text: """
  Mask R-CNN
  Common utility functions and classes.
  
  Copyright (c) 2017 Matterport, Inc.
  Licensed under the MIT License (see LICENSE for details)
  Written by Waleed Abdulla
  """
  
  import sys
  import os
  import math
  import random
  import numpy as np
  import tensorflow as tf
  import scipy.misc
  import skimage.color
  import skimage.io
  import urllib.request
  import shutil
  import warnings
  
  # URL from which to download the latest COCO trained weights
  COCO_MODEL_URL = "https://github.com/matterport/Mask_RCNN/releases/download/v2.0/mask_rcnn_coco.h5"
  
  
  ############################################################
  #  Bounding Boxes
  ############################################################
  
  def extract_bboxes(mask):
      """Compute bounding boxes from masks.
      mask: [height, width, num_instances]. Mask pixels are either 1 or 0.
  
      Returns: bbox array [num_instances, (y1, x1, y2, x2)].
      """
      boxes = np.zeros([mask.shape[-1], 4], dtype=np.int32)
      for i in range(mask.shape[-1]):
          m = mask[:, :, i]
          # Bounding box.
          horizontal_indicies = np.where(np.any(m, axis=0))[0]
          vertical_indicies = np.where(np.any(m, axis=1))[0]
          if horizontal_indicies.shape[0]:
              x1, x2 = horizontal_indicies[[0, -1]]
              y1, y2 = vertical_indicies[[0, -1]]
              # x2 and y2 should not be part of the box. Increment by 1.
              x2 += 1
              y2 += 1
          else:
              # No mask for this instance. Might happen due to
              # resizing or cropping. Set bbox to zeros
              x1, x2, y1, y2 = 0, 0, 0, 0
          boxes[i] = np.array([y1, x1, y2, x2])
      return boxes.astype(np.int32)
  
  
  def compute_iou(box, boxes, box_area, boxes_area):
      """Calculates IoU of the given box with the array of the given boxes.
      box: 1D vector [y1, x1, y2, x2]
      boxes: [boxes_count, (y1, x1, y2, x2)]
      box_area: float. the area of 'box'
      boxes_area: array of length boxes_count.
  
      Note: the areas are passed in rather than calculated here for
            efficency. Calculate once in the caller to avoid duplicate work.
      """
      # Calculate intersection areas
      y1 = np.maximum(box[0], boxes[:, 0])
      y2 = np.minimum(box[2], boxes[:, 2])
      x1 = np.maximum(box[1], boxes[:, 1])
      x2 = np.minimum(box[3], boxes[:, 3])
      intersection = np.maximum(x2 - x1, 0) * np.maximum(y2 - y1, 0)
      union = box_area + boxes_area[:] - intersection[:]
      iou = intersection / union
      return iou
  
  
  def compute_overlaps(boxes1, boxes2):
      """Computes IoU overlaps between two sets of boxes.
      boxes1, boxes2: [N, (y1, x1, y2, x2)].
  
      For better performance, pass the largest set first and the smaller second.
      """
      # Areas of anchors and GT boxes
      area1 = (boxes1[:, 2] - boxes1[:, 0]) * (boxes1[:, 3] - boxes1[:, 1])
      area2 = (boxes2[:, 2] - boxes2[:, 0]) * (boxes2[:, 3] - boxes2[:, 1])
  
      # Compute overlaps to generate matrix [boxes1 count, boxes2 count]
      # Each cell contains the IoU value.
      overlaps = np.zeros((boxes1.shape[0], boxes2.shape[0]))
      for i in range(overlaps.shape[1]):
          box2 = boxes2[i]
          overlaps[:, i] = compute_iou(box2, boxes1, area2[i], area1)
      return overlaps
  
  
  def compute_overlaps_masks(masks1, masks2):
      '''Computes IoU overlaps between two sets of masks.
      masks1, masks2: [Height, Width, instances]
      '''
      # flatten masks
      masks1 = np.reshape(masks1 > .5, (-1, masks1.shape[-1])).astype(np.float32)
      masks2 = np.reshape(masks2 > .5, (-1, masks2.shape[-1])).astype(np.float32)
      area1 = np.sum(masks1, axis=0)
      area2 = np.sum(masks2, axis=0)
  
