import torch
import torch.nn as nn
import torch.nn.functional as F
from mmcv.cnn import Scale
from mmcv.runner import force_fp32
from mmdet.core import distance2bbox, multi_apply, multiclass_nms, reduce_mean
from ..builder import HEADS, build_loss
from .anchor_free_head import AnchorFreeHead
INF = 1e8
[docs]@HEADS.register_module()
class FCOSHead(AnchorFreeHead):
"""Anchor-free head used in `FCOS <https://arxiv.org/abs/1904.01355>`_.
The FCOS head does not use anchor boxes. Instead bounding boxes are
predicted at each pixel and a centerness measure is used to suppress
low-quality predictions.
Here norm_on_bbox, centerness_on_reg, dcn_on_last_conv are training
tricks used in official repo, which will bring remarkable mAP gains
of up to 4.9. Please see https://github.com/tianzhi0549/FCOS for
more detail.
Args:
num_classes (int): Number of categories excluding the background
category.
in_channels (int): Number of channels in the input feature map.
strides (list[int] | list[tuple[int, int]]): Strides of points
in multiple feature levels. Default: (4, 8, 16, 32, 64).
regress_ranges (tuple[tuple[int, int]]): Regress range of multiple
level points.
center_sampling (bool): If true, use center sampling. Default: False.
center_sample_radius (float): Radius of center sampling. Default: 1.5.
norm_on_bbox (bool): If true, normalize the regression targets
with FPN strides. Default: False.
centerness_on_reg (bool): If true, position centerness on the
regress branch. Please refer to https://github.com/tianzhi0549/FCOS/issues/89#issuecomment-516877042.
Default: False.
conv_bias (bool | str): If specified as `auto`, it will be decided by the
norm_cfg. Bias of conv will be set as True if `norm_cfg` is None, otherwise
False. Default: "auto".
loss_cls (dict): Config of classification loss.
loss_bbox (dict): Config of localization loss.
loss_centerness (dict): Config of centerness loss.
norm_cfg (dict): dictionary to construct and config norm layer.
Default: norm_cfg=dict(type='GN', num_groups=32, requires_grad=True).
init_cfg (dict or list[dict], optional): Initialization config dict.
Example:
>>> self = FCOSHead(11, 7)
>>> feats = [torch.rand(1, 7, s, s) for s in [4, 8, 16, 32, 64]]
>>> cls_score, bbox_pred, centerness = self.forward(feats)
>>> assert len(cls_score) == len(self.scales)
""" # noqa: E501
def __init__(self,
num_classes,
in_channels,
regress_ranges=((-1, 64), (64, 128), (128, 256), (256, 512),
(512, INF)),
center_sampling=False,
center_sample_radius=1.5,
norm_on_bbox=False,
centerness_on_reg=False,
loss_cls=dict(
type='FocalLoss',
use_sigmoid=True,
gamma=2.0,
alpha=0.25,
loss_weight=1.0),
loss_bbox=dict(type='IoULoss', loss_weight=1.0),
loss_centerness=dict(
type='CrossEntropyLoss',
use_sigmoid=True,
loss_weight=1.0),
norm_cfg=dict(type='GN', num_groups=32, requires_grad=True),
init_cfg=dict(
type='Normal',
layer='Conv2d',
std=0.01,
override=dict(
type='Normal',
name='conv_cls',
std=0.01,
bias_prob=0.01)),
**kwargs):
self.regress_ranges = regress_ranges
self.center_sampling = center_sampling
self.center_sample_radius = center_sample_radius
self.norm_on_bbox = norm_on_bbox
self.centerness_on_reg = centerness_on_reg
super().__init__(
num_classes,
in_channels,
loss_cls=loss_cls,
loss_bbox=loss_bbox,
norm_cfg=norm_cfg,
init_cfg=init_cfg,
**kwargs)
self.loss_centerness = build_loss(loss_centerness)
def _init_layers(self):
"""Initialize layers of the head."""
super()._init_layers()
self.conv_centerness = nn.Conv2d(self.feat_channels, 1, 3, padding=1)
self.scales = nn.ModuleList([Scale(1.0) for _ in self.strides])
[docs] 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:
cls_scores (list[Tensor]): Box scores for each scale level, \
each is a 4D-tensor, the channel number is \
num_points * num_classes.
bbox_preds (list[Tensor]): Box energies / deltas for each \
scale level, each is a 4D-tensor, the channel number is \
num_points * 4.
centernesses (list[Tensor]): centerness for each scale level, \
each is a 4D-tensor, the channel number is num_points * 1.
