boxes remain.
  bool ColPartition::ReleaseNonLeaderBoxes() {
    BLOBNBOX_C_IT bb_it(&boxes_);
    for (bb_it.mark_cycle_pt(); !bb_it.cycled_list(); bb_it.forward()) {
      BLOBNBOX *bblob = bb_it.data();
      if (bblob->flow() != BTFT_LEADER) {
        if (bblob->owner() == this) {
          bblob->set_owner(nullptr);
        }
        bb_it.extract();
      }
    }
    if (bb_it.empty()) {
      return false;
    }
    flow_ = BTFT_LEADER;
    ComputeLimits();
    return true;
  }
  
  // Delete the boxes that this partition owns.
  void ColPartition::DeleteBoxes() {
    // Although the boxes_ list is a C_LIST, in some cases it owns the
    // BLOBNBOXes, as the ColPartition takes ownership from the grid,
    // and the BLOBNBOXes own the underlying C_BLOBs.
    for (BLOBNBOX_C_IT bb_it(&boxes_); !bb_it.empty(); bb_it.forward()) {
      BLOBNBOX *bblob = bb_it.extract();
      delete bblob->cblob();
      delete bblob;
    }
  }
  
  // Reflects the partition in the y-axis, assuming that its blobs have
  // already been done. Corrects only a limited part of the members, since
  // this function is assumed to be used shortly after initial creation, which
  // is before a lot of the members are used.
  void ColPartition::ReflectInYAxis() {
    BLOBNBOX_CLIST reversed_boxes;
    BLOBNBOX_C_IT reversed_it(&reversed_boxes);
    // Reverse the order of the boxes_.
    BLOBNBOX_C_IT bb_it(&boxes_);
    for (bb_it.mark_cycle_pt(); !bb_it.cycled_list(); bb_it.forward()) {
      reversed_it.add_before_then_move(bb_it.extract());
    }
    bb_it.add_list_after(&reversed_boxes);
    ASSERT_HOST(!left_key_tab_ && !right_key_tab_);
    int tmp = left_margin_;
    left_margin_ = -right_margin_;
    right_margin_ = -tmp;
    ComputeLimits();
  }
  
  // Returns true if this is a legal partition - meaning that the conditions
  // left_margin <= bounding_box left
  // left_key <= bounding box left key
  // bounding box left <= bounding box right
  // and likewise for right margin and key
  // are all met.
  bool ColPartition::IsLegal() {
    if (bounding_box_.left() > bounding_box_.right()) {
      if (textord_debug_bugs) {
        tprintf("Bounding box invalid\n");
        Print();
      }
      return false; // Bounding box invalid.
    }
    if (left_margin_ > bounding_box_.left() || right_margin_ < bounding_box_.right()) {
      if (textord_debug_bugs) {
        tprintf("Margins invalid\n");
        Print();
      }
      return false; // Margins invalid.
    }
    if (left_key_ > BoxLeftKey() || right_key_ < BoxRightKey()) {
      if (textord_debug_bugs) {
        tprintf("Key inside box: %d v %d or %d v %d\n", left_key_, BoxLeftKey(), right_key_,
                BoxRightKey());
        Print();
      }
      return false; // Keys inside the box.
    }
    return true;
  }
  
  // Returns true if the left and right edges are approximately equal.
  bool ColPartition::MatchingColumns(const ColPartition &other) const {
    int y = (MidY() + other.MidY()) / 2;
    if (!NearlyEqual(other.LeftAtY(y) / kColumnWidthFactor, LeftAtY(y) / kColumnWidthFactor, 1)) {
      return false;
    }
    if (!NearlyEqual(other.RightAtY(y) / kColumnWidthFactor, RightAtY(y) / kColumnWidthFactor, 1)) {
      return false;
    }
    return true;
  }
  
  // Returns true if the colors match for two text partitions.
  bool ColPartition::MatchingTextColor(const ColPartition &other) const {
    if (color1_[L_ALPHA_CHANNEL] > kMaxRMSColorNoise &&
        other.color1_[L_ALPHA_CHANNEL] > kMaxRMSColorNoise) {
      return false; // Too noisy.
    }
  
    // Colors must match for other to count.
    double d_this1_o = ImageFind::ColorDistanceFromLine(other.color1_, other.color2_, color1_);
    double d_this2_o = ImageFind::ColorDistanceFromLine(other.color1_, other.color2_, color2_);
    double d_o1_this = ImageFind::ColorDistanceFromLine(color1_, color2_, other.color1_);
    double d_o2_this = ImageFind::ColorDistanceFromLine(color1_, color2_, other.color2_);
    // All 4 distances must be small enough.
    return d_this1_o < kMaxColorDistance && d_this2_o < kMaxColorDistance &&
           d_o1_this < kMaxColorDistance && d_o2_this < kMaxColorDistance;
  }
  
  // Returns true if the sizes match for two text partitions,
  // taking orientation into account. See also SizesSimilar.
  bool ColPartition::MatchingSizes(const ColPartition &other) const {
    if (blob_type_ == BRT_VERT_TEXT || other.blob_type_ == BRT_VERT_TEXT) {
      return !TabFind::DifferentSizes(median_width_, other.median_width_);
    } else {
      return !TabFind::DifferentSizes(median_height_, other.median_height_);
    }
  }
  
  // Returns true if there is no tabstop violation in merging this and other.
  bool ColPartition::ConfirmNoTabViolation(const ColPartition &other) const {
    if (bounding_box_.right() < other.bounding_box_.left() &&
        bounding_box_.right() < other.LeftBlobRule()) {
      return false;
    }
    if (other.bounding_box_.right() < bounding_box_.left() &&
        other.bounding_box_.right() < LeftBlobRule()) {
      return false;
    }
    if (bounding_box_.left() > other.bounding_box_.right() &&
        bounding_box_.left() > other.RightBlobRule()) {
      return false;
    }
    if (other.bounding_box_.left() > bounding_box_.right() &&
        other.bounding_box_.left() > RightBlobRule()) {
      return false;
    }
    return true;
  }
  
  // Returns true if other has a similar stroke width to this.
  bool ColPartition::MatchingStrokeWidth(const ColPartition &other, double fractional_tolerance,
                                         double constant_tolerance) const {
    int match_count = 0;
    int nonmatch_count = 0;
    BLOBNBOX_C_IT box_it(const_cast<BLOBNBOX_CLIST *>(&boxes_));
    BLOBNBOX_C_IT other_it(const_cast<BLOBNBOX_CLIST *>(&other.boxes_));
    box_it.mark_cycle_pt();
    other_it.mark_cycle_pt();
    while (!box_it.cycled_list() && !other_it.cycled_list()) {
      if (box_it.data()->MatchingStrokeWidth(*other_it.data(), fractional_tolerance,
                                             constant_tolerance)) {
        ++match_count;
      } else {
        ++nonmatch_count;
      }
      box_it.forward();
      other_it.forward();
    }
    return match_count > nonmatch_count;
  }
  
  // Returns true if base is an acceptable diacritic base char merge
  // with this as the diacritic.
  // Returns true if:
  // (1) this is a ColPartition containing only diacritics, and
  // (2) the base characters indicated on the diacritics all believably lie
  // within the text line of the candidate ColPartition.
  bool ColPartition::OKDiacriticMerge(const ColPartition &candidate, bool debug) const {
    BLOBNBOX_C_IT it(const_cast<BLOBNBOX_CLIST *>(&boxes_));
    int min_top = INT32_MAX;
    int max_bottom = -INT32_MAX;
    for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
      BLOBNBOX *blob = it.data();
      if (!blob->IsDiacritic()) {
        if (debug) {
          tprintf("Blob is not a diacritic:");
          blob->bounding_box().print();
        }
        return false; // All blobs must have diacritic bases.
      }
      if (blob->base_char_top() < min_top) {
        min_top = blob->base_char_top();
      }
      if (blob->base_char_bottom() > max_bottom) {
        max_bottom = blob->base_char_bottom();
      }
    }
    // If the intersection of all vertical ranges of all base characters
    // overlaps the median range of this, then it is OK.
    bool result = min_top > candidate.median_bottom_ && max_bottom < candidate.median_top_;
    if (debug) {
      if (result) {
        tprintf("OKDiacritic!\n");
      } else {
        tprintf("y ranges don\'t overlap: %d-%d / %d-%d\n", max_bottom, min_top, median_bottom_,
                median_top_);
      }
    }
    return result;
  }
  
  // Sets the sort key using either the tab vector, or the bounding box if
  // the tab vector is nullptr. If the tab_vector lies inside the bounding_box,
  // use the edge of the box as a key any way.
  void ColPartition::SetLeftTab(const TabVector *tab_vector) {
    if (tab_vector != nullptr) {
      left_key_ = tab_vector->sort_key();
      left_key_tab_ = left_key_ <= BoxLeftKey();
    } else {
      left_key_tab_ = false;
    }
    if (!left_key_tab_) {
      left_key_ = BoxLeftKey();
    }
  }
  
  // As SetLeftTab, but with the right.
  void ColPartition::SetRightTab(const TabVector *tab_vector) {
    if (tab_vector != nullptr) {
      right_key_ = tab_vector->sort_key();
      right_key_tab_ = right_key_ >= BoxRightKey();
    } else {
      right_key_tab_ = false;
    }
    if (!right_key_tab_) {
      right_key_ = BoxRightKey();
    }
  }
  
  // Copies the left/right tab from the src partition, but if take_box is
  // true, copies the box instead and uses that as a key.
  void ColPartition::CopyLeftTab(const ColPartition &src, bool take_box) {
    left_key_tab_ = take_box ? false : src.left_key_tab_;
    if (left_key_tab_) {
      left_key_ = src.left_key_;
    } else {
      bounding_box_.set_left(XAtY(src.BoxLeftKey(), MidY()));
      left_key_ = BoxLeftKey();
    }
    if (left_margin_ > bounding_box_.left()) {
      left_margin_ = src.left_margin_;
    }
  }
  
  // As CopyLeftTab, but with the right.
  void ColPartition::CopyRightTab(const ColPartition &src, bool take_box) {
    right_key_tab_ = take_box ? false : src.right_key_tab_;
    if (right_key_tab_) {
      right_key_ = src.right_key_;
    } else {
      bounding_box_.set_right(XAtY(src.BoxRightKey(), MidY()));
      right_key_ = BoxRightKey();
    }
    if (right_margin_ < bounding_box_.right()) {
      right_margin_ = src.right_margin_;
    }
  }
  
  // Returns the left rule line x coord of the leftmost blob.
  int ColPartition::LeftBlobRule() const {
    BLOBNBOX_C_IT it(const_cast<BLOBNBOX_CLIST *>(&boxes_));
    return it.data()->left_rule();
  }
  // Returns the right rule line x coord of the rightmost blob.
  int ColPartition::RightBlobRule() const {
    BLOBNBOX_C_IT it(const_cast<BLOBNBOX_CLIST *>(&boxes_));
    it.move_to_last();
    return it.data()->right_rule();
  }
  
  float ColPartition::SpecialBlobsDensity(const BlobSpecialTextType type) const {
    ASSERT_HOST(type < BSTT_COUNT);
    return special_blobs_densities_[type];
  }
  
  int ColPartition::SpecialBlobsCount(const BlobSpecialTextType type) {
    ASSERT_HOST(type < BSTT_COUNT);
    BLOBNBOX_C_IT blob_it(&boxes_);
    int count = 0;
    for (blob_it.mark_cycle_pt(); !blob_it.cycled_list(); blob_it.forward()) {
      BLOBNBOX *blob = blob_it.data();
      BlobSpecialTextType blob_type = blob->special_text_type();
      if (blob_type == type) {
        count++;
      }
    }
  
    return count;
  }
  
  void ColPartition::SetSpecialBlobsDensity(const BlobSpecialTextType type, const float density) {
    ASSERT_HOST(type < BSTT_COUNT);
    special_blobs_densities_[type] = density;
  }
  
  void ColPartition::ComputeSpecialBlobsDensity() {
    memset(special_blobs_densities_, 0, sizeof(special_blobs_densities_));
    if (boxes_.empty()) {
      return;
    }
  