      # intersections and union
      intersections = np.dot(masks1.T, masks2)
      union = area1[:, None] + area2[None, :] - intersections
      overlaps = intersections / union
  
      return overlaps
  
  
  def non_max_suppression(boxes, scores, threshold):
      """Performs non-maximum supression and returns indicies of kept boxes.
      boxes: [N, (y1, x1, y2, x2)]. Notice that (y2, x2) lays outside the box.
      scores: 1-D array of box scores.
      threshold: Float. IoU threshold to use for filtering.
      """
      assert boxes.shape[0] > 0
      if boxes.dtype.kind != "f":
          boxes = boxes.astype(np.float32)
  
      # Compute box areas
      y1 = boxes[:, 0]
      x1 = boxes[:, 1]
      y2 = boxes[:, 2]
      x2 = boxes[:, 3]
      area = (y2 - y1) * (x2 - x1)
  
      # Get indicies of boxes sorted by scores (highest first)
      ixs = scores.argsort()[::-1]
  
      pick = []
      while len(ixs) > 0:
          # Pick top box and add its index to the list
          i = ixs[0]
          pick.append(i)
          # Compute IoU of the picked box with the rest
          iou = compute_iou(boxes[i], boxes[ixs[1:]], area[i], area[ixs[1:]])
          # Identify boxes with IoU over the threshold. This
          # returns indicies into ixs[1:], so add 1 to get
          # indicies into ixs.
          remove_ixs = np.where(iou > threshold)[0] + 1
          # Remove indicies of the picked and overlapped boxes.
          ixs = np.delete(ixs, remove_ixs)
          ixs = np.delete(ixs, 0)
      return np.array(pick, dtype=np.int32)
  
  
  def apply_box_deltas(boxes, deltas):
      """Applies the given deltas to the given boxes.
      boxes: [N, (y1, x1, y2, x2)]. Note that (y2, x2) is outside the box.
      deltas: [N, (dy, dx, log(dh), log(dw))]
      """
      boxes = boxes.astype(np.float32)
      # Convert to y, x, h, w
      height = boxes[:, 2] - boxes[:, 0]
      width = boxes[:, 3] - boxes[:, 1]
      center_y = boxes[:, 0] + 0.5 * height
      center_x = boxes[:, 1] + 0.5 * width
      # Apply deltas
      center_y += deltas[:, 0] * height
      center_x += deltas[:, 1] * width
      height *= np.exp(deltas[:, 2])
      width *= np.exp(deltas[:, 3])
      # Convert back to y1, x1, y2, x2
      y1 = center_y - 0.5 * height
      x1 = center_x - 0.5 * width
      y2 = y1 + height
      x2 = x1 + width
      return np.stack([y1, x1, y2, x2], axis=1)
  
  
  def box_refinement_graph(box, gt_box):
      """Compute refinement needed to transform box to gt_box.
      box and gt_box are [N, (y1, x1, y2, x2)]
      """
      box = tf.cast(box, tf.float32)
      gt_box = tf.cast(gt_box, tf.float32)
  
      height = box[:, 2] - box[:, 0]
      width = box[:, 3] - box[:, 1]
      center_y = box[:, 0] + 0.5 * height
      center_x = box[:, 1] + 0.5 * width
  
      gt_height = gt_box[:, 2] - gt_box[:, 0]
      gt_width = gt_box[:, 3] - gt_box[:, 1]
      gt_center_y = gt_box[:, 0] + 0.5 * gt_height
      gt_center_x = gt_box[:, 1] + 0.5 * gt_width
  
      dy = (gt_center_y - center_y) / height
      dx = (gt_center_x - center_x) / width
      dh = tf.log(gt_height / height)
      dw = tf.log(gt_width / width)
  