"""
return multi_apply(self.forward_single, feats, self.scales,
self.strides)
[docs] def forward_single(self, x, scale, stride):
"""Forward features of a single scale level.
Args:
x (Tensor): FPN feature maps of the specified stride.
scale (:obj: `mmcv.cnn.Scale`): Learnable scale module to resize
the bbox prediction.
stride (int): The corresponding stride for feature maps, only
used to normalize the bbox prediction when self.norm_on_bbox
is True.
Returns:
tuple: scores for each class, bbox predictions and centerness \
predictions of input feature maps.
"""
cls_score, bbox_pred, cls_feat, reg_feat = super().forward_single(x)
if self.centerness_on_reg:
centerness = self.conv_centerness(reg_feat)
else:
centerness = self.conv_centerness(cls_feat)
# scale the bbox_pred of different level
# float to avoid overflow when enabling FP16
bbox_pred = scale(bbox_pred).float()
if self.norm_on_bbox:
bbox_pred = F.relu(bbox_pred)
if not self.training:
bbox_pred *= stride
else:
bbox_pred = bbox_pred.exp()
return cls_score, bbox_pred, centerness
[docs] @force_fp32(apply_to=('cls_scores', 'bbox_preds', 'centernesses'))
def loss(self,
cls_scores,
bbox_preds,
centernesses,
gt_bboxes,
gt_labels,
img_metas,
gt_bboxes_ignore=None):
"""Compute loss of the head.
Args:
cls_scores (list[Tensor]): Box scores for each scale level,
each is a 4D-tensor, the channel number is
num_points * num_classes.
bbox_preds (list[Tensor]): Box energies / deltas for each scale
level, each is a 4D-tensor, the channel number is
num_points * 4.
centernesses (list[Tensor]): centerness for each scale level, each
is a 4D-tensor, the channel number is num_points * 1.
gt_bboxes (list[Tensor]): Ground truth bboxes for each image with
shape (num_gts, 4) in [tl_x, tl_y, br_x, br_y] 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 (None | list[Tensor]): specify which bounding
boxes can be ignored when computing the loss.
Returns:
dict[str, Tensor]: A dictionary of loss components.
"""
assert len(cls_scores) == len(bbox_preds) == len(centernesses)
featmap_sizes = [featmap.size()[-2:] for featmap in cls_scores]
all_level_points = self.get_points(featmap_sizes, bbox_preds[0].dtype,
bbox_preds[0].device)
labels, bbox_targets = self.get_targets(all_level_points, gt_bboxes,
gt_labels)
num_imgs = cls_scores[0].size(0)
# flatten cls_scores, bbox_preds and centerness
flatten_cls_scores = [
cls_score.permute(0, 2, 3, 1).reshape(-1, self.cls_out_channels)
for cls_score in cls_scores
]
flatten_bbox_preds = [
bbox_pred.permute(0, 2, 3, 1).reshape(-1, 4)
for bbox_pred in bbox_preds
]
flatten_centerness = [
centerness.permute(0, 2, 3, 1).reshape(-1)
for centerness in centernesses
]
flatten_cls_scores = torch.cat(flatten_cls_scores)
flatten_bbox_preds = torch.cat(flatten_bbox_preds)
flatten_centerness = torch.cat(flatten_centerness)
flatten_labels = torch.cat(labels)
flatten_bbox_targets = torch.cat(bbox_targets)
# repeat points to align with bbox_preds
flatten_points = torch.cat(
[points.repeat(num_imgs, 1) for points in all_level_points])
# FG cat_id: [0, num_classes -1], BG cat_id: num_classes
bg_class_ind = self.num_classes
pos_inds = ((flatten_labels >= 0)
& (flatten_labels < bg_class_ind)).nonzero().reshape(-1)
num_pos = torch.tensor(
len(pos_inds), dtype=torch.float, device=bbox_preds[0].device)
num_pos = max(reduce_mean(num_pos), 1.0)
loss_cls = self.loss_cls(
