code: from abc import abstractmethod
  from math import ceil, log
  
  import torch
  import torch.nn as nn
  import torch.nn.functional as F
  from mmcv.cnn import ConvModule, bias_init_with_prob
  from mmcv.ops import CornerPool, batched_nms
  
  from mmdet.core import multi_apply
  from ..builder import HEADS, build_loss
  from ..utils import gaussian_radius, gen_gaussian_target
  from .base_dense_head import BaseDenseHead
  
  
  class BiCornerPool(nn.Module):
      """Bidirectional Corner Pooling Module (TopLeft, BottomRight, etc.)
  
      Args:
          in_channels (int): Input channels of module.
          out_channels (int): Output channels of module.
          feat_channels (int): Feature channels of module.
          directions (list[str]): Directions of two CornerPools.
          norm_cfg (dict): Dictionary to construct and config norm layer.
      """
  
      def __init__(self,
                   in_channels,
                   directions,
                   feat_channels=128,
                   out_channels=128,
                   norm_cfg=dict(type='BN', requires_grad=True)):
          super(BiCornerPool, self).__init__()
          self.direction1_conv = ConvModule(
              in_channels, feat_channels, 3, padding=1, norm_cfg=norm_cfg)
          self.direction2_conv = ConvModule(
              in_channels, feat_channels, 3, padding=1, norm_cfg=norm_cfg)
  
          self.aftpool_conv = ConvModule(
              feat_channels,
              out_channels,
              3,
              padding=1,
              norm_cfg=norm_cfg,
              act_cfg=None)
  
          self.conv1 = ConvModule(
              in_channels, out_channels, 1, norm_cfg=norm_cfg, act_cfg=None)
          self.conv2 = ConvModule(
              in_channels, out_channels, 3, padding=1, norm_cfg=norm_cfg)
  
          self.direction1_pool = CornerPool(directions[0])
          self.direction2_pool = CornerPool(directions[1])
          self.relu = nn.ReLU(inplace=True)
  
      def forward(self, x):
          """Forward features from the upstream network.
  
          Args:
              x (tensor): Input feature of BiCornerPool.
  
          Returns:
              conv2 (tensor): Output feature of BiCornerPool.
          """
          direction1_conv = self.direction1_conv(x)
          direction2_conv = self.direction2_conv(x)
          direction1_feat = self.direction1_pool(direction1_conv)
          direction2_feat = self.direction2_pool(direction2_conv)
          aftpool_conv = self.aftpool_conv(direction1_feat + direction2_feat)
          conv1 = self.conv1(x)
          relu = self.relu(aftpool_conv + conv1)
          conv2 = self.conv2(relu)
          return conv2
  
  USE_MMDET_OFFICIAL = False
  
  class CornerBaseHead(BaseDenseHead):
      """Base class for DenseHeads."""
  
      def __init__(self,
                   num_classes,
                   in_channels,
                   train_cfg=None,
                   test_cfg=None):
          super(CornerBaseHead, self).__init__()
          self.num_classes = num_classes
          self.in_channels = in_channels
          self.train_cfg = train_cfg
          self.test_cfg = test_cfg
          self._init_layers()
  
      @abstractmethod
      def _init_layers(self):
          pass
  
      def build_convs(self, in_channel, feat_channel, stacked_convs):
          head_convs = []
          for i in range(stacked_convs):
              chn = in_channel if i == 0 else feat_channel
              head_convs.append(ConvModule(
                  chn, feat_channel, 3,
                  padding=1, bias=True, act_cfg=dict(type='ReLU', inplace=True)))
          return head_convs
  
      def build_share_convs(self, in_channel, feat_channel, stacked_convs):
          if stacked_convs == 0:
              return nn.Identity()
          return nn.Sequential(*self.build_convs(in_channel, feat_channel, stacked_convs))
  
      def build_head(self, in_channel, feat_channel, stacked_convs, out_channel):
          head_convs = self.build_convs(in_channel, feat_channel, stacked_convs)
          head_convs.append(nn.Conv2d(feat_channel, out_channel, 1))
          return nn.Sequential(*head_convs)
  
      def _gather_feat(self, feat, ind, mask=None):
          """Gather feature according to index.
  
          Args:
              feat (Tensor): Target feature map.
              ind (Tensor): Target coord index.
              mask (Tensor | None): Mask of featuremap. Default: None.
  
          Returns:
              feat (Tensor): Gathered feature.
          """
          dim = feat.size(2)
          if USE_MMDET_OFFICIAL:
              # [old]
              ind = ind.unsqueeze(2).repeat(1, 1, dim)
          else:
              # [new]
              ind = ind.unsqueeze(len(ind.shape)).expand(*ind.shape, dim)
          feat = feat.gather(1, ind)
          if mask is not None:
              mask = mask.unsqueeze(2).expand_as(feat)
              feat = feat[mask]
              feat = feat.view(-1, dim)
          return feat
  
      def _local_maximum(self, heat, kernel=3):
          """Extract local maximum pixel with given kernal.
  
          Args:
              heat (Tensor): Target heatmap.
              kernel (int): Kernel size of max pooling. Default: 3.
  
          Returns:
              heat (Tensor): A heatmap where local maximum pixels maintain its
                  own value and other positions are 0.
          """
          pad = (kernel - 1) // 2
          hmax = F.max_pool2d(heat, kernel, stride=1, padding=pad)
          keep = (hmax == heat).float()
          return heat * keep
  
      def _transpose_and_gather_feat(self, feat, ind):
          """Transpose and gather feature according to index.
  
          Args:
              feat (Tensor): Target feature map.
              ind (Tensor): Target coord index.
  
          Returns:
              feat (Tensor): Transposed and gathered feature.
          """
          feat = feat.permute(0, 2, 3, 1).contiguous()
          feat = feat.view(feat.size(0), -1, feat.size(3))
          feat = self._gather_feat(feat, ind)
          return feat
  
      def _topk(self, scores, k=20):
          """Get top k positions from heatmap.
  