      result = tf.stack([dy, dx, dh, dw], axis=1)
      return result
  
  
  def box_refinement(box, gt_box):
      """Compute refinement needed to transform box to gt_box.
      box and gt_box are [N, (y1, x1, y2, x2)]. (y2, x2) is
      assumed to be outside the box.
      """
      box = box.astype(np.float32)
      gt_box = gt_box.astype(np.float32)
  
      height = box[:, 2] - box[:, 0]
      width = box[:, 3] - box[:, 1]
      center_y = box[:, 0] + 0.5 * height
      center_x = box[:, 1] + 0.5 * width
  
      gt_height = gt_box[:, 2] - gt_box[:, 0]
      gt_width = gt_box[:, 3] - gt_box[:, 1]
      gt_center_y = gt_box[:, 0] + 0.5 * gt_height
      gt_center_x = gt_box[:, 1] + 0.5 * gt_width
  
      dy = (gt_center_y - center_y) / height
      dx = (gt_center_x - center_x) / width
      dh = np.log(gt_height / height)
      dw = np.log(gt_width / width)
  
      return np.stack([dy, dx, dh, dw], axis=1)
  
  
  ############################################################
  #  Dataset
  ############################################################
  
  class Dataset(object):
      """The base class for dataset classes.
      To use it, create a new class that adds functions specific to the dataset
      you want to use. For example:
  
      class CatsAndDogsDataset(Dataset):
          def load_cats_and_dogs(self):
              ...
          def load_mask(self, image_id):
              ...
          def image_reference(self, image_id):
              ...
  
      See COCODataset and ShapesDataset as examples.
      """
  
      def __init__(self, class_map=None):
          self._image_ids = []
          self.image_info = []
          # Background is always the first class
          self.class_info = [{"source": "", "id": 0, "name": "BG"}]
          self.source_class_ids = {}
  
      def add_class(self, source, class_id, class_name):
          assert "." not in source, "Source name cannot contain a dot"
          # Does the class exist already?
          for info in self.class_info:
              if info['source'] == source and info["id"] == class_id:
                  # source.class_id combination already available, skip
                  return
          # Add the class
          self.class_info.append({
              "source": source,
              "id": class_id,
              "name": class_name,
          })
  
      def add_image(self, source, image_id, path, **kwargs):
          image_info = {
              "id": image_id,
              "source": source,
              "path": path,
          }
          image_info.update(kwargs)
          self.image_info.append(image_info)
  
      def image_reference(self, image_id):
          """Return a link to the image in its source Website or details about
          the image that help looking it up or debugging it.
  
          Override for your dataset, but pass to this function
          if you encounter images not in your dataset.
          """
          return ""
  
      def prepare(self, class_map=None):
          """Prepares the Dataset class for use.
  
          TODO: class map is not supported yet. When done, it should handle mapping
                classes from different datasets to the same class ID.
          """
  
          def clean_name(name):
              """Returns a shorter version of object names for cleaner display."""
              return ",".join(name.split(",")[:1])
  
          # Build (or rebuild) everything else from the info dicts.
          self.num_classes = len(self.class_info)
          self.class_ids = np.arange(self.num_classes)
          self.class_names = [clean_name(c["name"]) for c in self.class_info]
          self.num_images = len(self.image_info)
          self._image_ids = np.arange(self.num_images)
  
          self.class_from_source_map = {"{}.{}".format(info['source'], info['id']): id
                                        for info, id in zip(self.class_info, self.class_ids)}
  
          # Map sources to class_ids they support
          self.sources = list(set([i['source'] for i in self.class_info]))
          self.source_class_ids = {}
          # Loop over datasets
          for source in self.sources:
              self.source_class_ids[source] = []
              # Find classes that belong to this dataset
              for i, info in enumerate(self.class_info):
                  # Include BG class in all datasets
                  if i == 0 or source == info['source']:
                      self.source_class_ids[source].append(i)
  
      def map_source_class_id(self, source_class_id):
          """Takes a source class ID and returns the int class ID assigned to it.
  