flatten_cls_scores, flatten_labels, avg_factor=num_pos)
pos_bbox_preds = flatten_bbox_preds[pos_inds]
pos_centerness = flatten_centerness[pos_inds]
pos_bbox_targets = flatten_bbox_targets[pos_inds]
pos_centerness_targets = self.centerness_target(pos_bbox_targets)
# centerness weighted iou loss
centerness_denorm = max(
reduce_mean(pos_centerness_targets.sum().detach()), 1e-6)
if len(pos_inds) > 0:
pos_points = flatten_points[pos_inds]
pos_decoded_bbox_preds = distance2bbox(pos_points, pos_bbox_preds)
pos_decoded_target_preds = distance2bbox(pos_points,
pos_bbox_targets)
loss_bbox = self.loss_bbox(
pos_decoded_bbox_preds,
pos_decoded_target_preds,
weight=pos_centerness_targets,
avg_factor=centerness_denorm)
loss_centerness = self.loss_centerness(
pos_centerness, pos_centerness_targets, avg_factor=num_pos)
else:
loss_bbox = pos_bbox_preds.sum()
loss_centerness = pos_centerness.sum()
return dict(
loss_cls=loss_cls,
loss_bbox=loss_bbox,
loss_centerness=loss_centerness)
[docs] @force_fp32(apply_to=('cls_scores', 'bbox_preds', 'centernesses'))
def get_bboxes(self,
cls_scores,
bbox_preds,
centernesses,
img_metas,
cfg=None,
rescale=False,
with_nms=True):
"""Transform network output for a batch into bbox predictions.
Args:
cls_scores (list[Tensor]): Box scores for each scale level
with shape (N, num_points * num_classes, H, W).
bbox_preds (list[Tensor]): Box energies / deltas for each scale
level with shape (N, num_points * 4, H, W).
centernesses (list[Tensor]): Centerness for each scale level with
shape (N, num_points * 1, H, W).
img_metas (list[dict]): Meta information of each image, e.g.,
image size, scaling factor, etc.
cfg (mmcv.Config | None): Test / postprocessing configuration,
if None, test_cfg would be used. Default: None.
rescale (bool): If True, return boxes in original image space.
Default: False.
with_nms (bool): If True, do nms before return boxes.
Default: True.
Returns:
list[tuple[Tensor, Tensor]]: Each item in result_list is 2-tuple.
The first item is an (n, 5) tensor, where 5 represent
(tl_x, tl_y, br_x, br_y, score) and the score between 0 and 1.
The shape of the second tensor in the tuple is (n,), and
each element represents the class label of the corresponding
box.
"""
assert len(cls_scores) == len(bbox_preds)
num_levels = len(cls_scores)
featmap_sizes = [featmap.size()[-2:] for featmap in cls_scores]
mlvl_points = self.get_points(featmap_sizes, bbox_preds[0].dtype,
bbox_preds[0].device)
cls_score_list = [cls_scores[i].detach() for i in range(num_levels)]
bbox_pred_list = [bbox_preds[i].detach() for i in range(num_levels)]
centerness_pred_list = [
centernesses[i].detach() for i in range(num_levels)
]
if torch.onnx.is_in_onnx_export():
assert len(
img_metas
) == 1, 'Only support one input image while in exporting to ONNX'
img_shapes = img_metas[0]['img_shape_for_onnx']
else:
img_shapes = [
img_metas[i]['img_shape']
for i in range(cls_scores[0].shape[0])
]
scale_factors = [
img_metas[i]['scale_factor'] for i in range(cls_scores[0].shape[0])
]
result_list = self._get_bboxes(cls_score_list, bbox_pred_list,
centerness_pred_list, mlvl_points,
img_shapes, scale_factors, cfg, rescale,
with_nms)
return result_list
def _get_bboxes(self,
cls_scores,
bbox_preds,
centernesses,
mlvl_points,
img_shapes,
scale_factors,
cfg,
rescale=False,
with_nms=True):
"""Transform outputs for a single batch item into bbox predictions.