          Args:
              scores (Tensor): Target heatmap with shape
                  [batch, num_classes, height, width].
              k (int): Target number. Default: 20.
  
          Returns:
              tuple[torch.Tensor]: Scores, indexes, categories and coords of
                  topk keypoint. Containing following Tensors:
  
              - topk_scores (Tensor): Max scores of each topk keypoint.
              - topk_inds (Tensor): Indexes of each topk keypoint.
              - topk_clses (Tensor): Categories of each topk keypoint.
              - topk_ys (Tensor): Y-coord of each topk keypoint.
              - topk_xs (Tensor): X-coord of each topk keypoint.
          """
          # [old]
          if USE_MMDET_OFFICIAL:
              batch, _, height, width = scores.size()
              topk_scores, topk_inds = torch.topk(scores.view(batch, -1), k)
              topk_clses = topk_inds // (height * width)
              topk_inds = topk_inds % (height * width)
              topk_ys = topk_inds // width
              topk_xs = (topk_inds % width).int().float()
          else:
              # [new]
              batch, channel, height, width = scores.size()
              topk_scores, topk_inds = torch.topk(scores.view(batch, channel, -1), k)
  
              topk_inds = topk_inds % (height * width)  # (B, #cls, K)
              topk_ys = (topk_inds // width).float()  # (B, #cls, K)
              topk_xs = (topk_inds % width).float()  # (B, #cls, K)
  
              topk_scores, topk_ind = torch.topk(topk_scores.view(batch, -1), k)
              topk_clses = topk_ind // k
              topk_inds = self._gather_feat(topk_inds.view(batch, -1, 1), topk_ind).view(batch, k)
              topk_ys = self._gather_feat(topk_ys.view(batch, -1, 1), topk_ind).view(batch, k)
              topk_xs = self._gather_feat(topk_xs.view(batch, -1, 1), topk_ind).view(batch, k)
          return topk_scores, topk_inds, topk_clses, topk_ys, topk_xs
  
  
  @HEADS.register_module()
  class CornerHead(CornerBaseHead):
      """Head of CornerNet: Detecting Objects as Paired Keypoints.
  
      Code is modified from the `official github repo
      <https://github.com/princeton-vl/CornerNet/blob/master/models/py_utils/
      kp.py#L73>`_ .
  
      More details can be found in the `paper
      <https://arxiv.org/abs/1808.01244>`_ .
  
      Args:
          num_classes (int): Number of categories excluding the background
              category.
          in_channels (int): Number of channels in the input feature map.
          num_feat_levels (int): Levels of feature from the previous module. 2
              for HourglassNet-104 and 1 for HourglassNet-52. Because
              HourglassNet-104 outputs the final feature and intermediate
              supervision feature and HourglassNet-52 only outputs the final
              feature. Default: 2.
          corner_emb_channels (int): Channel of embedding vector. Default: 1.
          train_cfg (dict | None): Training config. Useless in CornerHead,
              but we keep this variable for SingleStageDetector. Default: None.
          test_cfg (dict | None): Testing config of CornerHead. Default: None.
          loss_heatmap (dict | None): Config of corner heatmap loss. Default:
              GaussianFocalLoss.
          loss_embedding (dict | None): Config of corner embedding loss. Default:
              AssociativeEmbeddingLoss.
          loss_offset (dict | None): Config of corner offset loss. Default:
              SmoothL1Loss.
      """
  
      def __init__(self,
                   *args,
                   num_feat_levels=2,
                   corner_emb_channels=1,
                   loss_heatmap=dict(
                       type='GaussianFocalLoss',
                       alpha=2.0,
                       gamma=4.0,
                       loss_weight=1),
                   loss_embedding=dict(
                       type='AssociativeEmbeddingLoss',
                       pull_weight=0.25,
                       push_weight=0.25),
                   loss_offset=dict(
                       type='SmoothL1Loss', beta=1.0, loss_weight=1),
                   **kwargs):
          self.corner_emb_channels = corner_emb_channels
          self.with_corner_emb = self.corner_emb_channels > 0
          self.corner_offset_channels = 2
          self.num_feat_levels = num_feat_levels
          super(CornerHead, self).__init__(*args, **kwargs)
          self.loss_heatmap = build_loss(
              loss_heatmap) if loss_heatmap is not None else None
          self.loss_embedding = build_loss(
              loss_embedding) if loss_embedding is not None else None
          self.loss_offset = build_loss(
              loss_offset) if loss_offset is not None else None
  
      def _make_layers(self, out_channels, in_channels=256, feat_channels=256):
          """Initialize conv sequential for CornerHead."""
          return nn.Sequential(
              ConvModule(in_channels, feat_channels, 3, padding=1),
              ConvModule(
                  feat_channels, out_channels, 1, norm_cfg=None, act_cfg=None))
  
      def _init_corner_kpt_layers(self):
          """Initialize corner keypoint layers.
  
          Including corner heatmap branch and corner offset branch. Each branch
          has two parts: prefix `tl_` for top-left and `br_` for bottom-right.
          """
          self.tl_pool, self.br_pool = nn.ModuleList(), nn.ModuleList()
          self.tl_heat, self.br_heat = nn.ModuleList(), nn.ModuleList()
          self.tl_off, self.br_off = nn.ModuleList(), nn.ModuleList()
  
          for _ in range(self.num_feat_levels):
              self.tl_pool.append(
                  BiCornerPool(
                      self.in_channels, ['top', 'left'],
                      out_channels=self.in_channels))
              self.br_pool.append(
                  BiCornerPool(
                      self.in_channels, ['bottom', 'right'],
                      out_channels=self.in_channels))
  
              self.tl_heat.append(
                  self._make_layers(
                      out_channels=self.num_classes,
                      in_channels=self.in_channels))
              self.br_heat.append(
                  self._make_layers(
                      out_channels=self.num_classes,
                      in_channels=self.in_channels))
  
              self.tl_off.append(
                  self._make_layers(
                      out_channels=self.corner_offset_channels,
                      in_channels=self.in_channels))
              self.br_off.append(
                  self._make_layers(
                      out_channels=self.corner_offset_channels,
                      in_channels=self.in_channels))
  
      def _init_corner_emb_layers(self):
          """Initialize corner embedding layers.
  