          For example:
          dataset.map_source_class_id("coco.12") -> 23
          """
          return self.class_from_source_map[source_class_id]
  
      def get_source_class_id(self, class_id, source):
          """Map an internal class ID to the corresponding class ID in the source dataset."""
          info = self.class_info[class_id]
          assert info['source'] == source
          return info['id']
  
      def append_data(self, class_info, image_info):
          self.external_to_class_id = {}
          for i, c in enumerate(self.class_info):
              for ds, id in c["map"]:
                  self.external_to_class_id[ds + str(id)] = i
  
          # Map external image IDs to internal ones.
          self.external_to_image_id = {}
          for i, info in enumerate(self.image_info):
              self.external_to_image_id[info["ds"] + str(info["id"])] = i
  
      @property
      def image_ids(self):
          return self._image_ids
  
      def source_image_link(self, image_id):
          """Returns the path or URL to the image.
          Override this to return a URL to the image if it's availble online for easy
          debugging.
          """
          return self.image_info[image_id]["path"]
  
      def load_image(self, image_id):
          """Load the specified image and return a [H,W,3] Numpy array.
          """
          # Load image
          image = skimage.io.imread(self.image_info[image_id]['path'])
          # If grayscale. Convert to RGB for consistency.
          if image.ndim != 3:
              image = skimage.color.gray2rgb(image)
          # If has an alpha channel, remove it for consistency
          if image.shape[-1] == 4:
              image = image[..., :3]
          return image
  
      def load_mask(self, image_id):
          """Load instance masks for the given image.
  
          Different datasets use different ways to store masks. Override this
          method to load instance masks and return them in the form of am
          array of binary masks of shape [height, width, instances].
  
          Returns:
              masks: A bool array of shape [height, width, instance count] with
                  a binary mask per instance.
              class_ids: a 1D array of class IDs of the instance masks.
          """
          # Override this function to load a mask from your dataset.
          # Otherwise, it returns an empty mask.
          mask = np.empty([0, 0, 0])
          class_ids = np.empty([0], np.int32)
          return mask, class_ids
  
  
  def resize_image(image, min_dim=None, max_dim=None, padding=False):
      """
      Resizes an image keeping the aspect ratio.
  
      min_dim: if provided, resizes the image such that it's smaller
          dimension == min_dim
      max_dim: if provided, ensures that the image longest side doesn't
          exceed this value.
      padding: If true, pads image with zeros so it's size is max_dim x max_dim
  
      Returns:
      image: the resized image
      window: (y1, x1, y2, x2). If max_dim is provided, padding might
          be inserted in the returned image. If so, this window is the
          coordinates of the image part of the full image (excluding
          the padding). The x2, y2 pixels are not included.
      scale: The scale factor used to resize the image
      padding: Padding added to the image [(top, bottom), (left, right), (0, 0)]
      """
      # Default window (y1, x1, y2, x2) and default scale == 1.
      h, w = image.shape[:2]
      window = (0, 0, h, w)
      scale = 1
  
      # Scale?
      if min_dim:
          # Scale up but not down
          scale = max(1, min_dim / min(h, w))
      # Does it exceed max dim?
      if max_dim:
          image_max = max(h, w)
          if round(image_max * scale) > max_dim:
              scale = max_dim / image_max
      # Resize image and mask
      if scale != 1:
          image = scipy.misc.imresize(
              image, (round(h * scale), round(w * scale)))
      # Need padding?
      if padding:
          # Get new height and width
          h, w = image.shape[:2]
          top_pad = (max_dim - h) // 2
          bottom_pad = max_dim - h - top_pad
          left_pad = (max_dim - w) // 2
          right_pad = max_dim - w - left_pad
          padding = [(top_pad, bottom_pad), (left_pad, right_pad), (0, 0)]
          image = np.pad(image, padding, mode='constant', constant_values=0)
          window = (top_pad, left_pad, h + top_pad, w + left_pad)
      return image, window, scale, padding
  
  
  def resize_mask(mask, scale, padding):
      """Resizes a mask using the given scale and padding.
      Typically, you get the scale and padding from resize_image() to
      ensure both, the image and the mask, are resized consistently.
  