Args:
cls_scores (list[Tensor]): Box scores for a single scale level
with shape (N, num_points * num_classes, H, W).
bbox_preds (list[Tensor]): Box energies / deltas for a single scale
level with shape (N, num_points * 4, H, W).
centernesses (list[Tensor]): Centerness for a single scale level
with shape (N, num_points, H, W).
mlvl_points (list[Tensor]): Box reference for a single scale level
with shape (num_total_points, 4).
img_shapes (list[tuple[int]]): Shape of the input image,
list[(height, width, 3)].
scale_factors (list[ndarray]): Scale factor of the image arrange as
(w_scale, h_scale, w_scale, h_scale).
cfg (mmcv.Config | None): Test / postprocessing configuration,
if None, test_cfg would be used.
rescale (bool): If True, return boxes in original image space.
Default: False.
with_nms (bool): If True, do nms before return boxes.
Default: True.
Returns:
tuple(Tensor):
det_bboxes (Tensor): BBox predictions in shape (n, 5), where
the first 4 columns are bounding box positions
(tl_x, tl_y, br_x, br_y) and the 5-th column is a score
between 0 and 1.
det_labels (Tensor): A (n,) tensor where each item is the
predicted class label of the corresponding box.
"""
cfg = self.test_cfg if cfg is None else cfg
assert len(cls_scores) == len(bbox_preds) == len(mlvl_points)
device = cls_scores[0].device
batch_size = cls_scores[0].shape[0]
# convert to tensor to keep tracing
nms_pre_tensor = torch.tensor(
cfg.get('nms_pre', -1), device=device, dtype=torch.long)
mlvl_bboxes = []
mlvl_scores = []
mlvl_centerness = []
for cls_score, bbox_pred, centerness, points in zip(
cls_scores, bbox_preds, centernesses, mlvl_points):
assert cls_score.size()[-2:] == bbox_pred.size()[-2:]
scores = cls_score.permute(0, 2, 3, 1).reshape(
batch_size, -1, self.cls_out_channels).sigmoid()
centerness = centerness.permute(0, 2, 3,
1).reshape(batch_size,
-1).sigmoid()
bbox_pred = bbox_pred.permute(0, 2, 3,
1).reshape(batch_size, -1, 4)
points = points.expand(batch_size, -1, 2)
# Get top-k prediction
from mmdet.core.export import get_k_for_topk
nms_pre = get_k_for_topk(nms_pre_tensor, bbox_pred.shape[1])
if nms_pre > 0:
max_scores, _ = (scores * centerness[..., None]).max(-1)
_, topk_inds = max_scores.topk(nms_pre)
batch_inds = torch.arange(batch_size).view(
-1, 1).expand_as(topk_inds).long()
# Avoid onnx2tensorrt issue in https://github.com/NVIDIA/TensorRT/issues/1134 # noqa: E501
if torch.onnx.is_in_onnx_export():
transformed_inds = bbox_pred.shape[
1] * batch_inds + topk_inds
points = points.reshape(-1,
2)[transformed_inds, :].reshape(
batch_size, -1, 2)
bbox_pred = bbox_pred.reshape(
-1, 4)[transformed_inds, :].reshape(batch_size, -1, 4)
scores = scores.reshape(
-1, self.num_classes)[transformed_inds, :].reshape(
batch_size, -1, self.num_classes)
centerness = centerness.reshape(
-1, 1)[transformed_inds].reshape(batch_size, -1)
else:
points = points[batch_inds, topk_inds, :]
bbox_pred = bbox_pred[batch_inds, topk_inds, :]
scores = scores[batch_inds, topk_inds, :]
centerness = centerness[batch_inds, topk_inds]
bboxes = distance2bbox(points, bbox_pred, max_shape=img_shapes)
mlvl_bboxes.append(bboxes)
mlvl_scores.append(scores)
mlvl_centerness.append(centerness)
batch_mlvl_bboxes = torch.cat(mlvl_bboxes, dim=1)
if rescale:
batch_mlvl_bboxes /= batch_mlvl_bboxes.new_tensor(
scale_factors).unsqueeze(1)
batch_mlvl_scores = torch.cat(mlvl_scores, dim=1)
batch_mlvl_centerness = torch.cat(mlvl_centerness, dim=1)
# Replace multiclass_nms with ONNX::NonMaxSuppression in deployment
if torch.onnx.is_in_onnx_export() and with_nms:
from mmdet.core.export import add_dummy_nms_for_onnx