          Only include corner embedding branch with two parts: prefix `tl_` for
          top-left and `br_` for bottom-right.
          """
          self.tl_emb, self.br_emb = nn.ModuleList(), nn.ModuleList()
  
          for _ in range(self.num_feat_levels):
              self.tl_emb.append(
                  self._make_layers(
                      out_channels=self.corner_emb_channels,
                      in_channels=self.in_channels))
              self.br_emb.append(
                  self._make_layers(
                      out_channels=self.corner_emb_channels,
                      in_channels=self.in_channels))
  
      def _init_layers(self):
          """Initialize layers for CornerHead.
  
          Including two parts: corner keypoint layers and corner embedding layers
          """
          self._init_corner_kpt_layers()
          if self.with_corner_emb:
              self._init_corner_emb_layers()
  
      def init_weights(self):
          """Initialize weights of the head."""
          bias_init = bias_init_with_prob(0.1)
          for i in range(self.num_feat_levels):
              # The initialization of parameters are different between nn.Conv2d
              # and ConvModule. Our experiments show that using the original
              # initialization of nn.Conv2d increases the final mAP by about 0.2%
              self.tl_heat[i][-1].conv.reset_parameters()
              self.tl_heat[i][-1].conv.bias.data.fill_(bias_init)
              self.br_heat[i][-1].conv.reset_parameters()
              self.br_heat[i][-1].conv.bias.data.fill_(bias_init)
              self.tl_off[i][-1].conv.reset_parameters()
              self.br_off[i][-1].conv.reset_parameters()
              if self.with_corner_emb:
                  self.tl_emb[i][-1].conv.reset_parameters()
                  self.br_emb[i][-1].conv.reset_parameters()
  
      def forward(self, feats):
          """Forward features from the upstream network.
  
          Args:
              feats (tuple[Tensor]): Features from the upstream network, each is
                  a 4D-tensor.
  
          Returns:
              tuple: Usually a tuple of corner heatmaps, offset heatmaps and
              embedding heatmaps.
                  - tl_heats (list[Tensor]): Top-left corner heatmaps for all
                    levels, each is a 4D-tensor, the channels number is
                    num_classes.
                  - br_heats (list[Tensor]): Bottom-right corner heatmaps for all
                    levels, each is a 4D-tensor, the channels number is
                    num_classes.
                  - tl_embs (list[Tensor] | list[None]): Top-left embedding
                    heatmaps for all levels, each is a 4D-tensor or None.
                    If not None, the channels number is corner_emb_channels.
                  - br_embs (list[Tensor] | list[None]): Bottom-right embedding
                    heatmaps for all levels, each is a 4D-tensor or None.
                    If not None, the channels number is corner_emb_channels.
                  - tl_offs (list[Tensor]): Top-left offset heatmaps for all
                    levels, each is a 4D-tensor. The channels number is
                    corner_offset_channels.
                  - br_offs (list[Tensor]): Bottom-right offset heatmaps for all
                    levels, each is a 4D-tensor. The channels number is
                    corner_offset_channels.
          """
          lvl_ind = list(range(self.num_feat_levels))
          return multi_apply(self.forward_single, feats, lvl_ind)
  
      def forward_single(self, x, lvl_ind, return_pool=False):
          """Forward feature of a single level.
  
          Args:
              x (Tensor): Feature of a single level.
              lvl_ind (int): Level index of current feature.
              return_pool (bool): Return corner pool feature or not.
  
          Returns:
              tuple[Tensor]: A tuple of CornerHead's output for current feature
              level. Containing the following Tensors:
  
                  - tl_heat (Tensor): Predicted top-left corner heatmap.
                  - br_heat (Tensor): Predicted bottom-right corner heatmap.
                  - tl_emb (Tensor | None): Predicted top-left embedding heatmap.
                    None for `self.with_corner_emb == False`.
                  - br_emb (Tensor | None): Predicted bottom-right embedding
                    heatmap. None for `self.with_corner_emb == False`.
                  - tl_off (Tensor): Predicted top-left offset heatmap.
                  - br_off (Tensor): Predicted bottom-right offset heatmap.
                  - tl_pool (Tensor): Top-left corner pool feature. Not must
                    have.
                  - br_pool (Tensor): Bottom-right corner pool feature. Not must
                    have.
          """
          tl_pool = self.tl_pool[lvl_ind](x)
          tl_heat = self.tl_heat[lvl_ind](tl_pool)
          br_pool = self.br_pool[lvl_ind](x)
          br_heat = self.br_heat[lvl_ind](br_pool)
  
          tl_emb, br_emb = None, None
          if self.with_corner_emb:
              tl_emb = self.tl_emb[lvl_ind](tl_pool)
              br_emb = self.br_emb[lvl_ind](br_pool)
  
          tl_off = self.tl_off[lvl_ind](tl_pool)
          br_off = self.br_off[lvl_ind](br_pool)
  
          result_list = [tl_heat, br_heat, tl_emb, br_emb, tl_off, br_off]
          if return_pool:
              result_list.append(tl_pool)
              result_list.append(br_pool)
  
          return result_list
  
      def get_targets(self,
                      gt_bboxes,
                      gt_labels,
                      feat_shape,
                      img_shape,
                      with_corner_emb=False,
                      with_guiding_shift=False,
                      with_centripetal_shift=False):
          """Generate corner targets.
  
          Including corner heatmap, corner offset.
  
          Optional: corner embedding, corner guiding shift, centripetal shift.
  
          For CornerNet, we generate corner heatmap, corner offset and corner
          embedding from this function.
  
          For CentripetalNet, we generate corner heatmap, corner offset, guiding
          shift and centripetal shift from this function.
  