    BLOBNBOX_C_IT blob_it(&boxes_);
    for (blob_it.mark_cycle_pt(); !blob_it.cycled_list(); blob_it.forward()) {
      BLOBNBOX *blob = blob_it.data();
      BlobSpecialTextType type = blob->special_text_type();
      special_blobs_densities_[type]++;
    }
  
    for (float &special_blobs_density : special_blobs_densities_) {
      special_blobs_density /= boxes_.length();
    }
  }
  
  // Add a partner above if upper, otherwise below.
  // Add them uniquely and keep the list sorted by box left.
  // Partnerships are added symmetrically to partner and this.
  void ColPartition::AddPartner(bool upper, ColPartition *partner) {
    if (upper) {
      partner->lower_partners_.add_sorted(SortByBoxLeft<ColPartition>, true, this);
      upper_partners_.add_sorted(SortByBoxLeft<ColPartition>, true, partner);
    } else {
      partner->upper_partners_.add_sorted(SortByBoxLeft<ColPartition>, true, this);
      lower_partners_.add_sorted(SortByBoxLeft<ColPartition>, true, partner);
    }
  }
  
  // Removes the partner from this, but does not remove this from partner.
  // This asymmetric removal is so as not to mess up the iterator that is
  // working on partner's partner list.
  void ColPartition::RemovePartner(bool upper, ColPartition *partner) {
    ColPartition_C_IT it(upper ? &upper_partners_ : &lower_partners_);
    for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
      if (it.data() == partner) {
        it.extract();
        break;
      }
    }
  }
  
  // Returns the partner if the given partner is a singleton, otherwise nullptr.
  ColPartition *ColPartition::SingletonPartner(bool upper) {
    ColPartition_CLIST *partners = upper ? &upper_partners_ : &lower_partners_;
    if (!partners->singleton()) {
      return nullptr;
    }
    ColPartition_C_IT it(partners);
    return it.data();
  }
  
  // Merge with the other partition and delete it.
  void ColPartition::Absorb(ColPartition *other, WidthCallback cb) {
    // The result has to either own all of the blobs or none of them.
    // Verify the flag is consistent.
    ASSERT_HOST(owns_blobs() == other->owns_blobs());
    // TODO(nbeato): check owns_blobs better. Right now owns_blobs
    // should always be true when this is called. So there is no issues.
    if (TabFind::WithinTestRegion(2, bounding_box_.left(), bounding_box_.bottom()) ||
        TabFind::WithinTestRegion(2, other->bounding_box_.left(), other->bounding_box_.bottom())) {
      tprintf("Merging:");
      Print();
      other->Print();
    }
  
    // Update the special_blobs_densities_.
    memset(special_blobs_densities_, 0, sizeof(special_blobs_densities_));
    for (int type = 0; type < BSTT_COUNT; ++type) {
      unsigned w1 = boxes_.length();
      unsigned w2 = other->boxes_.length();
      float new_val =
          special_blobs_densities_[type] * w1 + other->special_blobs_densities_[type] * w2;
      if (!w1 || !w2) {
        ASSERT_HOST((w1 + w2) > 0);
        special_blobs_densities_[type] = new_val / (w1 + w2);
      }
    }
  
    // Merge the two sorted lists.
    BLOBNBOX_C_IT it(&boxes_);
    BLOBNBOX_C_IT it2(&other->boxes_);
    for (; !it2.empty(); it2.forward()) {
      BLOBNBOX *bbox2 = it2.extract();
      ColPartition *prev_owner = bbox2->owner();
      if (prev_owner != other && prev_owner != nullptr) {
        // A blob on other's list is owned by someone else; let them have it.
        continue;
      }
      ASSERT_HOST(prev_owner == other || prev_owner == nullptr);
      if (prev_owner == other) {
        bbox2->set_owner(this);
      }
      it.add_to_end(bbox2);
    }
    left_margin_ = std::min(left_margin_, other->left_margin_);
    right_margin_ = std::max(right_margin_, other->right_margin_);
    if (other->left_key_ < left_key_) {
      left_key_ = other->left_key_;
      left_key_tab_ = other->left_key_tab_;
    }
    if (other->right_key_ > right_key_) {
      right_key_ = other->right_key_;
      right_key_tab_ = other->right_key_tab_;
    }
    // Combine the flow and blob_type in a sensible way.
    // Dominant flows stay.
    if (!DominatesInMerge(flow_, other->flow_)) {
      flow_ = other->flow_;
      blob_type_ = other->blob_type_;
    }
    SetBlobTypes();
    if (IsVerticalType()) {
      boxes_.sort(SortByBoxBottom<BLOBNBOX>);
      last_add_was_vertical_ = true;
    } else {
      boxes_.sort(SortByBoxLeft<BLOBNBOX>);
      last_add_was_vertical_ = false;
    }
    ComputeLimits();
    // Fix partner lists. other is going away, so remove it as a
    // partner of all its partners and add this in its place.
    for (int upper = 0; upper < 2; ++upper) {
      ColPartition_CLIST partners;
      ColPartition_C_IT part_it(&partners);
      part_it.add_list_after(upper ? &other->upper_partners_ : &other->lower_partners_);
      for (part_it.move_to_first(); !part_it.empty(); part_it.forward()) {
        ColPartition *partner = part_it.extract();
        partner->RemovePartner(!upper, other);
        partner->RemovePartner(!upper, this);
        partner->AddPartner(!upper, this);
      }
    }
    delete other;
    if (cb != nullptr) {
      SetColumnGoodness(cb);
    }
  }
  
  // Merge1 and merge2 are candidates to be merged, yet their combined box
  // overlaps this. Is that allowed?
  // Returns true if the overlap between this and the merged pair of
  // merge candidates is sufficiently trivial to be allowed.
  // The merged box can graze the edge of this by the ok_box_overlap
  // if that exceeds the margin to the median top and bottom.
  // ok_box_overlap should be set by the caller appropriate to the sizes of
  // the text involved, and is usually a fraction of the median size of merge1
  // and/or merge2, or this.
  // TODO(rays) Determine whether vertical text needs to be considered.
  bool ColPartition::OKMergeOverlap(const ColPartition &merge1, const ColPartition &merge2,
                                    int ok_box_overlap, bool debug) {
    // Vertical partitions are not allowed to be involved.
    if (IsVerticalType() || merge1.IsVerticalType() || merge2.IsVerticalType()) {
      if (debug) {
        tprintf("Vertical partition\n");
      }
      return false;
    }
    // The merging partitions must strongly overlap each other.
    if (!merge1.VSignificantCoreOverlap(merge2)) {
      if (debug) {
        tprintf("Voverlap %d (%d)\n", merge1.VCoreOverlap(merge2),
                merge1.VSignificantCoreOverlap(merge2));
      }
      return false;
    }
    // The merged box must not overlap the median bounds of this.
    TBOX merged_box(merge1.bounding_box());
    merged_box += merge2.bounding_box();
    if (merged_box.bottom() < median_top_ && merged_box.top() > median_bottom_ &&
        merged_box.bottom() < bounding_box_.top() - ok_box_overlap &&
        merged_box.top() > bounding_box_.bottom() + ok_box_overlap) {
      if (debug) {
        tprintf("Excessive box overlap\n");
      }
      return false;
    }
    // Looks OK!
    return true;
  }
  
  // Find the blob at which to split this to minimize the overlap with the
  // given box. Returns the first blob to go in the second partition.
  BLOBNBOX *ColPartition::OverlapSplitBlob(const TBOX &box) {
    if (boxes_.empty() || boxes_.singleton()) {
      return nullptr;
    }
    BLOBNBOX_C_IT it(&boxes_);
    TBOX left_box(it.data()->bounding_box());
    for (it.forward(); !it.at_first(); it.forward()) {
      BLOBNBOX *bbox = it.data();
      left_box += bbox->bounding_box();
      if (left_box.overlap(box)) {
        return bbox;
      }
    }
    return nullptr;
  }
  
  // Split this partition keeping the first half in this and returning
  // the second half.
  // Splits by putting the split_blob and the blobs that follow
  // in the second half, and the rest in the first half.
  ColPartition *ColPartition::SplitAtBlob(BLOBNBOX *split_blob) {
    ColPartition *split_part = ShallowCopy();
    split_part->set_owns_blobs(owns_blobs());
    BLOBNBOX_C_IT it(&boxes_);
    for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
      BLOBNBOX *bbox = it.data();
      ColPartition *prev_owner = bbox->owner();
      ASSERT_HOST(!owns_blobs() || prev_owner == this || prev_owner == nullptr);
      if (bbox == split_blob || !split_part->boxes_.empty()) {
        split_part->AddBox(it.extract());
        if (owns_blobs() && prev_owner != nullptr) {
          bbox->set_owner(split_part);
        }
      }
    }
    ASSERT_HOST(!it.empty());
    if (split_part->IsEmpty()) {
      // Split part ended up with nothing. Possible if split_blob is not
      // in the list of blobs.
      delete split_part;
      return nullptr;
    }
    right_key_tab_ = false;
    split_part->left_key_tab_ = false;
    ComputeLimits();
    // TODO(nbeato) Merge Ray's CL like this:
    // if (owns_blobs())
    //  SetBlobTextlineGoodness();
    split_part->ComputeLimits();
    // TODO(nbeato) Merge Ray's CL like this:
    // if (split_part->owns_blobs())
    //   split_part->SetBlobTextlineGoodness();
    return split_part;
  }
  
  // Split this partition at the given x coordinate, returning the right
  // half and keeping the left half in this.
  ColPartition *ColPartition::SplitAt(int split_x) {
    if (split_x <= bounding_box_.left() || split_x >= bounding_box_.right()) {
      return nullptr; // There will be no change.
    }
    ColPartition *split_part = ShallowCopy();
    split_part->set_owns_blobs(owns_blobs());
    BLOBNBOX_C_IT it(&boxes_);
    for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
      BLOBNBOX *bbox = it.data();
      ColPartition *prev_owner = bbox->owner();
      ASSERT_HOST(!owns_blobs() || prev_owner == this || prev_owner == nullptr);
      const TBOX &box = bbox->bounding_box();
      if (box.left() >= split_x) {
        split_part->AddBox(it.extract());
        if (owns_blobs() && prev_owner != nullptr) {
          bbox->set_owner(split_part);
        }
      }
    }
    if (it.empty()) {
      // Possible if split-x passes through the first blob.
      it.add_list_after(&split_part->boxes_);
    }
    ASSERT_HOST(!it.empty());
    if (split_part->IsEmpty()) {
      // Split part ended up with nothing. Possible if split_x passes
      // through the last blob.
      delete split_part;
      return nullptr;
    }
    right_key_tab_ = false;
    split_part->left_key_tab_ = false;
    right_margin_ = split_x;
    split_part->left_margin_ = split_x;
    ComputeLimits();
    split_part->ComputeLimits();
    return split_part;
  }
  