batch_mlvl_scores = batch_mlvl_scores * (
batch_mlvl_centerness.unsqueeze(2))
max_output_boxes_per_class = cfg.nms.get(
'max_output_boxes_per_class', 200)
iou_threshold = cfg.nms.get('iou_threshold', 0.5)
score_threshold = cfg.score_thr
nms_pre = cfg.get('deploy_nms_pre', -1)
return add_dummy_nms_for_onnx(batch_mlvl_bboxes, batch_mlvl_scores,
max_output_boxes_per_class,
iou_threshold, score_threshold,
nms_pre, cfg.max_per_img)
# remind that we set FG labels to [0, num_class-1] since mmdet v2.0
# BG cat_id: num_class
padding = batch_mlvl_scores.new_zeros(batch_size,
batch_mlvl_scores.shape[1], 1)
batch_mlvl_scores = torch.cat([batch_mlvl_scores, padding], dim=-1)
if with_nms:
det_results = []
for (mlvl_bboxes, mlvl_scores,
mlvl_centerness) in zip(batch_mlvl_bboxes, batch_mlvl_scores,
batch_mlvl_centerness):
det_bbox, det_label = multiclass_nms(
mlvl_bboxes,
mlvl_scores,
cfg.score_thr,
cfg.nms,
cfg.max_per_img,
score_factors=mlvl_centerness)
det_results.append(tuple([det_bbox, det_label]))
else:
det_results = [
tuple(mlvl_bs)
for mlvl_bs in zip(batch_mlvl_bboxes, batch_mlvl_scores,
batch_mlvl_centerness)
]
return det_results
def _get_points_single(self,
featmap_size,
stride,
dtype,
device,
flatten=False):
"""Get points according to feature map sizes."""
y, x = super()._get_points_single(featmap_size, stride, dtype, device)
points = torch.stack((x.reshape(-1) * stride, y.reshape(-1) * stride),
dim=-1) + stride // 2
return points
[docs] def get_targets(self, points, gt_bboxes_list, gt_labels_list):
"""Compute regression, classification and centerness targets for points
in multiple images.
Args:
points (list[Tensor]): Points of each fpn level, each has shape
(num_points, 2).
gt_bboxes_list (list[Tensor]): Ground truth bboxes of each image,
each has shape (num_gt, 4).
gt_labels_list (list[Tensor]): Ground truth labels of each box,
each has shape (num_gt,).
Returns:
tuple:
concat_lvl_labels (list[Tensor]): Labels of each level. \
concat_lvl_bbox_targets (list[Tensor]): BBox targets of each \
level.
"""
assert len(points) == len(self.regress_ranges)
num_levels = len(points)
# expand regress ranges to align with points
expanded_regress_ranges = [
points[i].new_tensor(self.regress_ranges[i])[None].expand_as(
points[i]) for i in range(num_levels)
]
# concat all levels points and regress ranges
concat_regress_ranges = torch.cat(expanded_regress_ranges, dim=0)
concat_points = torch.cat(points, dim=0)
# the number of points per img, per lvl
num_points = [center.size(0) for center in points]
# get labels and bbox_targets of each image
labels_list, bbox_targets_list = multi_apply(
self._get_target_single,
gt_bboxes_list,
gt_labels_list,
points=concat_points,
regress_ranges=concat_regress_ranges,
num_points_per_lvl=num_points)
# split to per img, per level
labels_list = [labels.split(num_points, 0) for labels in labels_list]
bbox_targets_list = [
bbox_targets.split(num_points, 0)
for bbox_targets in bbox_targets_list
]
# concat per level image
concat_lvl_labels = []
concat_lvl_bbox_targets = []
for i in range(num_levels):
concat_lvl_labels.append(
torch.cat([labels[i] for labels in labels_list]))
bbox_targets = torch.cat(
[bbox_targets[i] for bbox_targets in bbox_targets_list])
if self.norm_on_bbox:
bbox_targets = bbox_targets / self.strides[i]
concat_lvl_bbox_targets.append(bbox_targets)
return concat_lvl_labels, concat_lvl_bbox_targets
def _get_target_single(self, gt_bboxes, gt_labels, points, regress_ranges,
num_points_per_lvl):
"""Compute regression and classification targets for a single image."""