          Args:
              gt_bboxes (list[Tensor]): Ground truth bboxes of each image, each
                  has shape (num_gt, 4).
              gt_labels (list[Tensor]): Ground truth labels of each box, each has
                  shape (num_gt,).
              feat_shape (list[int]): Shape of output feature,
                  [batch, channel, height, width].
              img_shape (list[int]): Shape of input image,
                  [height, width, channel].
              with_corner_emb (bool): Generate corner embedding target or not.
                  Default: False.
              with_guiding_shift (bool): Generate guiding shift target or not.
                  Default: False.
              with_centripetal_shift (bool): Generate centripetal shift target or
                  not. Default: False.
  
          Returns:
              dict: Ground truth of corner heatmap, corner offset, corner
              embedding, guiding shift and centripetal shift. Containing the
              following keys:
  
                  - topleft_heatmap (Tensor): Ground truth top-left corner
                    heatmap.
                  - bottomright_heatmap (Tensor): Ground truth bottom-right
                    corner heatmap.
                  - topleft_offset (Tensor): Ground truth top-left corner offset.
                  - bottomright_offset (Tensor): Ground truth bottom-right corner
                    offset.
                  - corner_embedding (list[list[list[int]]]): Ground truth corner
                    embedding. Not must have.
                  - topleft_guiding_shift (Tensor): Ground truth top-left corner
                    guiding shift. Not must have.
                  - bottomright_guiding_shift (Tensor): Ground truth bottom-right
                    corner guiding shift. Not must have.
                  - topleft_centripetal_shift (Tensor): Ground truth top-left
                    corner centripetal shift. Not must have.
                  - bottomright_centripetal_shift (Tensor): Ground truth
                    bottom-right corner centripetal shift. Not must have.
          """
          batch_size, _, height, width = feat_shape  # feat size (128, 128)
          img_h, img_w = img_shape[:2]  # > output size (511, 511)
          # > feat_size / output_size
          width_ratio = float(width / img_w)
          height_ratio = float(height / img_h)
          # > `gt_bboxes`: (#img, #obj, 4), `H/W`: 128
          gt_tl_heatmap = gt_bboxes[-1].new_zeros(
              [batch_size, self.num_classes, height, width])  # > (#img, #cls, H, W)
          gt_br_heatmap = gt_bboxes[-1].new_zeros(
              [batch_size, self.num_classes, height, width])  # > (#img, #cls, H, W)
          gt_tl_offset = gt_bboxes[-1].new_zeros([batch_size, 2, height, width])  # > (#img, 2, H, W)
          gt_br_offset = gt_bboxes[-1].new_zeros([batch_size, 2, height, width])  # > (#img, 2, H, W)
  
          if with_corner_emb:
              match = []
  
          # Guiding shift is a kind of offset, from center to corner
          if with_guiding_shift:
              gt_tl_guiding_shift = gt_bboxes[-1].new_zeros(
                  [batch_size, 2, height, width])
              gt_br_guiding_shift = gt_bboxes[-1].new_zeros(
                  [batch_size, 2, height, width])
          # Centripetal shift is also a kind of offset, from center to corner
          # and normalized by log.
          if with_centripetal_shift:
              gt_tl_centripetal_shift = gt_bboxes[-1].new_zeros(
                  [batch_size, 2, height, width])
              gt_br_centripetal_shift = gt_bboxes[-1].new_zeros(
                  [batch_size, 2, height, width])
  
          for batch_id in range(batch_size):  # > #img
              # Ground truth of corner embedding per image is a list of coord set
              corner_match = []
              for box_id in range(len(gt_labels[batch_id])):  # > #obj
                  left, top, right, bottom = gt_bboxes[batch_id][box_id]
                  center_x = (left + right) / 2.0
                  center_y = (top + bottom) / 2.0
                  label = gt_labels[batch_id][box_id]
  
                  # Use coords in the feature level to generate ground truth
                  scale_left = left * width_ratio
                  scale_right = right * width_ratio
                  scale_top = top * height_ratio
                  scale_bottom = bottom * height_ratio
                  scale_center_x = center_x * width_ratio
                  scale_center_y = center_y * height_ratio
  
                  # Int coords on feature map/ground truth tensor
                  left_idx = int(min(scale_left, width - 1))
                  right_idx = int(min(scale_right, width - 1))
                  top_idx = int(min(scale_top, height - 1))
                  bottom_idx = int(min(scale_bottom, height - 1))
  
                  # Generate gaussian heatmap
                  scale_box_width = ceil(scale_right - scale_left)
                  scale_box_height = ceil(scale_bottom - scale_top)
                  radius = gaussian_radius((scale_box_height, scale_box_width),
                                           min_overlap=0.3)
                  radius = max(0, int(radius))
                  gt_tl_heatmap[batch_id, label] = gen_gaussian_target(
                      gt_tl_heatmap[batch_id, label], [left_idx, top_idx],
                      radius)  # > (#img, #cls, H, W) -> (H, W)
                  gt_br_heatmap[batch_id, label] = gen_gaussian_target(
                      gt_br_heatmap[batch_id, label], [right_idx, bottom_idx],
                      radius)  # > (#img, #cls, H, W) -> (H, W)
  
                  # Generate corner offset
                  left_offset = scale_left - left_idx
                  top_offset = scale_top - top_idx
                  right_offset = scale_right - right_idx
                  bottom_offset = scale_bottom - bottom_idx
                  gt_tl_offset[batch_id, 0, top_idx, left_idx] = left_offset  # > (#img, 2, H, W)
                  gt_tl_offset[batch_id, 1, top_idx, left_idx] = top_offset  # > (#img, 2, H, W)
                  gt_br_offset[batch_id, 0, bottom_idx, right_idx] = right_offset  # > (#img, 2, H, W)
                  gt_br_offset[batch_id, 1, bottom_idx,
                               right_idx] = bottom_offset  # > (#img, 2, H, W)
  