  // Recalculates all the coordinate limits of the partition.
  void ColPartition::ComputeLimits() {
    bounding_box_ = TBOX(); // Clear it
    BLOBNBOX_C_IT it(&boxes_);
    BLOBNBOX *bbox = nullptr;
    int non_leader_count = 0;
    if (it.empty()) {
      bounding_box_.set_left(left_margin_);
      bounding_box_.set_right(right_margin_);
      bounding_box_.set_bottom(0);
      bounding_box_.set_top(0);
    } else {
      for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
        bbox = it.data();
        bounding_box_ += bbox->bounding_box();
        if (bbox->flow() != BTFT_LEADER) {
          ++non_leader_count;
        }
      }
    }
    if (!left_key_tab_) {
      left_key_ = BoxLeftKey();
    }
    if (left_key_ > BoxLeftKey() && textord_debug_bugs) {
      // TODO(rays) investigate the causes of these error messages, to find
      // out if they are genuinely harmful, or just indicative of junk input.
      tprintf("Computed left-illegal partition\n");
      Print();
    }
    if (!right_key_tab_) {
      right_key_ = BoxRightKey();
    }
    if (right_key_ < BoxRightKey() && textord_debug_bugs) {
      tprintf("Computed right-illegal partition\n");
      Print();
    }
    if (it.empty()) {
      return;
    }
    if (IsImageType() || blob_type() == BRT_RECTIMAGE || blob_type() == BRT_POLYIMAGE) {
      median_top_ = bounding_box_.top();
      median_bottom_ = bounding_box_.bottom();
      median_height_ = bounding_box_.height();
      median_left_ = bounding_box_.left();
      median_right_ = bounding_box_.right();
      median_width_ = bounding_box_.width();
    } else {
      STATS top_stats(bounding_box_.bottom(), bounding_box_.top() + 1);
      STATS bottom_stats(bounding_box_.bottom(), bounding_box_.top() + 1);
      STATS height_stats(0, bounding_box_.height() + 1);
      STATS left_stats(bounding_box_.left(), bounding_box_.right() + 1);
      STATS right_stats(bounding_box_.left(), bounding_box_.right() + 1);
      STATS width_stats(0, bounding_box_.width() + 1);
      for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
        bbox = it.data();
        if (non_leader_count == 0 || bbox->flow() != BTFT_LEADER) {
          const TBOX &box = bbox->bounding_box();
          int area = box.area();
          top_stats.add(box.top(), area);
          bottom_stats.add(box.bottom(), area);
          height_stats.add(box.height(), area);
          left_stats.add(box.left(), area);
          right_stats.add(box.right(), area);
          width_stats.add(box.width(), area);
        }
      }
      median_top_ = static_cast<int>(top_stats.median() + 0.5);
      median_bottom_ = static_cast<int>(bottom_stats.median() + 0.5);
      median_height_ = static_cast<int>(height_stats.median() + 0.5);
      median_left_ = static_cast<int>(left_stats.median() + 0.5);
      median_right_ = static_cast<int>(right_stats.median() + 0.5);
      median_width_ = static_cast<int>(width_stats.median() + 0.5);
    }
  
    if (right_margin_ < bounding_box_.right() && textord_debug_bugs) {
      tprintf("Made partition with bad right coords, %d < %d\n", right_margin_,
              bounding_box_.right());
      Print();
    }
    if (left_margin_ > bounding_box_.left() && textord_debug_bugs) {
      tprintf("Made partition with bad left coords, %d > %d\n", left_margin_, bounding_box_.left());
      Print();
    }
    // Fix partner lists. The bounding box has changed and partners are stored
    // in bounding box order, so remove and reinsert this as a partner
    // of all its partners.
    for (int upper = 0; upper < 2; ++upper) {
      ColPartition_CLIST partners;
      ColPartition_C_IT part_it(&partners);
      part_it.add_list_after(upper ? &upper_partners_ : &lower_partners_);
      for (part_it.move_to_first(); !part_it.empty(); part_it.forward()) {
        ColPartition *partner = part_it.extract();
        partner->RemovePartner(!upper, this);
        partner->AddPartner(!upper, this);
      }
    }
    if (TabFind::WithinTestRegion(2, bounding_box_.left(), bounding_box_.bottom())) {
      tprintf("Recomputed box for partition %p\n", this);
      Print();
    }
  }
  
  // Returns the number of boxes that overlap the given box.
  int ColPartition::CountOverlappingBoxes(const TBOX &box) {
    BLOBNBOX_C_IT it(&boxes_);
    int overlap_count = 0;
    for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
      BLOBNBOX *bbox = it.data();
      if (box.overlap(bbox->bounding_box())) {
        ++overlap_count;
      }
    }
    return overlap_count;
  }
  
  // Computes and sets the type_ and first_column_, last_column_ and column_set_.
  // resolution refers to the ppi resolution of the image.
  void ColPartition::SetPartitionType(int resolution, ColPartitionSet *columns) {
    int first_spanned_col = -1;
    ColumnSpanningType span_type = columns->SpanningType(
        resolution, bounding_box_.left(), bounding_box_.right(),
        std::min(bounding_box_.height(), bounding_box_.width()), MidY(), left_margin_, right_margin_,
        &first_column_, &last_column_, &first_spanned_col);
    column_set_ = columns;
    if (first_column_ < last_column_ && span_type == CST_PULLOUT && !IsLineType()) {
      // Unequal columns may indicate that the pullout spans one of the columns
      // it lies in, so force it to be allocated to just that column.
      if (first_spanned_col >= 0) {
        first_column_ = first_spanned_col;
        last_column_ = first_spanned_col;
      } else {
        if ((first_column_ & 1) == 0) {
          last_column_ = first_column_;
        } else if ((last_column_ & 1) == 0) {
          first_column_ = last_column_;
        } else {
          first_column_ = last_column_ = (first_column_ + last_column_) / 2;
        }
      }
    }
    type_ = PartitionType(span_type);
  }
  
  // Returns the PartitionType from the current BlobRegionType and a column
  // flow spanning type ColumnSpanningType, generated by
  // ColPartitionSet::SpanningType, that indicates how the partition sits
  // in the columns.
  PolyBlockType ColPartition::PartitionType(ColumnSpanningType flow) const {
    if (flow == CST_NOISE) {
      if (blob_type_ != BRT_HLINE && blob_type_ != BRT_VLINE && blob_type_ != BRT_RECTIMAGE &&
          blob_type_ != BRT_VERT_TEXT) {
        return PT_NOISE;
      }
      flow = CST_FLOWING;
    }
  
    switch (blob_type_) {
      case BRT_NOISE:
        return PT_NOISE;
      case BRT_HLINE:
        return PT_HORZ_LINE;
      case BRT_VLINE:
        return PT_VERT_LINE;
      case BRT_RECTIMAGE:
      case BRT_POLYIMAGE:
        switch (flow) {
          case CST_FLOWING:
            return PT_FLOWING_IMAGE;
          case CST_HEADING:
            return PT_HEADING_IMAGE;
          case CST_PULLOUT:
            return PT_PULLOUT_IMAGE;
          default:
            ASSERT_HOST(!"Undefined flow type for image!");
        }
        break;
      case BRT_VERT_TEXT:
        return PT_VERTICAL_TEXT;
      case BRT_TEXT:
      case BRT_UNKNOWN:
      default:
        switch (flow) {
          case CST_FLOWING:
            return PT_FLOWING_TEXT;
          case CST_HEADING:
            return PT_HEADING_TEXT;
          case CST_PULLOUT:
            return PT_PULLOUT_TEXT;
          default:
            ASSERT_HOST(!"Undefined flow type for text!");
        }
    }
    ASSERT_HOST(!"Should never get here!");
    return PT_NOISE;
  }
  
  // Returns the first and last column touched by this partition.
  // resolution refers to the ppi resolution of the image.
  void ColPartition::ColumnRange(int resolution, ColPartitionSet *columns, int *first_col,
                                 int *last_col) {
    int first_spanned_col = -1;
    ColumnSpanningType span_type =
        columns->SpanningType(resolution, bounding_box_.left(), bounding_box_.right(),
                              std::min(bounding_box_.height(), bounding_box_.width()), MidY(),
                              left_margin_, right_margin_, first_col, last_col, &first_spanned_col);
    type_ = PartitionType(span_type);
  }
  
  // Sets the internal flags good_width_ and good_column_.
  void ColPartition::SetColumnGoodness(WidthCallback cb) {
    int y = MidY();
    int width = RightAtY(y) - LeftAtY(y);
    good_width_ = cb(width);
    good_column_ = blob_type_ == BRT_TEXT && left_key_tab_ && right_key_tab_;
  }
  
  // Determines whether the blobs in this partition mostly represent
  // a leader (fixed pitch sequence) and sets the member blobs accordingly.
  // Note that height is assumed to have been tested elsewhere, and that this
  // function will find most fixed-pitch text as leader without a height filter.
  // Leader detection is limited to sequences of identical width objects,
  // such as .... or ----, so patterns, such as .-.-.-.-. will not be found.
  bool ColPartition::MarkAsLeaderIfMonospaced() {
    bool result = false;
    // Gather statistics on the gaps between blobs and the widths of the blobs.
    int part_width = bounding_box_.width();
    STATS gap_stats(0, part_width);
    STATS width_stats(0, part_width);
    BLOBNBOX_C_IT it(&boxes_);
    BLOBNBOX *prev_blob = it.data();
    prev_blob->set_flow(BTFT_NEIGHBOURS);
    width_stats.add(prev_blob->bounding_box().width(), 1);
    int blob_count = 1;
    for (it.forward(); !it.at_first(); it.forward()) {
      BLOBNBOX *blob = it.data();
      int left = blob->bounding_box().left();
      int right = blob->bounding_box().right();
      gap_stats.add(left - prev_blob->bounding_box().right(), 1);
      width_stats.add(right - left, 1);
      blob->set_flow(BTFT_NEIGHBOURS);
      prev_blob = blob;
      ++blob_count;
    }
    double median_gap = gap_stats.median();
    double median_width = width_stats.median();
    double max_width = std::max(median_gap, median_width);
    double min_width = std::min(median_gap, median_width);
    double gap_iqr = gap_stats.ile(0.75f) - gap_stats.ile(0.25f);
    if (textord_debug_tabfind >= 4) {
      tprintf("gap iqr = %g, blob_count=%d, limits=%g,%g\n", gap_iqr, blob_count,
              max_width * kMaxLeaderGapFractionOfMax, min_width * kMaxLeaderGapFractionOfMin);
    }
    if (gap_iqr < max_width * kMaxLeaderGapFractionOfMax &&
        gap_iqr < min_width * kMaxLeaderGapFractionOfMin && blob_count >= kMinLeaderCount) {
      // This is stable enough to be called a leader, so check the widths.
      // Since leader dashes can join, run a dp cutting algorithm and go
      // on the cost.
      int offset = static_cast<int>(ceil(gap_iqr * 2));
      int min_step = static_cast<int>(median_gap + median_width + 0.5);
      int max_step = min_step + offset;
      min_step -= offset;
      // Pad the buffer with min_step/2 on each end.
      int part_left = bounding_box_.left() - min_step / 2;
      part_width += min_step;
      auto *projection = new DPPoint[part_width];
      for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
        BLOBNBOX *blob = it.data();
        int left = blob->bounding_box().left();
        int right = blob->bounding_box().right();
        int height = blob->bounding_box().height();
        for (int x = left; x < right; ++x) {
          projection[left - part_left].AddLocalCost(height);
        }
      }
      DPPoint *best_end = DPPoint::Solve(min_step, max_step, false, &DPPoint::CostWithVariance,
                                         part_width, projection);
      if (best_end != nullptr && best_end->total_cost() < blob_count) {
        // Good enough. Call it a leader.
        result = true;
        bool modified_blob_list = false;
        for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
          BLOBNBOX *blob = it.data();
          // If the first or last blob is spaced too much, don't mark it.
          if (it.at_first()) {
            int gap = it.data_relative(1)->bounding_box().left() - blob->bounding_box().right();
            if (blob->bounding_box().width() + gap > max_step) {
              it.extract();
              modified_blob_list = true;
              continue;
            }
          }
          if (it.at_last()) {
            int gap = blob->bounding_box().left() - it.data_relative(-1)->bounding_box().right();
            if (blob->bounding_box().width() + gap > max_step) {
              it.extract();
              modified_blob_list = true;
              break;
            }
          }
          blob->set_region_type(BRT_TEXT);
          blob->set_flow(BTFT_LEADER);
        }
        if (modified_blob_list) {
          ComputeLimits();
        }
        blob_type_ = BRT_TEXT;
        flow_ = BTFT_LEADER;
      } else if (textord_debug_tabfind) {
        if (best_end == nullptr) {
          tprintf("No path\n");
        } else {
          tprintf("Total cost = %d vs allowed %d\n", best_end->total_cost(), blob_count);
        }
      }
      delete[] projection;
    }
    return result;
  }
  