      scale: mask scaling factor
      padding: Padding to add to the mask in the form
              [(top, bottom), (left, right), (0, 0)]
      """
      h, w = mask.shape[:2]
      # Suppress warning from scipy 0.13.0, the output shape of zoom() is
      # calculated with round() instead of int()
      with warnings.catch_warnings():
          warnings.simplefilter("ignore")
          mask = scipy.ndimage.zoom(mask, zoom=[scale, scale, 1], order=0)
      mask = np.pad(mask, padding, mode='constant', constant_values=0)
      return mask
  
  
  def minimize_mask(bbox, mask, mini_shape):
      """Resize masks to a smaller version to cut memory load.
      Mini-masks can then resized back to image scale using expand_masks()
  
      See inspect_data.ipynb notebook for more details.
      """
      mini_mask = np.zeros(mini_shape + (mask.shape[-1],), dtype=bool)
      for i in range(mask.shape[-1]):
          m = mask[:, :, i]
          y1, x1, y2, x2 = bbox[i][:4]
          m = m[y1:y2, x1:x2]
          if m.size == 0:
              raise Exception("Invalid bounding box with area of zero")
          m = scipy.misc.imresize(m.astype(float), mini_shape, interp='bilinear')
          mini_mask[:, :, i] = np.where(m >= 128, 1, 0)
      return mini_mask
  
  
  def expand_mask(bbox, mini_mask, image_shape):
      """Resizes mini masks back to image size. Reverses the change
      of minimize_mask().
  
      See inspect_data.ipynb notebook for more details.
      """
      mask = np.zeros(image_shape[:2] + (mini_mask.shape[-1],), dtype=bool)
      for i in range(mask.shape[-1]):
          m = mini_mask[:, :, i]
          y1, x1, y2, x2 = bbox[i][:4]
          h = y2 - y1
          w = x2 - x1
          m = scipy.misc.imresize(m.astype(float), (h, w), interp='bilinear')
          mask[y1:y2, x1:x2, i] = np.where(m >= 128, 1, 0)
      return mask
  
  
  # TODO: Build and use this function to reduce code duplication
  def mold_mask(mask, config):
      pass
  
  
  def unmold_mask(mask, bbox, image_shape):
      """Converts a mask generated by the neural network into a format similar
      to it's original shape.
      mask: [height, width] of type float. A small, typically 28x28 mask.
      bbox: [y1, x1, y2, x2]. The box to fit the mask in.
  
      Returns a binary mask with the same size as the original image.
      """
      threshold = 0.5
      y1, x1, y2, x2 = bbox
      mask = scipy.misc.imresize(
          mask, (y2 - y1, x2 - x1), interp='bilinear').astype(np.float32) / 255.0
      mask = np.where(mask >= threshold, 1, 0).astype(np.uint8)
  
      # Put the mask in the right location.
      full_mask = np.zeros(image_shape[:2], dtype=np.uint8)
      full_mask[y1:y2, x1:x2] = mask
      return full_mask
  
  
  ############################################################
  #  Anchors
  ############################################################
  
  def generate_anchors(scales, ratios, shape, feature_stride, anchor_stride):
      """
      scales: 1D array of anchor sizes in pixels. Example: [32, 64, 128]
      ratios: 1D array of anchor ratios of width/height. Example: [0.5, 1, 2]
      shape: [height, width] spatial shape of the feature map over which
              to generate anchors.
      feature_stride: Stride of the feature map relative to the image in pixels.
      anchor_stride: Stride of anchors on the feature map. For example, if the
          value is 2 then generate anchors for every other feature map pixel.
      """
      # Get all combinations of scales and ratios
      scales, ratios = np.meshgrid(np.array(scales), np.array(ratios))
      scales = scales.flatten()
      ratios = ratios.flatten()
  
      # Enumerate heights and widths from scales and ratios
      heights = scales / np.sqrt(ratios)
      widths = scales * np.sqrt(ratios)
  