                  # Generate corner embedding
                  if with_corner_emb:
                      corner_match.append([[top_idx, left_idx],
                                           [bottom_idx, right_idx]])
                  # Generate guiding shift
                  if with_guiding_shift:
                      gt_tl_guiding_shift[batch_id, 0, top_idx,
                                          left_idx] = scale_center_x - left_idx
                      gt_tl_guiding_shift[batch_id, 1, top_idx,
                                          left_idx] = scale_center_y - top_idx
                      gt_br_guiding_shift[batch_id, 0, bottom_idx,
                                          right_idx] = right_idx - scale_center_x
                      gt_br_guiding_shift[
                          batch_id, 1, bottom_idx,
                          right_idx] = bottom_idx - scale_center_y
                  # Generate centripetal shift
                  if with_centripetal_shift:
                      gt_tl_centripetal_shift[batch_id, 0, top_idx,
                                              left_idx] = log(scale_center_x -
                                                              scale_left)
                      gt_tl_centripetal_shift[batch_id, 1, top_idx,
                                              left_idx] = log(scale_center_y -
                                                              scale_top)
                      gt_br_centripetal_shift[batch_id, 0, bottom_idx,
                                              right_idx] = log(scale_right -
                                                               scale_center_x)
                      gt_br_centripetal_shift[batch_id, 1, bottom_idx,
                                              right_idx] = log(scale_bottom -
                                                               scale_center_y)
  
              if with_corner_emb:
                  match.append(corner_match)
  
          target_result = dict(
              topleft_heatmap=gt_tl_heatmap,
              topleft_offset=gt_tl_offset,
              bottomright_heatmap=gt_br_heatmap,
              bottomright_offset=gt_br_offset)
  
          if with_corner_emb:
              target_result.update(corner_embedding=match)
          if with_guiding_shift:
              target_result.update(
                  topleft_guiding_shift=gt_tl_guiding_shift,
                  bottomright_guiding_shift=gt_br_guiding_shift)
          if with_centripetal_shift:
              target_result.update(
                  topleft_centripetal_shift=gt_tl_centripetal_shift,
                  bottomright_centripetal_shift=gt_br_centripetal_shift)
  
          return target_result
  
      def loss(self,
               tl_heats,
               br_heats,
               tl_embs,
               br_embs,
               tl_offs,
               br_offs,
               gt_bboxes,
               gt_labels,
               img_metas,
               gt_bboxes_ignore=None):
          """Compute losses of the head.
  
          Args:
              tl_heats (list[Tensor]): Top-left corner heatmaps for each level
                  with shape (N, num_classes, H, W).
              br_heats (list[Tensor]): Bottom-right corner heatmaps for each
                  level with shape (N, num_classes, H, W).
              tl_embs (list[Tensor]): Top-left corner embeddings for each level
                  with shape (N, corner_emb_channels, H, W).
              br_embs (list[Tensor]): Bottom-right corner embeddings for each
                  level with shape (N, corner_emb_channels, H, W).
              tl_offs (list[Tensor]): Top-left corner offsets for each level
                  with shape (N, corner_offset_channels, H, W).
              br_offs (list[Tensor]): Bottom-right corner offsets for each level
                  with shape (N, corner_offset_channels, H, W).
              gt_bboxes (list[Tensor]): Ground truth bboxes for each image with
                  shape (num_gts, 4) in [left, top, right, bottom] format.
              gt_labels (list[Tensor]): Class indices corresponding to each box.
              img_metas (list[dict]): Meta information of each image, e.g.,
                  image size, scaling factor, etc.
              gt_bboxes_ignore (list[Tensor] | None): Specify which bounding
                  boxes can be ignored when computing the loss.
  
          Returns:
              dict[str, Tensor]: A dictionary of loss components. Containing the
              following losses:
  
                  - det_loss (list[Tensor]): Corner keypoint losses of all
                    feature levels.
                  - pull_loss (list[Tensor]): Part one of AssociativeEmbedding
                    losses of all feature levels.
                  - push_loss (list[Tensor]): Part two of AssociativeEmbedding
                    losses of all feature levels.
                  - off_loss (list[Tensor]): Corner offset losses of all feature
                    levels.
          """
          targets = self.get_targets(
              gt_bboxes,
              gt_labels,
              tl_heats[-1].shape,
              img_metas[0]['pad_shape'],
              with_corner_emb=self.with_corner_emb)
          mlvl_targets = [targets for _ in range(self.num_feat_levels)]
          det_losses, pull_losses, push_losses, off_losses = multi_apply(
              self.loss_single, tl_heats, br_heats, tl_embs, br_embs, tl_offs,
              br_offs, mlvl_targets)
          loss_dict = dict(det_loss=det_losses, off_loss=off_losses)
          if self.with_corner_emb:
              loss_dict.update(pull_loss=pull_losses, push_loss=push_losses)
          return loss_dict
  
      def loss_single(self, tl_hmp, br_hmp, tl_emb, br_emb, tl_off, br_off,
                      targets):
          """Compute losses for single level.
  
          Args:
              tl_hmp (Tensor): Top-left corner heatmap for current level with
                  shape (N, num_classes, H, W).
              br_hmp (Tensor): Bottom-right corner heatmap for current level with
                  shape (N, num_classes, H, W).
              tl_emb (Tensor): Top-left corner embedding for current level with
                  shape (N, corner_emb_channels, H, W).
              br_emb (Tensor): Bottom-right corner embedding for current level
                  with shape (N, corner_emb_channels, H, W).
              tl_off (Tensor): Top-left corner offset for current level with
                  shape (N, corner_offset_channels, H, W).
              br_off (Tensor): Bottom-right corner offset for current level with
                  shape (N, corner_offset_channels, H, W).
              targets (dict): Corner target generated by `get_targets`.
  