num_points = points.size(0)
num_gts = gt_labels.size(0)
if num_gts == 0:
return gt_labels.new_full((num_points,), self.num_classes), \
gt_bboxes.new_zeros((num_points, 4))
areas = (gt_bboxes[:, 2] - gt_bboxes[:, 0]) * (
gt_bboxes[:, 3] - gt_bboxes[:, 1])
# TODO: figure out why these two are different
# areas = areas[None].expand(num_points, num_gts)
areas = areas[None].repeat(num_points, 1)
regress_ranges = regress_ranges[:, None, :].expand(
num_points, num_gts, 2)
gt_bboxes = gt_bboxes[None].expand(num_points, num_gts, 4)
xs, ys = points[:, 0], points[:, 1]
xs = xs[:, None].expand(num_points, num_gts)
ys = ys[:, None].expand(num_points, num_gts)
left = xs - gt_bboxes[..., 0]
right = gt_bboxes[..., 2] - xs
top = ys - gt_bboxes[..., 1]
bottom = gt_bboxes[..., 3] - ys
bbox_targets = torch.stack((left, top, right, bottom), -1)
if self.center_sampling:
# condition1: inside a `center bbox`
radius = self.center_sample_radius
center_xs = (gt_bboxes[..., 0] + gt_bboxes[..., 2]) / 2
center_ys = (gt_bboxes[..., 1] + gt_bboxes[..., 3]) / 2
center_gts = torch.zeros_like(gt_bboxes)
stride = center_xs.new_zeros(center_xs.shape)
# project the points on current lvl back to the `original` sizes
lvl_begin = 0
for lvl_idx, num_points_lvl in enumerate(num_points_per_lvl):
lvl_end = lvl_begin + num_points_lvl
stride[lvl_begin:lvl_end] = self.strides[lvl_idx] * radius
lvl_begin = lvl_end
x_mins = center_xs - stride
y_mins = center_ys - stride
x_maxs = center_xs + stride
y_maxs = center_ys + stride
center_gts[..., 0] = torch.where(x_mins > gt_bboxes[..., 0],
x_mins, gt_bboxes[..., 0])
center_gts[..., 1] = torch.where(y_mins > gt_bboxes[..., 1],
y_mins, gt_bboxes[..., 1])
center_gts[..., 2] = torch.where(x_maxs > gt_bboxes[..., 2],
gt_bboxes[..., 2], x_maxs)
center_gts[..., 3] = torch.where(y_maxs > gt_bboxes[..., 3],
gt_bboxes[..., 3], y_maxs)
cb_dist_left = xs - center_gts[..., 0]
cb_dist_right = center_gts[..., 2] - xs
cb_dist_top = ys - center_gts[..., 1]
cb_dist_bottom = center_gts[..., 3] - ys
center_bbox = torch.stack(
(cb_dist_left, cb_dist_top, cb_dist_right, cb_dist_bottom), -1)
inside_gt_bbox_mask = center_bbox.min(-1)[0] > 0
else:
# condition1: inside a gt bbox
inside_gt_bbox_mask = bbox_targets.min(-1)[0] > 0
# condition2: limit the regression range for each location
max_regress_distance = bbox_targets.max(-1)[0]
inside_regress_range = (
(max_regress_distance >= regress_ranges[..., 0])
& (max_regress_distance <= regress_ranges[..., 1]))
# if there are still more than one objects for a location,
# we choose the one with minimal area
areas[inside_gt_bbox_mask == 0] = INF
areas[inside_regress_range == 0] = INF
min_area, min_area_inds = areas.min(dim=1)
labels = gt_labels[min_area_inds]
labels[min_area == INF] = self.num_classes # set as BG
bbox_targets = bbox_targets[range(num_points), min_area_inds]
return labels, bbox_targets
[docs] def centerness_target(self, pos_bbox_targets):
"""Compute centerness targets.
Args:
pos_bbox_targets (Tensor): BBox targets of positive bboxes in shape
(num_pos, 4)
Returns:
Tensor: Centerness target.
"""
# only calculate pos centerness targets, otherwise there may be nan
left_right = pos_bbox_targets[:, [0, 2]]
top_bottom = pos_bbox_targets[:, [1, 3]]
if len(left_right) == 0:
centerness_targets = left_right[..., 0]
else:
centerness_targets = (
left_right.min(dim=-1)[0] / left_right.max(dim=-1)[0]) * (
top_bottom.min(dim=-1)[0] / top_bottom.max(dim=-1)[0])
return torch.sqrt(centerness_targets)