  // Given the result of TextlineProjection::EvaluateColPartition, (positive for
  // horizontal text, negative for vertical text, and near zero for non-text),
  // sets the blob_type_ and flow_ for this partition to indicate whether it
  // is strongly or weakly vertical or horizontal text, or non-text.
  // The function assumes that the blob neighbours are valid (from
  // StrokeWidth::SetNeighbours) and that those neighbours have their
  // region_type() set.
  void ColPartition::SetRegionAndFlowTypesFromProjectionValue(int value) {
    int blob_count = 0;       // Total # blobs.
    int good_blob_score_ = 0; // Total # good strokewidth neighbours.
    int noisy_count = 0;      // Total # neighbours marked as noise.
    int hline_count = 0;
    int vline_count = 0;
    BLOBNBOX_C_IT it(&boxes_);
    for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
      BLOBNBOX *blob = it.data();
      ++blob_count;
      noisy_count += blob->NoisyNeighbours();
      good_blob_score_ += blob->GoodTextBlob();
      if (blob->region_type() == BRT_HLINE) {
        ++hline_count;
      }
      if (blob->region_type() == BRT_VLINE) {
        ++vline_count;
      }
    }
    flow_ = BTFT_NEIGHBOURS;
    blob_type_ = BRT_UNKNOWN;
    if (hline_count > vline_count) {
      flow_ = BTFT_NONE;
      blob_type_ = BRT_HLINE;
    } else if (vline_count > hline_count) {
      flow_ = BTFT_NONE;
      blob_type_ = BRT_VLINE;
    } else if (value < -1 || 1 < value) {
      int long_side;
      int short_side;
      if (value > 0) {
        long_side = bounding_box_.width();
        short_side = bounding_box_.height();
        blob_type_ = BRT_TEXT;
      } else {
        long_side = bounding_box_.height();
        short_side = bounding_box_.width();
        blob_type_ = BRT_VERT_TEXT;
      }
      // We will combine the old metrics using aspect ratio and blob counts
      // with the input value by allowing a strong indication to flip the
      // STRONG_CHAIN/CHAIN flow values.
      int strong_score = blob_count >= kHorzStrongTextlineCount ? 1 : 0;
      if (short_side > kHorzStrongTextlineHeight) {
        ++strong_score;
      }
      if (short_side * kHorzStrongTextlineAspect < long_side) {
        ++strong_score;
      }
      if (abs(value) >= kMinStrongTextValue) {
        flow_ = BTFT_STRONG_CHAIN;
      } else if (abs(value) >= kMinChainTextValue) {
        flow_ = BTFT_CHAIN;
      } else {
        flow_ = BTFT_NEIGHBOURS;
      }
      // Upgrade chain to strong chain if the other indicators are good
      if (flow_ == BTFT_CHAIN && strong_score == 3) {
        flow_ = BTFT_STRONG_CHAIN;
      }
      // Downgrade strong vertical text to chain if the indicators are bad.
      if (flow_ == BTFT_STRONG_CHAIN && value < 0 && strong_score < 2) {
        flow_ = BTFT_CHAIN;
      }
    }
    if (flow_ == BTFT_NEIGHBOURS) {
      // Check for noisy neighbours.
      if (noisy_count >= blob_count) {
        flow_ = BTFT_NONTEXT;
        blob_type_ = BRT_NOISE;
      }
    }
    if (TabFind::WithinTestRegion(2, bounding_box_.left(), bounding_box_.bottom())) {
      tprintf("RegionFlowTypesFromProjectionValue count=%d, noisy=%d, score=%d,", blob_count,
              noisy_count, good_blob_score_);
      tprintf(" Projection value=%d, flow=%d, blob_type=%d\n", value, flow_, blob_type_);
      Print();
    }
    SetBlobTypes();
  }
  
  // Sets all blobs with the partition blob type and flow, but never overwrite
  // leader blobs, as we need to be able to identify them later.
  void ColPartition::SetBlobTypes() {
    if (!owns_blobs()) {
      return;
    }
    BLOBNBOX_C_IT it(&boxes_);
    for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
      BLOBNBOX *blob = it.data();
      if (blob->flow() != BTFT_LEADER) {
        blob->set_flow(flow_);
      }
      blob->set_region_type(blob_type_);
      ASSERT_HOST(blob->owner() == nullptr || blob->owner() == this);
    }
  }
  
  // Returns true if a decent baseline can be fitted through the blobs.
  // Works for both horizontal and vertical text.
  bool ColPartition::HasGoodBaseline() {
    // Approximation of the baseline.
    DetLineFit linepoints;
    // Calculation of the mean height on this line segment. Note that these
    // variable names apply to the context of a horizontal line, and work
    // analogously, rather than literally in the case of a vertical line.
    int total_height = 0;
    int coverage = 0;
    int height_count = 0;
    int width = 0;
    BLOBNBOX_C_IT it(&boxes_);
    TBOX box(it.data()->bounding_box());
    // Accumulate points representing the baseline at the middle of each blob,
    // but add an additional point for each end of the line. This makes it
    // harder to fit a severe skew angle, as it is most likely not right.
    if (IsVerticalType()) {
      // For a vertical line, use the right side as the baseline.
      ICOORD first_pt(box.right(), box.bottom());
      // Use the bottom-right of the first (bottom) box, the top-right of the
      // last, and the middle-right of all others.
      linepoints.Add(first_pt);
      for (it.forward(); !it.at_last(); it.forward()) {
        BLOBNBOX *blob = it.data();
        box = blob->bounding_box();
        ICOORD box_pt(box.right(), (box.top() + box.bottom()) / 2);
        linepoints.Add(box_pt);
        total_height += box.width();
        coverage += box.height();
        ++height_count;
      }
      box = it.data()->bounding_box();
      ICOORD last_pt(box.right(), box.top());
      linepoints.Add(last_pt);
      width = last_pt.y() - first_pt.y();
  
    } else {
      // Horizontal lines use the bottom as the baseline.
      TBOX box(it.data()->bounding_box());
      // Use the bottom-left of the first box, the the bottom-right of the last,
      // and the middle of all others.
      ICOORD first_pt(box.left(), box.bottom());
      linepoints.Add(first_pt);
      for (it.forward(); !it.at_last(); it.forward()) {
        BLOBNBOX *blob = it.data();
        box = blob->bounding_box();
        ICOORD box_pt((box.left() + box.right()) / 2, box.bottom());
        linepoints.Add(box_pt);
        total_height += box.height();
        coverage += box.width();
        ++height_count;
      }
      box = it.data()->bounding_box();
      ICOORD last_pt(box.right(), box.bottom());
      linepoints.Add(last_pt);
      width = last_pt.x() - first_pt.x();
    }
    // Maximum median error allowed to be a good text line.
    if (height_count == 0) {
      return false;
    }
    double max_error = kMaxBaselineError * total_height / height_count;
    ICOORD start_pt, end_pt;
    double error = linepoints.Fit(&start_pt, &end_pt);
    return error < max_error && coverage >= kMinBaselineCoverage * width;
  }
  
  // Adds this ColPartition to a matching WorkingPartSet if one can be found,
  // otherwise starts a new one in the appropriate column, ending the previous.
  void ColPartition::AddToWorkingSet(const ICOORD &bleft, const ICOORD &tright, int resolution,
                                     ColPartition_LIST *used_parts,
                                     WorkingPartSet_LIST *working_sets) {
    if (block_owned_) {
      return; // Done it already.
    }
    block_owned_ = true;
    WorkingPartSet_IT it(working_sets);
    // If there is an upper partner use its working_set_ directly.
    ColPartition *partner = SingletonPartner(true);
    if (partner != nullptr && partner->working_set_ != nullptr) {
      working_set_ = partner->working_set_;
      working_set_->AddPartition(this);
      return;
    }
    if (partner != nullptr && textord_debug_bugs) {
      tprintf("Partition with partner has no working set!:");
      Print();
      partner->Print();
    }
    // Search for the column that the left edge fits in.
    WorkingPartSet *work_set = nullptr;
    it.move_to_first();
    int col_index = 0;
    for (it.mark_cycle_pt(); !it.cycled_list() && col_index != first_column_;
         it.forward(), ++col_index) {
      ;
    }
    if (textord_debug_tabfind >= 2) {
      tprintf("Match is %s for:", (col_index & 1) ? "Real" : "Between");
      Print();
    }
    if (it.cycled_list() && textord_debug_bugs) {
      tprintf("Target column=%d, only had %d\n", first_column_, col_index);
    }
    ASSERT_HOST(!it.cycled_list());
    work_set = it.data();
    // If last_column_ != first_column, then we need to scoop up all blocks
    // between here and the last_column_ and put back in work_set.
    if (!it.cycled_list() && last_column_ != first_column_ && !IsPulloutType()) {
      // Find the column that the right edge falls in.
      BLOCK_LIST completed_blocks;
      TO_BLOCK_LIST to_blocks;
      for (; !it.cycled_list() && col_index <= last_column_; it.forward(), ++col_index) {
        WorkingPartSet *end_set = it.data();
        end_set->ExtractCompletedBlocks(bleft, tright, resolution, used_parts, &completed_blocks,
                                        &to_blocks);
      }
      work_set->InsertCompletedBlocks(&completed_blocks, &to_blocks);
    }
    working_set_ = work_set;
    work_set->AddPartition(this);
  }
  
  // From the given block_parts list, builds one or more BLOCKs and
  // corresponding TO_BLOCKs, such that the line spacing is uniform in each.
  // Created blocks are appended to the end of completed_blocks and to_blocks.
  // The used partitions are put onto used_parts, as they may still be referred
  // to in the partition grid. bleft, tright and resolution are the bounds
  // and resolution of the original image.
  void ColPartition::LineSpacingBlocks(const ICOORD &bleft, const ICOORD &tright, int resolution,
                                       ColPartition_LIST *block_parts, ColPartition_LIST *used_parts,
                                       BLOCK_LIST *completed_blocks, TO_BLOCK_LIST *to_blocks) {
    int page_height = tright.y() - bleft.y();
    // Compute the initial spacing stats.
    ColPartition_IT it(block_parts);
    int part_count = 0;
    int max_line_height = 0;
  
    // TODO(joeliu): We should add some special logic for PT_INLINE_EQUATION type
    // because their line spacing with their neighbors maybe smaller and their
    // height may be slightly larger.
  
    for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
      ColPartition *part = it.data();
      ASSERT_HOST(!part->boxes()->empty());
      STATS side_steps(0, part->bounding_box().height());
      if (part->bounding_box().height() > max_line_height) {
        max_line_height = part->bounding_box().height();
      }
      BLOBNBOX_C_IT blob_it(part->boxes());
      int prev_bottom = blob_it.data()->bounding_box().bottom();
      for (blob_it.forward(); !blob_it.at_first(); blob_it.forward()) {
        BLOBNBOX *blob = blob_it.data();
        int bottom = blob->bounding_box().bottom();
        int step = bottom - prev_bottom;
        if (step < 0) {
          step = -step;
        }
        side_steps.add(step, 1);
        prev_bottom = bottom;
      }
      part->set_side_step(static_cast<int>(side_steps.median() + 0.5));
      if (!it.at_last()) {
        ColPartition *next_part = it.data_relative(1);
        part->set_bottom_spacing(part->median_bottom() - next_part->median_bottom());
        part->set_top_spacing(part->median_top() - next_part->median_top());
      } else {
        part->set_bottom_spacing(page_height);
        part->set_top_spacing(page_height);
      }
      if (textord_debug_tabfind) {
        part->Print();
        tprintf("side step = %.2f, top spacing = %d, bottom spacing=%d\n", side_steps.median(),
                part->top_spacing(), part->bottom_spacing());
      }
      ++part_count;
    }
    if (part_count == 0) {
      return;
    }
  
    SmoothSpacings(resolution, page_height, block_parts);
  