          Returns:
              tuple[torch.Tensor]: Losses of the head's differnet branches
              containing the following losses:
  
                  - det_loss (Tensor): Corner keypoint loss.
                  - pull_loss (Tensor): Part one of AssociativeEmbedding loss.
                  - push_loss (Tensor): Part two of AssociativeEmbedding loss.
                  - off_loss (Tensor): Corner offset loss.
          """
          gt_tl_hmp = targets['topleft_heatmap']
          gt_br_hmp = targets['bottomright_heatmap']
          gt_tl_off = targets['topleft_offset']
          gt_br_off = targets['bottomright_offset']
          gt_embedding = targets['corner_embedding']
  
          # Detection loss
          tl_det_loss = self.loss_heatmap(
              tl_hmp.sigmoid(),
              gt_tl_hmp,
              avg_factor=max(1,
                             gt_tl_hmp.eq(1).sum()))
          br_det_loss = self.loss_heatmap(
              br_hmp.sigmoid(),
              gt_br_hmp,
              avg_factor=max(1,
                             gt_br_hmp.eq(1).sum()))
          det_loss = (tl_det_loss + br_det_loss) / 2.0
  
          # AssociativeEmbedding loss
          if self.with_corner_emb and self.loss_embedding is not None:
              pull_loss, push_loss = self.loss_embedding(tl_emb, br_emb,
                                                         gt_embedding)
          else:
              pull_loss, push_loss = None, None
  
          # Offset loss
          # We only compute the offset loss at the real corner position.
          # The value of real corner would be 1 in heatmap ground truth.
          # The mask is computed in class agnostic mode and its shape is
          # batch * 1 * width * height.
          tl_off_mask = gt_tl_hmp.eq(1).sum(1).gt(0).unsqueeze(1).type_as(
              gt_tl_hmp)
          br_off_mask = gt_br_hmp.eq(1).sum(1).gt(0).unsqueeze(1).type_as(
              gt_br_hmp)
          tl_off_loss = self.loss_offset(
              tl_off,
              gt_tl_off,
              tl_off_mask,
              avg_factor=max(1, tl_off_mask.sum()))
          br_off_loss = self.loss_offset(
              br_off,
              gt_br_off,
              br_off_mask,
              avg_factor=max(1, br_off_mask.sum()))
  
          off_loss = (tl_off_loss + br_off_loss) / 2.0
  
          return det_loss, pull_loss, push_loss, off_loss
  
      def get_bboxes(self,
                     tl_heats,
                     br_heats,
                     tl_embs,
                     br_embs,
                     tl_offs,
                     br_offs,
                     img_metas,
                     rescale=False,
                     with_nms=True):
          """Transform network output for a batch into bbox predictions.
  
          Args:
              tl_heats (list[Tensor]): Top-left corner heatmaps for each level
                  with shape (N, num_classes, H, W).
              br_heats (list[Tensor]): Bottom-right corner heatmaps for each
                  level with shape (N, num_classes, H, W).
              tl_embs (list[Tensor]): Top-left corner embeddings for each level
                  with shape (N, corner_emb_channels, H, W).
              br_embs (list[Tensor]): Bottom-right corner embeddings for each
                  level with shape (N, corner_emb_channels, H, W).
              tl_offs (list[Tensor]): Top-left corner offsets for each level
                  with shape (N, corner_offset_channels, H, W).
              br_offs (list[Tensor]): Bottom-right corner offsets for each level
                  with shape (N, corner_offset_channels, H, W).
              img_metas (list[dict]): Meta information of each image, e.g.,
                  image size, scaling factor, etc.
              rescale (bool): If True, return boxes in original image space.
                  Default: False.
              with_nms (bool): If True, do nms before return boxes.
                  Default: True.
          """
          assert tl_heats[-1].shape[0] == br_heats[-1].shape[0] == len(img_metas)
          result_list = []
          for img_id in range(len(img_metas)):  # > #img
              result_list.append(
                  self._get_bboxes_single(
                      tl_heats[-1][img_id:img_id + 1, :],
                      br_heats[-1][img_id:img_id + 1, :],
                      tl_offs[-1][img_id:img_id + 1, :],
                      br_offs[-1][img_id:img_id + 1, :],
                      img_metas[img_id],
                      tl_emb=tl_embs[-1][img_id:img_id + 1, :],
                      br_emb=br_embs[-1][img_id:img_id + 1, :],
                      rescale=rescale,
                      with_nms=with_nms))
  
          return result_list
  
      def _get_bboxes_single(self,
                             tl_heat,
                             br_heat,
                             tl_off,
                             br_off,
                             img_meta,
                             tl_emb=None,
                             br_emb=None,
                             tl_centripetal_shift=None,
                             br_centripetal_shift=None,
                             rescale=False,
                             with_nms=True):
          """Transform outputs for a single batch item into bbox predictions.
  
          Args:
              tl_heat (Tensor): Top-left corner heatmap for current level with
                  shape (N, num_classes, H, W).
              br_heat (Tensor): Bottom-right corner heatmap for current level
                  with shape (N, num_classes, H, W).
              tl_off (Tensor): Top-left corner offset for current level with
                  shape (N, corner_offset_channels, H, W).
              br_off (Tensor): Bottom-right corner offset for current level with
                  shape (N, corner_offset_channels, H, W).
              img_meta (dict): Meta information of current image, e.g.,
                  image size, scaling factor, etc.
              tl_emb (Tensor): Top-left corner embedding for current level with
                  shape (N, corner_emb_channels, H, W).
              br_emb (Tensor): Bottom-right corner embedding for current level
                  with shape (N, corner_emb_channels, H, W).
              tl_centripetal_shift: Top-left corner's centripetal shift for
                  current level with shape (N, 2, H, W).
              br_centripetal_shift: Bottom-right corner's centripetal shift for
                  current level with shape (N, 2, H, W).
              rescale (bool): If True, return boxes in original image space.
                  Default: False.
              with_nms (bool): If True, do nms before return boxes.
                  Default: True.
          """
          if isinstance(img_meta, (list, tuple)):
              img_meta = img_meta[0]
  
          batch_bboxes, batch_scores, batch_clses = self.decode_heatmap(
              tl_heat=tl_heat.sigmoid(),
              br_heat=br_heat.sigmoid(),
              tl_off=tl_off,
              br_off=br_off,
              tl_emb=tl_emb,
              br_emb=br_emb,
              tl_centripetal_shift=tl_centripetal_shift,
              br_centripetal_shift=br_centripetal_shift,
              img_meta=img_meta,
              k=self.test_cfg.corner_topk,
              kernel=self.test_cfg.local_maximum_kernel,
              distance_threshold=self.test_cfg.distance_threshold)
  