      # Enumerate shifts in feature space
      shifts_y = np.arange(0, shape[0], anchor_stride) * feature_stride
      shifts_x = np.arange(0, shape[1], anchor_stride) * feature_stride
      shifts_x, shifts_y = np.meshgrid(shifts_x, shifts_y)
  
      # Enumerate combinations of shifts, widths, and heights
      box_widths, box_centers_x = np.meshgrid(widths, shifts_x)
      box_heights, box_centers_y = np.meshgrid(heights, shifts_y)
  
      # Reshape to get a list of (y, x) and a list of (h, w)
      box_centers = np.stack(
          [box_centers_y, box_centers_x], axis=2).reshape([-1, 2])
      box_sizes = np.stack([box_heights, box_widths], axis=2).reshape([-1, 2])
  
      # Convert to corner coordinates (y1, x1, y2, x2)
      boxes = np.concatenate([box_centers - 0.5 * box_sizes,
                              box_centers + 0.5 * box_sizes], axis=1)
      return boxes
  
  
  def generate_pyramid_anchors(scales, ratios, feature_shapes, feature_strides,
                               anchor_stride):
      """Generate anchors at different levels of a feature pyramid. Each scale
      is associated with a level of the pyramid, but each ratio is used in
      all levels of the pyramid.
  
      Returns:
      anchors: [N, (y1, x1, y2, x2)]. All generated anchors in one array. Sorted
          with the same order of the given scales. So, anchors of scale[0] come
          first, then anchors of scale[1], and so on.
      """
      # Anchors
      # [anchor_count, (y1, x1, y2, x2)]
      anchors = []
      for i in range(len(scales)):
          anchors.append(generate_anchors(scales[i], ratios, feature_shapes[i],
                                          feature_strides[i], anchor_stride))
      return np.concatenate(anchors, axis=0)
  
  
  ############################################################
  #  Miscellaneous
  ############################################################
  
  def trim_zeros(x):
      """It's common to have tensors larger than the available data and
      pad with zeros. This function removes rows that are all zeros.
  
      x: [rows, columns].
      """
      assert len(x.shape) == 2
      return x[~np.all(x == 0, axis=1)]
  
  
  def compute_ap(gt_boxes, gt_class_ids, gt_masks,
                 pred_boxes, pred_class_ids, pred_scores, pred_masks,
                 iou_threshold=0.5):
      """Compute Average Precision at a set IoU threshold (default 0.5).
  
      Returns:
      mAP: Mean Average Precision
      precisions: List of precisions at different class score thresholds.
      recalls: List of recall values at different class score thresholds.
      overlaps: [pred_boxes, gt_boxes] IoU overlaps.
      """
      # Trim zero padding and sort predictions by score from high to low
      # TODO: cleaner to do zero unpadding upstream
      gt_boxes = trim_zeros(gt_boxes)
      gt_masks = gt_masks[..., :gt_boxes.shape[0]]
      pred_boxes = trim_zeros(pred_boxes)
      pred_scores = pred_scores[:pred_boxes.shape[0]]
      indices = np.argsort(pred_scores)[::-1]
      pred_boxes = pred_boxes[indices]
      pred_class_ids = pred_class_ids[indices]
      pred_scores = pred_scores[indices]
      pred_masks = pred_masks[..., indices]
  
      # Compute IoU overlaps [pred_masks, gt_masks]
      overlaps = compute_overlaps_masks(pred_masks, gt_masks)
  
      # Loop through ground truth boxes and find matching predictions
      match_count = 0
      pred_match = np.zeros([pred_boxes.shape[0]])
      gt_match = np.zeros([gt_boxes.shape[0]])
      for i in range(len(pred_boxes)):
          # Find best matching ground truth box
          sorted_ixs = np.argsort(overlaps[i])[::-1]
          for j in sorted_ixs:
              # If ground truth box is already matched, go to next one
              if gt_match[j] == 1:
                  continue
              # If we reach IoU smaller than the threshold, end the loop
              iou = overlaps[i, j]
              if iou < iou_threshold:
                  break
              # Do we have a match?
              if pred_class_ids[i] == gt_class_ids[j]:
                  match_count += 1
                  gt_match[j] = 1
                  pred_match[i] = 1
                  break
  