    // Move the partitions into individual block lists and make the blocks.
    BLOCK_IT block_it(completed_blocks);
    TO_BLOCK_IT to_block_it(to_blocks);
    ColPartition_LIST spacing_parts;
    ColPartition_IT sp_block_it(&spacing_parts);
    int same_block_threshold = max_line_height * kMaxSameBlockLineSpacing;
    for (it.mark_cycle_pt(); !it.empty();) {
      ColPartition *part = it.extract();
      sp_block_it.add_to_end(part);
      it.forward();
      if (it.empty() || part->bottom_spacing() > same_block_threshold ||
          !part->SpacingsEqual(*it.data(), resolution)) {
        // There is a spacing boundary. Check to see if it.data() belongs
        // better in the current block or the next one.
        if (!it.empty() && part->bottom_spacing() <= same_block_threshold) {
          ColPartition *next_part = it.data();
          // If there is a size match one-way, then the middle line goes with
          // its matched size, otherwise it goes with the smallest spacing.
          ColPartition *third_part = it.at_last() ? nullptr : it.data_relative(1);
          if (textord_debug_tabfind) {
            tprintf(
                "Spacings unequal: upper:%d/%d, lower:%d/%d,"
                " sizes %d %d %d\n",
                part->top_spacing(), part->bottom_spacing(), next_part->top_spacing(),
                next_part->bottom_spacing(), part->median_height(), next_part->median_height(),
                third_part != nullptr ? third_part->median_height() : 0);
          }
          // We can only consider adding the next line to the block if the sizes
          // match and the lines are close enough for their size.
          if (part->SizesSimilar(*next_part) &&
              next_part->median_height() * kMaxSameBlockLineSpacing > part->bottom_spacing() &&
              part->median_height() * kMaxSameBlockLineSpacing > part->top_spacing()) {
            // Even now, we can only add it as long as the third line doesn't
            // match in the same way and have a smaller bottom spacing.
            if (third_part == nullptr || !next_part->SizesSimilar(*third_part) ||
                third_part->median_height() * kMaxSameBlockLineSpacing <=
                    next_part->bottom_spacing() ||
                next_part->median_height() * kMaxSameBlockLineSpacing <= next_part->top_spacing() ||
                next_part->bottom_spacing() > part->bottom_spacing()) {
              // Add to the current block.
              sp_block_it.add_to_end(it.extract());
              it.forward();
              if (textord_debug_tabfind) {
                tprintf("Added line to current block.\n");
              }
            }
          }
        }
        TO_BLOCK *to_block = MakeBlock(bleft, tright, &spacing_parts, used_parts);
        if (to_block != nullptr) {
          to_block_it.add_to_end(to_block);
          block_it.add_to_end(to_block->block);
        }
        sp_block_it.set_to_list(&spacing_parts);
      } else {
        if (textord_debug_tabfind && !it.empty()) {
          ColPartition *next_part = it.data();
          tprintf("Spacings equal: upper:%d/%d, lower:%d/%d, median:%d/%d\n", part->top_spacing(),
                  part->bottom_spacing(), next_part->top_spacing(), next_part->bottom_spacing(),
                  part->median_height(), next_part->median_height());
        }
      }
    }
  }
  
  // Helper function to clip the input pos to the given bleft, tright bounds.
  static void ClipCoord(const ICOORD &bleft, const ICOORD &tright, ICOORD *pos) {
    if (pos->x() < bleft.x()) {
      pos->set_x(bleft.x());
    }
    if (pos->x() > tright.x()) {
      pos->set_x(tright.x());
    }
    if (pos->y() < bleft.y()) {
      pos->set_y(bleft.y());
    }
    if (pos->y() > tright.y()) {
      pos->set_y(tright.y());
    }
  }
  
  // Helper moves the blobs from the given list of block_parts into the block
  // itself. Sets up the block for (old) textline formation correctly for
  // vertical and horizontal text. The partitions are moved to used_parts
  // afterwards, as they cannot be deleted yet.
  static TO_BLOCK *MoveBlobsToBlock(bool vertical_text, int line_spacing, BLOCK *block,
                                    ColPartition_LIST *block_parts, ColPartition_LIST *used_parts) {
    // Make a matching TO_BLOCK and put all the BLOBNBOXes from the parts in it.
    // Move all the parts to a done list as they are no longer needed, except
    // that have have to continue to exist until the part grid is deleted.
    // Compute the median blob size as we go, as the block needs to know.
    TBOX block_box(block->pdblk.bounding_box());
    STATS sizes(0, std::max(block_box.width(), block_box.height()));
    bool text_type = block->pdblk.poly_block()->IsText();
    ColPartition_IT it(block_parts);
    auto *to_block = new TO_BLOCK(block);
    BLOBNBOX_IT blob_it(&to_block->blobs);
    ColPartition_IT used_it(used_parts);
    for (it.move_to_first(); !it.empty(); it.forward()) {
      ColPartition *part = it.extract();
      // Transfer blobs from all regions to the output blocks.
      // Blobs for non-text regions will be used to define the polygonal
      // bounds of the region.
      for (BLOBNBOX_C_IT bb_it(part->boxes()); !bb_it.empty(); bb_it.forward()) {
        BLOBNBOX *bblob = bb_it.extract();
        if (bblob->owner() != part) {
          tprintf("Ownership incorrect for blob:");
          bblob->bounding_box().print();
          tprintf("Part=");
          part->Print();
          if (bblob->owner() == nullptr) {
            tprintf("Not owned\n");
          } else {
            tprintf("Owner part:");
            bblob->owner()->Print();
          }
        }
        ASSERT_HOST(bblob->owner() == part);
        // Assert failure here is caused by arbitrarily changing the partition
        // type without also changing the blob type, such as in
        // InsertSmallBlobsAsUnknowns.
        ASSERT_HOST(!text_type || bblob->region_type() >= BRT_UNKNOWN);
        C_OUTLINE_LIST *outlines = bblob->cblob()->out_list();
        C_OUTLINE_IT ol_it(outlines);
        ASSERT_HOST(!text_type || ol_it.data()->pathlength() > 0);
        if (vertical_text) {
          sizes.add(bblob->bounding_box().width(), 1);
        } else {
          sizes.add(bblob->bounding_box().height(), 1);
        }
        blob_it.add_after_then_move(bblob);
      }
      used_it.add_to_end(part);
    }
    if (text_type && blob_it.empty()) {
      delete block;
      delete to_block;
      return nullptr;
    }
    to_block->line_size = sizes.median();
    if (vertical_text) {
      int block_width = block->pdblk.bounding_box().width();
      if (block_width < line_spacing) {
        line_spacing = block_width;
      }
      to_block->line_spacing = static_cast<float>(line_spacing);
      to_block->max_blob_size = static_cast<float>(block_width + 1);
    } else {
      int block_height = block->pdblk.bounding_box().height();
      if (block_height < line_spacing) {
        line_spacing = block_height;
      }
      to_block->line_spacing = static_cast<float>(line_spacing);
      to_block->max_blob_size = static_cast<float>(block_height + 1);
    }
    return to_block;
  }
  
  // Constructs a block from the given list of partitions.
  // Arguments are as LineSpacingBlocks above.
  TO_BLOCK *ColPartition::MakeBlock(const ICOORD &bleft, const ICOORD &tright,
                                    ColPartition_LIST *block_parts, ColPartition_LIST *used_parts) {
    if (block_parts->empty()) {
      return nullptr; // Nothing to do.
    }
    // If the block_parts are not in reading order, then it will make an invalid
    // block polygon and bounding_box, so sort by bounding box now just to make
    // sure.
    block_parts->sort(&ColPartition::SortByBBox);
    ColPartition_IT it(block_parts);
    ColPartition *part = it.data();
    PolyBlockType type = part->type();
    if (type == PT_VERTICAL_TEXT) {
      return MakeVerticalTextBlock(bleft, tright, block_parts, used_parts);
    }
    // LineSpacingBlocks has handed us a collection of evenly spaced lines and
    // put the average spacing in each partition, so we can just take the
    // linespacing from the first partition.
    int line_spacing = part->bottom_spacing();
    if (line_spacing < part->median_height()) {
      line_spacing = part->bounding_box().height();
    }
    ICOORDELT_LIST vertices;
    ICOORDELT_IT vert_it(&vertices);
    ICOORD start, end;
    int min_x = INT32_MAX;
    int max_x = -INT32_MAX;
    int min_y = INT32_MAX;
    int max_y = -INT32_MAX;
    int iteration = 0;
    do {
      if (iteration == 0) {
        ColPartition::LeftEdgeRun(&it, &start, &end);
      } else {
        ColPartition::RightEdgeRun(&it, &start, &end);
      }
      ClipCoord(bleft, tright, &start);
      ClipCoord(bleft, tright, &end);
      vert_it.add_after_then_move(new ICOORDELT(start));
      vert_it.add_after_then_move(new ICOORDELT(end));
      UpdateRange(start.x(), &min_x, &max_x);
      UpdateRange(end.x(), &min_x, &max_x);
      UpdateRange(start.y(), &min_y, &max_y);
      UpdateRange(end.y(), &min_y, &max_y);
      if ((iteration == 0 && it.at_first()) || (iteration == 1 && it.at_last())) {
        ++iteration;
        it.move_to_last();
      }
    } while (iteration < 2);
    if (textord_debug_tabfind) {
      tprintf("Making block at (%d,%d)->(%d,%d)\n", min_x, min_y, max_x, max_y);
    }
    auto *block = new BLOCK("", true, 0, 0, min_x, min_y, max_x, max_y);
    block->pdblk.set_poly_block(new POLY_BLOCK(&vertices, type));
    return MoveBlobsToBlock(false, line_spacing, block, block_parts, used_parts);
  }
  
  // Constructs a block from the given list of vertical text partitions.
  // Currently only creates rectangular blocks.
  TO_BLOCK *ColPartition::MakeVerticalTextBlock(const ICOORD &bleft, const ICOORD &tright,
                                                ColPartition_LIST *block_parts,
                                                ColPartition_LIST *used_parts) {
    if (block_parts->empty()) {
      return nullptr; // Nothing to do.
    }
    ColPartition_IT it(block_parts);
    ColPartition *part = it.data();
    TBOX block_box = part->bounding_box();
    int line_spacing = block_box.width();
    PolyBlockType type = it.data()->type();
    for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
      block_box += it.data()->bounding_box();
    }
    if (textord_debug_tabfind) {
      tprintf("Making block at:");
      block_box.print();
    }
    auto *block = new BLOCK("", true, 0, 0, block_box.left(), block_box.bottom(), block_box.right(),
                            block_box.top());
    block->pdblk.set_poly_block(new POLY_BLOCK(block_box, type));
    return MoveBlobsToBlock(true, line_spacing, block, block_parts, used_parts);
  }
  
  // Makes a TO_ROW matching this and moves all the blobs to it, transferring
  // ownership to to returned TO_ROW.
  TO_ROW *ColPartition::MakeToRow() {
    BLOBNBOX_C_IT blob_it(&boxes_);
    TO_ROW *row = nullptr;
    int line_size = IsVerticalType() ? median_width_ : median_height_;
    // Add all the blobs to a single TO_ROW.
    for (; !blob_it.empty(); blob_it.forward()) {
      BLOBNBOX *blob = blob_it.extract();
      //    blob->compute_bounding_box();
      int top = blob->bounding_box().top();
      int bottom = blob->bounding_box().bottom();
      if (row == nullptr) {
        row = new TO_ROW(blob, static_cast<float>(top), static_cast<float>(bottom),
                         static_cast<float>(line_size));
      } else {
        row->add_blob(blob, static_cast<float>(top), static_cast<float>(bottom),
                      static_cast<float>(line_size));
      }
    }
    return row;
  }
  