          if rescale:
              batch_bboxes /= img_meta['scale_factor']
  
          bboxes = batch_bboxes.view([-1, 4])
          scores = batch_scores.view([-1, 1])
          clses = batch_clses.view([-1, 1])
  
          idx = scores.argsort(dim=0, descending=True)
          bboxes = bboxes[idx].view([-1, 4])
          scores = scores[idx].view(-1)
          clses = clses[idx].view(-1)
  
          detections = torch.cat([bboxes, scores.unsqueeze(-1)], -1)
          keepinds = (detections[:, -1] > -0.1)
          detections = detections[keepinds]
          labels = clses[keepinds]
  
          if with_nms:
              detections, labels = self._bboxes_nms(detections, labels,
                                                    self.test_cfg)
  
          return detections, labels
  
      def _bboxes_nms(self, bboxes, labels, cfg):
          out_bboxes, keep = batched_nms(bboxes[:, :4], bboxes[:, -1], labels,
                                         cfg.nms_cfg)
          out_labels = labels[keep]
  
          if len(out_bboxes) > 0:
              idx = torch.argsort(out_bboxes[:, -1], descending=True)
              idx = idx[:cfg.max_per_img]
              out_bboxes = out_bboxes[idx]
              out_labels = out_labels[idx]
  
          return out_bboxes, out_labels
  
      def decode_heatmap(self,
                         tl_heat,
                         br_heat,
                         tl_off,
                         br_off,
                         tl_emb=None,
                         br_emb=None,
                         tl_centripetal_shift=None,
                         br_centripetal_shift=None,
                         img_meta=None,
                         k=100,
                         kernel=3,
                         distance_threshold=0.5,
                         num_dets=1000):
          """Transform outputs for a single batch item into raw bbox predictions.
  
          Args:
              tl_heat (Tensor): Top-left corner heatmap for current level with
                  shape (N, num_classes, H, W).
              br_heat (Tensor): Bottom-right corner heatmap for current level
                  with shape (N, num_classes, H, W).
              tl_off (Tensor): Top-left corner offset for current level with
                  shape (N, corner_offset_channels, H, W).
              br_off (Tensor): Bottom-right corner offset for current level with
                  shape (N, corner_offset_channels, H, W).
              tl_emb (Tensor | None): Top-left corner embedding for current
                  level with shape (N, corner_emb_channels, H, W).
              br_emb (Tensor | None): Bottom-right corner embedding for current
                  level with shape (N, corner_emb_channels, H, W).
              tl_centripetal_shift (Tensor | None): Top-left centripetal shift
                  for current level with shape (N, 2, H, W).
              br_centripetal_shift (Tensor | None): Bottom-right centripetal
                  shift for current level with shape (N, 2, H, W).
              img_meta (dict): Meta information of current image, e.g.,
                  image size, scaling factor, etc.
              k (int): Get top k corner keypoints from heatmap.
              kernel (int): Max pooling kernel for extract local maximum pixels.
              distance_threshold (float): Distance threshold. Top-left and
                  bottom-right corner keypoints with feature distance less than
                  the threshold will be regarded as keypoints from same object.
              num_dets (int): Num of raw boxes before doing nms.
  
          Returns:
              tuple[torch.Tensor]: Decoded output of CornerHead, containing the
              following Tensors:
  
              - bboxes (Tensor): Coords of each box.
              - scores (Tensor): Scores of each box.
              - clses (Tensor): Categories of each box.
          """
          with_embedding = tl_emb is not None and br_emb is not None
          with_centripetal_shift = (
              tl_centripetal_shift is not None
              and br_centripetal_shift is not None)
          assert with_embedding + with_centripetal_shift == 1
          batch, _, height, width = tl_heat.size()
          inp_h, inp_w, _ = img_meta['pad_shape']
  
          # perform nms on heatmaps
          tl_heat = self._local_maximum(tl_heat, kernel=kernel)
          br_heat = self._local_maximum(br_heat, kernel=kernel)
  
          tl_scores, tl_inds, tl_clses, tl_ys, tl_xs = self._topk(tl_heat, k=k)
          br_scores, br_inds, br_clses, br_ys, br_xs = self._topk(br_heat, k=k)
  
          # We use repeat instead of expand here because expand is a
          # shallow-copy function. Thus it could cause unexpected testing result
          # sometimes. Using expand will decrease about 10% mAP during testing
          # compared to repeat.
          tl_ys = tl_ys.view(batch, k, 1).repeat(1, 1, k)
          tl_xs = tl_xs.view(batch, k, 1).repeat(1, 1, k)
          br_ys = br_ys.view(batch, 1, k).repeat(1, k, 1)
          br_xs = br_xs.view(batch, 1, k).repeat(1, k, 1)
  
          tl_off = self._transpose_and_gather_feat(tl_off, tl_inds)
          tl_off = tl_off.view(batch, k, 1, 2)
          br_off = self._transpose_and_gather_feat(br_off, br_inds)
          br_off = br_off.view(batch, 1, k, 2)
  
          tl_xs = tl_xs + tl_off[..., 0]
          tl_ys = tl_ys + tl_off[..., 1]
          br_xs = br_xs + br_off[..., 0]
          br_ys = br_ys + br_off[..., 1]
  
          if with_centripetal_shift:
              tl_centripetal_shift = self._transpose_and_gather_feat(
                  tl_centripetal_shift, tl_inds).view(batch, k, 1, 2).exp()
              br_centripetal_shift = self._transpose_and_gather_feat(
                  br_centripetal_shift, br_inds).view(batch, 1, k, 2).exp()
  
              tl_ctxs = tl_xs + tl_centripetal_shift[..., 0]
              tl_ctys = tl_ys + tl_centripetal_shift[..., 1]
              br_ctxs = br_xs - br_centripetal_shift[..., 0]
              br_ctys = br_ys - br_centripetal_shift[..., 1]
  