      # Compute precision and recall at each prediction box step
      precisions = np.cumsum(pred_match) / (np.arange(len(pred_match)) + 1)
      recalls = np.cumsum(pred_match).astype(np.float32) / len(gt_match)
  
      # Pad with start and end values to simplify the math
      precisions = np.concatenate([[0], precisions, [0]])
      recalls = np.concatenate([[0], recalls, [1]])
  
      # Ensure precision values decrease but don't increase. This way, the
      # precision value at each recall threshold is the maximum it can be
      # for all following recall thresholds, as specified by the VOC paper.
      for i in range(len(precisions) - 2, -1, -1):
          precisions[i] = np.maximum(precisions[i], precisions[i + 1])
  
      # Compute mean AP over recall range
      indices = np.where(recalls[:-1] != recalls[1:])[0] + 1
      mAP = np.sum((recalls[indices] - recalls[indices - 1]) *
                   precisions[indices])
  
      return mAP, precisions, recalls, overlaps
  
  
  def compute_recall(pred_boxes, gt_boxes, iou):
      """Compute the recall at the given IoU threshold. It's an indication
      of how many GT boxes were found by the given prediction boxes.
  
      pred_boxes: [N, (y1, x1, y2, x2)] in image coordinates
      gt_boxes: [N, (y1, x1, y2, x2)] in image coordinates
      """
      # Measure overlaps
      overlaps = compute_overlaps(pred_boxes, gt_boxes)
      iou_max = np.max(overlaps, axis=1)
      iou_argmax = np.argmax(overlaps, axis=1)
      positive_ids = np.where(iou_max >= iou)[0]
      matched_gt_boxes = iou_argmax[positive_ids]
  
      recall = len(set(matched_gt_boxes)) / gt_boxes.shape[0]
      return recall, positive_ids
  
  
  # ## Batch Slicing
  # Some custom layers support a batch size of 1 only, and require a lot of work
  # to support batches greater than 1. This function slices an input tensor
  # across the batch dimension and feeds batches of size 1. Effectively,
  # an easy way to support batches > 1 quickly with little code modification.
  # In the long run, it's more efficient to modify the code to support large
  # batches and getting rid of this function. Consider this a temporary solution
  def batch_slice(inputs, graph_fn, batch_size, names=None):
      """Splits inputs into slices and feeds each slice to a copy of the given
      computation graph and then combines the results. It allows you to run a
      graph on a batch of inputs even if the graph is written to support one
      instance only.
  
      inputs: list of tensors. All must have the same first dimension length
      graph_fn: A function that returns a TF tensor that's part of a graph.
      batch_size: number of slices to divide the data into.
      names: If provided, assigns names to the resulting tensors.
      """
      if not isinstance(inputs, list):
          inputs = [inputs]
  
      outputs = []
      for i in range(batch_size):
          inputs_slice = [x[i] for x in inputs]
          output_slice = graph_fn(*inputs_slice)
          if not isinstance(output_slice, (tuple, list)):
              output_slice = [output_slice]
          outputs.append(output_slice)
      # Change outputs from a list of slices where each is
      # a list of outputs to a list of outputs and each has
      # a list of slices
      outputs = list(zip(*outputs))
  
      if names is None:
          names = [None] * len(outputs)
  
      result = [tf.stack(o, axis=0, name=n)
                for o, n in zip(outputs, names)]
      if len(result) == 1:
          result = result[0]
  
      return result
  
  
  def download_trained_weights(coco_model_path, verbose=1):
      """Download COCO trained weights from Releases.
  
      coco_model_path: local path of COCO trained weights
      """
      if verbose > 0:
          print("Downloading pretrained model to " + coco_model_path + " ...")
      with urllib.request.urlopen(COCO_MODEL_URL) as resp, open(coco_model_path, 'wb') as out:
          shutil.copyfileobj(resp, out)
      if verbose > 0:
          print("... done downloading pretrained model!")
  