  // Returns a copy of everything except the list of boxes. The resulting
  // ColPartition is only suitable for keeping in a column candidate list.
  ColPartition *ColPartition::ShallowCopy() const {
    auto *part = new ColPartition(blob_type_, vertical_);
    part->left_margin_ = left_margin_;
    part->right_margin_ = right_margin_;
    part->bounding_box_ = bounding_box_;
    memcpy(part->special_blobs_densities_, special_blobs_densities_,
           sizeof(special_blobs_densities_));
    part->median_bottom_ = median_bottom_;
    part->median_top_ = median_top_;
    part->median_height_ = median_height_;
    part->median_left_ = median_left_;
    part->median_right_ = median_right_;
    part->median_width_ = median_width_;
    part->good_width_ = good_width_;
    part->good_column_ = good_column_;
    part->left_key_tab_ = left_key_tab_;
    part->right_key_tab_ = right_key_tab_;
    part->type_ = type_;
    part->flow_ = flow_;
    part->left_key_ = left_key_;
    part->right_key_ = right_key_;
    part->first_column_ = first_column_;
    part->last_column_ = last_column_;
    part->owns_blobs_ = false;
    return part;
  }
  
  ColPartition *ColPartition::CopyButDontOwnBlobs() {
    ColPartition *copy = ShallowCopy();
    copy->set_owns_blobs(false);
    BLOBNBOX_C_IT inserter(copy->boxes());
    BLOBNBOX_C_IT traverser(boxes());
    for (traverser.mark_cycle_pt(); !traverser.cycled_list(); traverser.forward()) {
      inserter.add_after_then_move(traverser.data());
    }
    return copy;
  }
  
  #ifndef GRAPHICS_DISABLED
  // Provides a color for BBGrid to draw the rectangle.
  // Must be kept in sync with PolyBlockType.
  ScrollView::Color ColPartition::BoxColor() const {
    if (type_ == PT_UNKNOWN) {
      return BLOBNBOX::TextlineColor(blob_type_, flow_);
    }
    return POLY_BLOCK::ColorForPolyBlockType(type_);
  }
  #endif // !GRAPHICS_DISABLED
  
  // Keep in sync with BlobRegionType.
  static char kBlobTypes[BRT_COUNT + 1] = "NHSRIUVT";
  
  // Prints debug information on this.
  void ColPartition::Print() const {
    int y = MidY();
    tprintf(
        "ColPart:%c(M%d-%c%d-B%d/%d,%d/%d)->(%dB-%d%c-%dM/%d,%d/%d)"
        " w-ok=%d, v-ok=%d, type=%d%c%d, fc=%d, lc=%d, boxes=%d"
        " ts=%d bs=%d ls=%d rs=%d\n",
        boxes_.empty() ? 'E' : ' ', left_margin_, left_key_tab_ ? 'T' : 'B', LeftAtY(y),
        bounding_box_.left(), median_left_, bounding_box_.bottom(), median_bottom_,
        bounding_box_.right(), RightAtY(y), right_key_tab_ ? 'T' : 'B', right_margin_, median_right_,
        bounding_box_.top(), median_top_, good_width_, good_column_, type_, kBlobTypes[blob_type_],
        flow_, first_column_, last_column_, boxes_.length(), space_above_, space_below_,
        space_to_left_, space_to_right_);
  }
  
  // Prints debug information on the colors.
  void ColPartition::PrintColors() {
    tprintf("Colors:(%d, %d, %d)%d -> (%d, %d, %d)\n", color1_[COLOR_RED], color1_[COLOR_GREEN],
            color1_[COLOR_BLUE], color1_[L_ALPHA_CHANNEL], color2_[COLOR_RED], color2_[COLOR_GREEN],
            color2_[COLOR_BLUE]);
  }
  
  // Sets the types of all partitions in the run to be the max of the types.
  void ColPartition::SmoothPartnerRun(int working_set_count) {
    STATS left_stats(0, working_set_count);
    STATS right_stats(0, working_set_count);
    PolyBlockType max_type = type_;
    ColPartition *partner;
    for (partner = SingletonPartner(false); partner != nullptr;
         partner = partner->SingletonPartner(false)) {
      if (partner->type_ > max_type) {
        max_type = partner->type_;
      }
      if (column_set_ == partner->column_set_) {
        left_stats.add(partner->first_column_, 1);
        right_stats.add(partner->last_column_, 1);
      }
    }
    type_ = max_type;
    // TODO(rays) Either establish that it isn't necessary to set the columns,
    // or find a way to do it that does not cause an assert failure in
    // AddToWorkingSet.
  #if 0
    first_column_ = left_stats.mode();
    last_column_ = right_stats.mode();
    if (last_column_ < first_column_)
      last_column_ = first_column_;
  #endif
  
    for (partner = SingletonPartner(false); partner != nullptr;
         partner = partner->SingletonPartner(false)) {
      partner->type_ = max_type;
  #if 0 // See TODO above
      if (column_set_ == partner->column_set_) {
        partner->first_column_ = first_column_;
        partner->last_column_ = last_column_;
      }
  #endif
    }
  }
  
  // ======= Scenario common to all Refine*Partners* functions =======
  // ColPartitions are aiming to represent textlines, or horizontal slices
  // of images, and we are trying to form bi-directional (upper/lower) chains
  // of UNIQUE partner ColPartitions that can be made into blocks.
  // The ColPartitions have previously been typed (see SetPartitionType)
  // according to a combination of the content type and
  // how they lie on the columns. We want to chain text into
  // groups of a single type, but image ColPartitions may have been typed
  // differently in different parts of the image, due to being non-rectangular.
  //
  // We previously ran a search for upper and lower partners, but there may
  // be more than one, and they may be of mixed types, so now we wish to
  // refine the partners down to at most one.
  // A heading may have multiple partners:
  // ===============================
  // ========  ==========  =========
  // ========  ==========  =========
  // but it should be a different type.
  // A regular flowing text line may have multiple partners:
  // ==================   ===================
  // =======   =================  ===========
  // This could be the start of a pull-out, or it might all be in a single
  // column and might be caused by tightly spaced text, bold words, bullets,
  // funny punctuation etc, all of which can cause textlines to be split into
  // multiple ColPartitions. Pullouts and figure captions should now be different
  // types so we can more aggressively merge groups of partners that all sit
  // in a single column.
  //
  // Cleans up the partners of the given type so that there is at most
  // one partner. This makes block creation simpler.
  // If get_desperate is true, goes to more desperate merge methods
  // to merge flowing text before breaking partnerships.
  void ColPartition::RefinePartners(PolyBlockType type, bool get_desperate, ColPartitionGrid *grid) {
    if (TypesSimilar(type_, type)) {
      RefinePartnersInternal(true, get_desperate, grid);
      RefinePartnersInternal(false, get_desperate, grid);
    } else if (type == PT_COUNT) {
      // This is the final pass. Make sure only the correctly typed
      // partners surivive, however many there are.
      RefinePartnersByType(true, &upper_partners_);
      RefinePartnersByType(false, &lower_partners_);
      // It is possible for a merge to have given a partition multiple
      // partners again, so the last resort is to use overlap which is
      // guaranteed to leave at most one partner left.
      if (!upper_partners_.empty() && !upper_partners_.singleton()) {
        RefinePartnersByOverlap(true, &upper_partners_);
      }
      if (!lower_partners_.empty() && !lower_partners_.singleton()) {
        RefinePartnersByOverlap(false, &lower_partners_);
      }
    }
  }
  
  ////////////////// PRIVATE CODE /////////////////////////////
  
  // Cleans up the partners above if upper is true, else below.
  // If get_desperate is true, goes to more desperate merge methods
  // to merge flowing text before breaking partnerships.
  void ColPartition::RefinePartnersInternal(bool upper, bool get_desperate, ColPartitionGrid *grid) {
    ColPartition_CLIST *partners = upper ? &upper_partners_ : &lower_partners_;
    if (!partners->empty() && !partners->singleton()) {
      RefinePartnersByType(upper, partners);
      if (!partners->empty() && !partners->singleton()) {
        // Check for transitive partnerships and break the cycle.
        RefinePartnerShortcuts(upper, partners);
        if (!partners->empty() && !partners->singleton()) {
          // Types didn't fix it. Flowing text keeps the one with the longest
          // sequence of singleton matching partners. All others max overlap.
          if (TypesSimilar(type_, PT_FLOWING_TEXT) && get_desperate) {
            RefineTextPartnersByMerge(upper, false, partners, grid);
            if (!partners->empty() && !partners->singleton()) {
              RefineTextPartnersByMerge(upper, true, partners, grid);
            }
          }
          // The last resort is to use overlap.
          if (!partners->empty() && !partners->singleton()) {
            RefinePartnersByOverlap(upper, partners);
          }
        }
      }
    }
  }
  
  // Cleans up the partners above if upper is true, else below.
  // Restricts the partners to only desirable types. For text and BRT_HLINE this
  // means the same type_ , and for image types it means any image type.
  void ColPartition::RefinePartnersByType(bool upper, ColPartition_CLIST *partners) {
    bool debug = TabFind::WithinTestRegion(2, bounding_box_.left(), bounding_box_.bottom());
    if (debug) {
      tprintf("Refining %d %s partners by type for:\n", partners->length(),
              upper ? "Upper" : "Lower");
      Print();
    }
    ColPartition_C_IT it(partners);
    // Purify text by type.
    if (!IsImageType() && !IsLineType() && type() != PT_TABLE) {
      // Keep only partners matching type_.
      // Exception: PT_VERTICAL_TEXT is allowed to stay with the other
      // text types if it is the only partner.
      for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
        ColPartition *partner = it.data();
        if (!TypesSimilar(type_, partner->type_)) {
          if (debug) {
            tprintf("Removing partner:");
            partner->Print();
          }
          partner->RemovePartner(!upper, this);
          it.extract();
        } else if (debug) {
          tprintf("Keeping partner:");
          partner->Print();
        }
      }
    } else {
      // Only polyimages are allowed to have partners of any kind!
      for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
        ColPartition *partner = it.data();
        if (partner->blob_type() != BRT_POLYIMAGE || blob_type() != BRT_POLYIMAGE) {
          if (debug) {
            tprintf("Removing partner:");
            partner->Print();
          }
          partner->RemovePartner(!upper, this);
          it.extract();
        } else if (debug) {
          tprintf("Keeping partner:");
          partner->Print();
        }
      }
    }
  }
  
  // Cleans up the partners above if upper is true, else below.
  // Remove transitive partnerships: this<->a, and a<->b and this<->b.
  // Gets rid of this<->b, leaving a clean chain.
  // Also if we have this<->a and a<->this, then gets rid of this<->a, as
  // this has multiple partners.
  void ColPartition::RefinePartnerShortcuts(bool upper, ColPartition_CLIST *partners) {
    bool done_any = false;
    do {
      done_any = false;
      ColPartition_C_IT it(partners);
      for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
        ColPartition *a = it.data();
        // Check for a match between all of a's partners (it1/b1) and all
        // of this's partners (it2/b2).
        ColPartition_C_IT it1(upper ? &a->upper_partners_ : &a->lower_partners_);
        for (it1.mark_cycle_pt(); !it1.cycled_list(); it1.forward()) {
          ColPartition *b1 = it1.data();
          if (b1 == this) {
            done_any = true;
            it.extract();
            a->RemovePartner(!upper, this);
            break;
          }
          ColPartition_C_IT it2(partners);
          for (it2.mark_cycle_pt(); !it2.cycled_list(); it2.forward()) {
            ColPartition *b2 = it2.data();
            if (b1 == b2) {
              // Jackpot! b2 should not be a partner of this.
              it2.extract();
              b2->RemovePartner(!upper, this);
              done_any = true;
              // That potentially invalidated all the iterators, so break out
              // and start again.
              break;
            }
          }
          if (done_any) {
            break;
          }
        }
        if (done_any) {
          break;
        }
      }
    } while (done_any && !partners->empty() && !partners->singleton());
  }
  