          # all possible boxes based on top k corners (ignoring class)
          tl_xs *= (inp_w / width)
          tl_ys *= (inp_h / height)
          br_xs *= (inp_w / width)
          br_ys *= (inp_h / height)
  
          if with_centripetal_shift:
              tl_ctxs *= (inp_w / width)
              tl_ctys *= (inp_h / height)
              br_ctxs *= (inp_w / width)
              br_ctys *= (inp_h / height)
  
          x_off = img_meta['border'][2]
          y_off = img_meta['border'][0]
  
          tl_xs -= x_off
          tl_ys -= y_off
          br_xs -= x_off
          br_ys -= y_off
  
          tl_xs *= tl_xs.gt(0.0).type_as(tl_xs)
          tl_ys *= tl_ys.gt(0.0).type_as(tl_ys)
          br_xs *= br_xs.gt(0.0).type_as(br_xs)
          br_ys *= br_ys.gt(0.0).type_as(br_ys)
  
          bboxes = torch.stack((tl_xs, tl_ys, br_xs, br_ys), dim=3)
          area_bboxes = ((br_xs - tl_xs) * (br_ys - tl_ys)).abs()
  
          if with_centripetal_shift:
              tl_ctxs -= x_off
              tl_ctys -= y_off
              br_ctxs -= x_off
              br_ctys -= y_off
  
              tl_ctxs *= tl_ctxs.gt(0.0).type_as(tl_ctxs)
              tl_ctys *= tl_ctys.gt(0.0).type_as(tl_ctys)
              br_ctxs *= br_ctxs.gt(0.0).type_as(br_ctxs)
              br_ctys *= br_ctys.gt(0.0).type_as(br_ctys)
  
              ct_bboxes = torch.stack((tl_ctxs, tl_ctys, br_ctxs, br_ctys),
                                      dim=3)
              area_ct_bboxes = ((br_ctxs - tl_ctxs) * (br_ctys - tl_ctys)).abs()
  
              rcentral = torch.zeros_like(ct_bboxes)
              # magic nums from paper section 4.1
              mu = torch.ones_like(area_bboxes) / 2.4
              mu[area_bboxes > 3500] = 1 / 2.1  # large bbox have smaller mu
  
              bboxes_center_x = (bboxes[..., 0] + bboxes[..., 2]) / 2
              bboxes_center_y = (bboxes[..., 1] + bboxes[..., 3]) / 2
              rcentral[..., 0] = bboxes_center_x - mu * (bboxes[..., 2] -
                                                         bboxes[..., 0]) / 2
              rcentral[..., 1] = bboxes_center_y - mu * (bboxes[..., 3] -
                                                         bboxes[..., 1]) / 2
              rcentral[..., 2] = bboxes_center_x + mu * (bboxes[..., 2] -
                                                         bboxes[..., 0]) / 2
              rcentral[..., 3] = bboxes_center_y + mu * (bboxes[..., 3] -
                                                         bboxes[..., 1]) / 2
              area_rcentral = ((rcentral[..., 2] - rcentral[..., 0]) *
                               (rcentral[..., 3] - rcentral[..., 1])).abs()
              dists = area_ct_bboxes / area_rcentral
  
              tl_ctx_inds = (ct_bboxes[..., 0] <= rcentral[..., 0]) | (
                  ct_bboxes[..., 0] >= rcentral[..., 2])
              tl_cty_inds = (ct_bboxes[..., 1] <= rcentral[..., 1]) | (
                  ct_bboxes[..., 1] >= rcentral[..., 3])
              br_ctx_inds = (ct_bboxes[..., 2] <= rcentral[..., 0]) | (
                  ct_bboxes[..., 2] >= rcentral[..., 2])
              br_cty_inds = (ct_bboxes[..., 3] <= rcentral[..., 1]) | (
                  ct_bboxes[..., 3] >= rcentral[..., 3])
  
          if with_embedding:
              tl_emb = self._transpose_and_gather_feat(tl_emb, tl_inds)
              tl_emb = tl_emb.view(batch, k, 1)
              br_emb = self._transpose_and_gather_feat(br_emb, br_inds)
              br_emb = br_emb.view(batch, 1, k)
              dists = torch.abs(tl_emb - br_emb)
  
          tl_scores = tl_scores.view(batch, k, 1).repeat(1, 1, k)
          br_scores = br_scores.view(batch, 1, k).repeat(1, k, 1)
  
          scores = (tl_scores + br_scores) / 2  # scores for all possible boxes
  
          # tl and br should have same class
          tl_clses = tl_clses.view(batch, k, 1).repeat(1, 1, k)
          br_clses = br_clses.view(batch, 1, k).repeat(1, k, 1)
          cls_inds = (tl_clses != br_clses)
  
          # reject boxes based on distances
          dist_inds = dists > distance_threshold
  
          # reject boxes based on widths and heights
          width_inds = (br_xs <= tl_xs)
          height_inds = (br_ys <= tl_ys)
  
          scores[cls_inds] = -1
          scores[width_inds] = -1
          scores[height_inds] = -1
          scores[dist_inds] = -1
          if with_centripetal_shift:
              scores[tl_ctx_inds] = -1
              scores[tl_cty_inds] = -1
              scores[br_ctx_inds] = -1
              scores[br_cty_inds] = -1
  
          scores = scores.view(batch, -1)
          scores, inds = torch.topk(scores, num_dets)
          scores = scores.unsqueeze(2)
  
          bboxes = bboxes.view(batch, -1, 4)
          bboxes = self._gather_feat(bboxes, inds)
  
          clses = tl_clses.contiguous().view(batch, -1, 1)
          clses = self._gather_feat(clses, inds).float()
  
          return bboxes, scores, clses
apis: torch.ones_like torch.stack torch.nn.functional.max_pool2d torch.argsort torch.zeros_like torch.topk torch.nn.Conv2d torch.nn.ModuleList torch.nn.Sequential torch.nn.Identity torch.abs torch.nn.ReLU