  // Cleans up the partners above if upper is true, else below.
  // If multiple text partners can be merged, (with each other, NOT with this),
  // then do so.
  // If desperate is true, then an increase in overlap with the merge is
  // allowed. If the overlap increases, then the desperately_merged_ flag
  // is set, indicating that the textlines probably need to be regenerated
  // by aggressive line fitting/splitting, as there are probably vertically
  // joined blobs that cross textlines.
  void ColPartition::RefineTextPartnersByMerge(bool upper, bool desperate,
                                               ColPartition_CLIST *partners, ColPartitionGrid *grid) {
    bool debug = TabFind::WithinTestRegion(2, bounding_box_.left(), bounding_box_.bottom());
    if (debug) {
      tprintf("Refining %d %s partners by merge for:\n", partners->length(),
              upper ? "Upper" : "Lower");
      Print();
    }
    while (!partners->empty() && !partners->singleton()) {
      // Absorb will mess up the iterators, so we have to merge one partition
      // at a time and rebuild the iterators each time.
      ColPartition_C_IT it(partners);
      ColPartition *part = it.data();
      // Gather a list of merge candidates, from the list of partners, that
      // are all in the same single column. See general scenario comment above.
      ColPartition_CLIST candidates;
      ColPartition_C_IT cand_it(&candidates);
      for (it.forward(); !it.at_first(); it.forward()) {
        ColPartition *candidate = it.data();
        if (part->first_column_ == candidate->last_column_ &&
            part->last_column_ == candidate->first_column_) {
          cand_it.add_after_then_move(it.data());
        }
      }
      int overlap_increase;
      ColPartition *candidate =
          grid->BestMergeCandidate(part, &candidates, debug, nullptr, &overlap_increase);
      if (candidate != nullptr && (overlap_increase <= 0 || desperate)) {
        if (debug) {
          tprintf("Merging:hoverlap=%d, voverlap=%d, OLI=%d\n", part->HCoreOverlap(*candidate),
                  part->VCoreOverlap(*candidate), overlap_increase);
        }
        // Remove before merge and re-insert to keep the integrity of the grid.
        grid->RemoveBBox(candidate);
        grid->RemoveBBox(part);
        part->Absorb(candidate, nullptr);
        // We modified the box of part, so re-insert it into the grid.
        grid->InsertBBox(true, true, part);
        if (overlap_increase > 0) {
          part->desperately_merged_ = true;
        }
      } else {
        break; // Can't merge.
      }
    }
  }
  
  // Cleans up the partners above if upper is true, else below.
  // Keep the partner with the biggest overlap.
  void ColPartition::RefinePartnersByOverlap(bool upper, ColPartition_CLIST *partners) {
    bool debug = TabFind::WithinTestRegion(2, bounding_box_.left(), bounding_box_.bottom());
    if (debug) {
      tprintf("Refining %d %s partners by overlap for:\n", partners->length(),
              upper ? "Upper" : "Lower");
      Print();
    }
    ColPartition_C_IT it(partners);
    ColPartition *best_partner = it.data();
    // Find the partner with the best overlap.
    int best_overlap = 0;
    for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
      ColPartition *partner = it.data();
      int overlap = std::min(bounding_box_.right(), partner->bounding_box_.right()) -
                    std::max(bounding_box_.left(), partner->bounding_box_.left());
      if (overlap > best_overlap) {
        best_overlap = overlap;
        best_partner = partner;
      }
    }
    // Keep only the best partner.
    for (it.mark_cycle_pt(); !it.cycled_list(); it.forward()) {
      ColPartition *partner = it.data();
      if (partner != best_partner) {
        if (debug) {
          tprintf("Removing partner:");
          partner->Print();
        }
        partner->RemovePartner(!upper, this);
        it.extract();
      }
    }
  }
  
  // Return true if bbox belongs better in this than other.
  bool ColPartition::ThisPartitionBetter(BLOBNBOX *bbox, const ColPartition &other) {
    const TBOX &box = bbox->bounding_box();
    // Margins take priority.
    int left = box.left();
    int right = box.right();
    if (left < left_margin_ || right > right_margin_) {
      return false;
    }
    if (left < other.left_margin_ || right > other.right_margin_) {
      return true;
    }
    int top = box.top();
    int bottom = box.bottom();
    int this_overlap = std::min(top, median_top_) - std::max(bottom, median_bottom_);
    int other_overlap = std::min(top, other.median_top_) - std::max(bottom, other.median_bottom_);
    int this_miss = median_top_ - median_bottom_ - this_overlap;
    int other_miss = other.median_top_ - other.median_bottom_ - other_overlap;
    if (TabFind::WithinTestRegion(3, box.left(), box.bottom())) {
      tprintf("Unique on (%d,%d)->(%d,%d) overlap %d/%d, miss %d/%d, mt=%d/%d\n", box.left(),
              box.bottom(), box.right(), box.top(), this_overlap, other_overlap, this_miss,
              other_miss, median_top_, other.median_top_);
    }
    if (this_miss < other_miss) {
      return true;
    }
    if (this_miss > other_miss) {
      return false;
    }
    if (this_overlap > other_overlap) {
      return true;
    }
    if (this_overlap < other_overlap) {
      return false;
    }
    return median_top_ >= other.median_top_;
  }
  
  // Returns the median line-spacing between the current position and the end
  // of the list.
  // The iterator is passed by value so the iteration does not modify the
  // caller's iterator.
  static int MedianSpacing(int page_height, ColPartition_IT it) {
    STATS stats(0, page_height);
    while (!it.cycled_list()) {
      ColPartition *part = it.data();
      it.forward();
      stats.add(part->bottom_spacing(), 1);
      stats.add(part->top_spacing(), 1);
    }
    return static_cast<int>(stats.median() + 0.5);
  }
  
  // Returns true if this column partition is in the same column as
  // part. This function will only work after the SetPartitionType function
  // has been called on both column partitions. This is useful for
  // doing a SideSearch when you want things in the same page column.
  //
  // Currently called by the table detection code to identify if potential table
  // partitions exist in the same column.
  bool ColPartition::IsInSameColumnAs(const ColPartition &part) const {
    // Overlap does not occur when last < part.first or first > part.last.
    // In other words, one is completely to the side of the other.
    // This is just DeMorgan's law applied to that so the function returns true.
    return (last_column_ >= part.first_column_) && (first_column_ <= part.last_column_);
  }
  
  // Smoothes the spacings in the list into groups of equal linespacing.
  // resolution is the resolution of the original image, used as a basis
  // for thresholds in change of spacing. page_height is in pixels.
  void ColPartition::SmoothSpacings(int resolution, int page_height, ColPartition_LIST *parts) {
    // The task would be trivial if we didn't have to allow for blips -
    // occasional offsets in spacing caused by anomalous text, such as all
    // caps, groups of descenders, joined words, Arabic etc.
    // The neighbourhood stores a consecutive group of partitions so that
    // blips can be detected correctly, yet conservatively enough to not
    // mistake genuine spacing changes for blips. See example below.
    ColPartition *neighbourhood[PN_COUNT];
    ColPartition_IT it(parts);
    it.mark_cycle_pt();
    // Although we know nothing about the spacings is this list, the median is
    // used as an approximation to allow blips.
    // If parts of this block aren't spaced to the median, then we can't
    // accept blips in those parts, but we'll recalculate it each time we
    // split the block, so the median becomes more likely to match all the text.
    int median_space = MedianSpacing(page_height, it);
    ColPartition_IT start_it(it);
    ColPartition_IT end_it(it);
    for (int i = 0; i < PN_COUNT; ++i) {
      if (i < PN_UPPER || it.cycled_list()) {
        neighbourhood[i] = nullptr;
      } else {
        if (i == PN_LOWER) {
          end_it = it;
        }
        neighbourhood[i] = it.data();
        it.forward();
      }
    }
    while (neighbourhood[PN_UPPER] != nullptr) {
      // Test for end of a group. Normally SpacingsEqual is true within a group,
      // but in the case of a blip, it will be false. Here is an example:
      // Line enum   Spacing below (spacing between tops of lines)
      //  1   ABOVE2    20
      //  2   ABOVE1    20
      //  3   UPPER     15
      //  4   LOWER     25
      //  5   BELOW1    20
      //  6   BELOW2    20
      // Line 4 is all in caps (regular caps), so the spacing between line 3
      // and line 4 (looking at the tops) is smaller than normal, and the
      // spacing between line 4 and line 5 is larger than normal, but the
      // two of them add to twice the normal spacing.
      // The following if has to accept unequal spacings 3 times to pass the
      // blip (20/15, 15/25 and 25/20)
      // When the blip is in the middle, OKSpacingBlip tests that one of
      // ABOVE1 and BELOW1 matches the median.
      // The first time, everything is shifted down 1, so we present
      // OKSpacingBlip with neighbourhood+1 and check that PN_UPPER is median.
      // The last time, everything is shifted up 1, so we present OKSpacingBlip
      // with neighbourhood-1 and check that PN_LOWER matches the median.
      if (neighbourhood[PN_LOWER] == nullptr ||
          (!neighbourhood[PN_UPPER]->SpacingsEqual(*neighbourhood[PN_LOWER], resolution) &&
           (neighbourhood[PN_UPPER] == nullptr || neighbourhood[PN_LOWER] == nullptr ||
            !OKSpacingBlip(resolution, median_space, neighbourhood, 0)) &&
           (neighbourhood[PN_UPPER - 1] == nullptr || neighbourhood[PN_LOWER - 1] == nullptr ||
            !OKSpacingBlip(resolution, median_space, neighbourhood, -1) ||
            !neighbourhood[PN_LOWER]->SpacingEqual(median_space, resolution)) &&
           (neighbourhood[PN_UPPER + 1] == nullptr || neighbourhood[PN_LOWER + 1] == nullptr ||
            !OKSpacingBlip(resolution, median_space, neighbourhood, 1) ||
            !neighbourhood[PN_UPPER]->SpacingEqual(median_space, resolution)))) {
        // The group has ended. PN_UPPER is the last member.
        // Compute the mean spacing over the group.
        ColPartition_IT sum_it(start_it);
        ColPartition *last_part = neighbourhood[PN_UPPER];
        double total_bottom = 0.0;
        double total_top = 0.0;
        int total_count = 0;
        ColPartition *upper = sum_it.data();
        // We do not process last_part, as its spacing is different.
        while (upper != last_part) {
          total_bottom += upper->bottom_spacing();
          total_top += upper->top_spacing();
          ++total_count;
          sum_it.forward();
          upper = sum_it.data();
        }
        if (total_count > 0) {
          // There were at least 2 lines, so set them all to the mean.
          int top_spacing = static_cast<int>(total_top / total_count + 0.5);
          int bottom_spacing = static_cast<int>(total_bottom / total_count + 0.5);
          if (textord_debug_tabfind) {
            tprintf("Spacing run ended. Cause:");
            if (neighbourhood[PN_LOWER] == nullptr) {
              tprintf("No more lines\n");
            } else {
              tprintf("Spacing change. Spacings:\n");
              for (int i = 0; i < PN_COUNT; ++i) {
                if (neighbourhood[i] == nullptr) {
                  tprintf("NULL");
                  if (i > 0 && neighbourhood[i - 1] != nullptr) {
                    if (neighbourhood[i - 1]->SingletonPartner(false) != nullptr) {
                      tprintf(" Lower partner:");
                      neighbourhood[i - 1]->SingletonPartner(false)->Print();
                    } else {
                      tprintf(" nullptr lower partner:\n");
                    }
                  } else {
                    tprintf("\n");
                  }
                } else {
                  tprintf("Top = %d, bottom = %d\n", neighbourhood[i]->top_spacing(),
                          neighbourhood[i]->bottom_spacing());
                }
              }
            }
            tprintf("Mean spacing = %d/%d\n", top_spacing, bottom_spacing);
          }
          sum_it = start_it;
          upper = sum_it.data();
          while (upper != last_part) {
            upper->set_top_spacing(top_spacing);
            upper->set_bottom_spacing(bottom_spacing);
            if (textord_debug_tabfind) {
              tprintf("Setting mean on:");
              upper->Print();
            }
            sum_it.forward();
            upper = sum_it.data();
          }
        }
        // PN_LOWER starts the next group and end_it is the next start_it.
        start_it = end_it;
        // Recalculate the median spacing to maximize the chances of detecting
        // spacing blips.
        median_space = MedianSpacing(page_height, end_it);
      }
      // Shuffle pointers.
      for (int j = 1; j < PN_COUNT; ++j) {
        neighbourhood[j - 1] = neighbourhood[j];
      }
      if (it.cycled_list()) {
        neighbourhood[PN_COUNT - 1] = nullptr;
      } else {
        neighbourhood[PN_COUNT - 1] = it.data();
        it.forward();
      }
      end_it.forward();
    }
  }
  
  // Returns true if the parts array of pointers to partitions matches the
  // condition for a spacing blip. See SmoothSpacings for what this means
  // and how it is used.
  bool ColPartition::OKSpacingBlip(int resolution, int median_spacing, ColPartition **parts,
                                   int offset) {
    // The blip is OK if upper and lower sum to an OK value and at least
    // one of above1 and below1 is equal to the median.
    parts += offset;
    return parts[PN_UPPER]->SummedSpacingOK(*parts[PN_LOWER], median_spacing, resolution) &&
           ((parts[PN_ABOVE1] != nullptr &&
             parts[PN_ABOVE1]->SpacingEqual(median_spacing, resolution)) ||
            (parts[PN_BELOW1] != nullptr &&
             parts[PN_BELOW1]->SpacingEqual(median_spacing, resolution)));
  }
  
  // Returns true if both the top and bottom spacings of this match the given
  // spacing to within suitable margins dictated by the image resolution.
  bool ColPartition::SpacingEqual(int spacing, int resolution) const {
    int bottom_error = BottomSpacingMargin(resolution);
    int top_error = TopSpacingMargin(resolution);
    return NearlyEqual(bottom_spacing_, spacing, bottom_error) &&
           NearlyEqual(top_spacing_, spacing, top_error);
  }
  
  // Returns true if both the top and bottom spacings of this and other
  // match to within suitable margins dictated by the image resolution.
  bool ColPartition::SpacingsEqual(const ColPartition &other, int resolution) const {
    int bottom_error =
        std::max(BottomSpacingMargin(resolution), other.BottomSpacingMargin(resolution));
    int top_error = std::max(TopSpacingMargin(resolution), other.TopSpacingMargin(resolution));
    return NearlyEqual(bottom_spacing_, other.bottom_spacing_, bottom_error) &&
           (NearlyEqual(top_spacing_, other.top_spacing_, top_error) ||
            NearlyEqual(top_spacing_ + other.top_spacing_, bottom_spacing_ * 2, bottom_error));
  }
  
  // Returns true if the sum spacing of this and other match the given
  // spacing (or twice the given spacing) to within a suitable margin dictated
  // by the image resolution.
  bool ColPartition::SummedSpacingOK(const ColPartition &other, int spacing, int resolution) const {
    int bottom_error =
        std::max(BottomSpacingMargin(resolution), other.BottomSpacingMargin(resolution));
    int top_error = std::max(TopSpacingMargin(resolution), other.TopSpacingMargin(resolution));
    int bottom_total = bottom_spacing_ + other.bottom_spacing_;
    int top_total = top_spacing_ + other.top_spacing_;
    return (NearlyEqual(spacing, bottom_total, bottom_error) &&
            NearlyEqual(spacing, top_total, top_error)) ||
           (NearlyEqual(spacing * 2, bottom_total, bottom_error) &&
            NearlyEqual(spacing * 2, top_total, top_error));
  }
  
  // Returns a suitable spacing margin that can be applied to bottoms of
  // text lines, based on the resolution and the stored side_step_.
  int ColPartition::BottomSpacingMargin(int resolution) const {
    return static_cast<int>(kMaxSpacingDrift * resolution + 0.5) + side_step_;
  }
  
  // Returns a suitable spacing margin that can be applied to tops of
  // text lines, based on the resolution and the stored side_step_.
  int ColPartition::TopSpacingMargin(int resolution) const {
    return static_cast<int>(kMaxTopSpacingFraction * median_height_ + 0.5) +
           BottomSpacingMargin(resolution);
  }
  
  // Returns true if the median text sizes of this and other agree to within
  // a reasonable multiplicative factor.
  bool ColPartition::SizesSimilar(const ColPartition &other) const {
    return median_height_ <= other.median_height_ * kMaxSizeRatio &&
           other.median_height_ <= median_height_ * kMaxSizeRatio;
  }
  
  // Helper updates margin_left and margin_right, being the bounds of the left
  // margin of part of a block. Returns false and does not update the bounds if
  // this partition has a disjoint margin with the established margin.
  static bool UpdateLeftMargin(const ColPartition &part, int *margin_left, int *margin_right) {
    const TBOX &part_box = part.bounding_box();
    int top = part_box.top();
    int bottom = part_box.bottom();
    int tl_key = part.SortKey(part.left_margin(), top);
    int tr_key = part.SortKey(part_box.left(), top);
    int bl_key = part.SortKey(part.left_margin(), bottom);
    int br_key = part.SortKey(part_box.left(), bottom);
    int left_key = std::max(tl_key, bl_key);
    int right_key = std::min(tr_key, br_key);
    if (left_key <= *margin_right && right_key >= *margin_left) {
      // This part is good - let's keep it.
      *margin_right = std::min(*margin_right, right_key);
      *margin_left = std::max(*margin_left, left_key);
      return true;
    }
    return false;
  }
  
  // Computes and returns in start, end a line segment formed from a
  // forwards-iterated group of left edges of partitions that satisfy the
  // condition that the intersection of the left margins is non-empty, ie the
  // rightmost left margin is to the left of the leftmost left bounding box edge.
  // On return the iterator is set to the start of the next run.
  void ColPartition::LeftEdgeRun(ColPartition_IT *part_it, ICOORD *start, ICOORD *end) {
    ColPartition *part = part_it->data();
    ColPartition *start_part = part;
    int start_y = part->bounding_box_.top();
    if (!part_it->at_first()) {
      int prev_bottom = part_it->data_relative(-1)->bounding_box_.bottom();
      if (prev_bottom < start_y) {
        start_y = prev_bottom;
      } else if (prev_bottom > start_y) {
        start_y = (start_y + prev_bottom) / 2;
      }
    }
    int end_y = part->bounding_box_.bottom();
    int margin_right = INT32_MAX;
    int margin_left = -INT32_MAX;
    UpdateLeftMargin(*part, &margin_left, &margin_right);
    do {
      part_it->forward();
      part = part_it->data();
    } while (!part_it->at_first() && UpdateLeftMargin(*part, &margin_left, &margin_right));
    // The run ended. If we were pushed inwards, compute the next run and
    // extend it backwards into the run we just calculated to find the end of
    // this run that provides a tight box.
    int next_margin_right = INT32_MAX;
    int next_margin_left = -INT32_MAX;
    UpdateLeftMargin(*part, &next_margin_left, &next_margin_right);
    if (next_margin_left > margin_right) {
      ColPartition_IT next_it(*part_it);
      do {
        next_it.forward();
        part = next_it.data();
      } while (!next_it.at_first() && UpdateLeftMargin(*part, &next_margin_left, &next_margin_right));
      // Now extend the next run backwards into the original run to get the
      // tightest fit.
      do {
        part_it->backward();
        part = part_it->data();
      } while (part != start_part && UpdateLeftMargin(*part, &next_margin_left, &next_margin_right));
      part_it->forward();
    }
    // Now calculate the end_y.
    part = part_it->data_relative(-1);
    end_y = part->bounding_box_.bottom();
    if (!part_it->at_first() && part_it->data()->bounding_box_.top() < end_y) {
      end_y = (end_y + part_it->data()->bounding_box_.top()) / 2;
    }
    start->set_y(start_y);
    start->set_x(part->XAtY(margin_right, start_y));
    end->set_y(end_y);
    end->set_x(part->XAtY(margin_right, end_y));
    if (textord_debug_tabfind && !part_it->at_first()) {
      tprintf("Left run from y=%d to %d terminated with sum %d-%d, new %d-%d\n", start_y, end_y,
              part->XAtY(margin_left, end_y), end->x(), part->left_margin_,
              part->bounding_box_.left());
    }
  }
  
  // Helper updates margin_left and margin_right, being the bounds of the right
  // margin of part of a block. Returns false and does not update the bounds if
  // this partition has a disjoint margin with the established margin.
  static bool UpdateRightMargin(const ColPartition &part, int *margin_left, int *margin_right) {
    const TBOX &part_box = part.bounding_box();
    int top = part_box.top();
    int bottom = part_box.bottom();
    int tl_key = part.SortKey(part_box.right(), top);
    int tr_key = part.SortKey(part.right_margin(), top);
    int bl_key = part.SortKey(part_box.right(), bottom);
    int br_key = part.SortKey(part.right_margin(), bottom);
    int left_key = std::max(tl_key, bl_key);
    int right_key = std::min(tr_key, br_key);
    if (left_key <= *margin_right && right_key >= *margin_left) {
      // This part is good - let's keep it.
      *margin_right = std::min(*margin_right, right_key);
      *margin_left = std::max(*margin_left, left_key);
      return true;
    }
    return false;
  }
  
  // Computes and returns in start, end a line segment formed from a
  // backwards-iterated group of right edges of partitions that satisfy the
  // condition that the intersection of the right margins is non-empty, ie the
  // leftmost right margin is to the right of the rightmost right bounding box
  // edge.
  // On return the iterator is set to the start of the next run.
  void ColPartition::RightEdgeRun(ColPartition_IT *part_it, ICOORD *start, ICOORD *end) {
    ColPartition *part = part_it->data();
    ColPartition *start_part = part;
    int start_y = part->bounding_box_.bottom();
    if (!part_it->at_last()) {
      int next_y = part_it->data_relative(1)->bounding_box_.top();
      if (next_y > start_y) {
        start_y = next_y;
      } else if (next_y < start_y) {
        start_y = (start_y + next_y) / 2;
      }
    }
    int end_y = part->bounding_box_.top();
    int margin_right = INT32_MAX;
    int margin_left = -INT32_MAX;
    UpdateRightMargin(*part, &margin_left, &margin_right);
    do {
      part_it->backward();
      part = part_it->data();
    } while (!part_it->at_last() && UpdateRightMargin(*part, &margin_left, &margin_right));
    // The run ended. If we were pushed inwards, compute the next run and
    // extend it backwards to find the end of this run for a tight box.
    int next_margin_right = INT32_MAX;
    int next_margin_left = -INT32_MAX;
    UpdateRightMargin(*part, &next_margin_left, &next_margin_right);
    if (next_margin_right < margin_left) {
      ColPartition_IT next_it(*part_it);
      do {
        next_it.backward();
        part = next_it.data();
      } while (!next_it.at_last() && UpdateRightMargin(*part, &next_margin_left, &next_margin_right));
      // Now extend the next run forwards into the original run to get the
      // tightest fit.
      do {
        part_it->forward();
        part = part_it->data();
      } while (part != start_part && UpdateRightMargin(*part, &next_margin_left, &next_margin_right));
      part_it->backward();
    }
    // Now calculate the end_y.
    part = part_it->data_relative(1);
    end_y = part->bounding_box().top();
    if (!part_it->at_last() && part_it->data()->bounding_box_.bottom() > end_y) {
      end_y = (end_y + part_it->data()->bounding_box_.bottom()) / 2;
    }
    start->set_y(start_y);
    start->set_x(part->XAtY(margin_left, start_y));
    end->set_y(end_y);
    end->set_x(part->XAtY(margin_left, end_y));
    if (textord_debug_tabfind && !part_it->at_last()) {
      tprintf("Right run from y=%d to %d terminated with sum %d-%d, new %d-%d\n", start_y, end_y,
              end->x(), part->XAtY(margin_right, end_y), part->bounding_box_.right(),
              part->right_margin_);
    }
  }
  
  } // namespace tesseract.
  