FreeAnchor
作者：互联网
论文 FreeAnchor: Learning to Match Anchors for Visual Object Detection
官方代码 https://github.com/zhangxiaosong18/FreeAnchor
作者指出IoU-based label assignment对于acentric, slinder, crowded objects，其正负样本的分配可能效果不好。比如以下图的月亮为例，其中绿框是gt box，红框是anchor，在基于IoU的规则下可能将该anchor分配给该gt作为正样本，但从图中可以看到anchor box中只包含了月亮的一小部分，大部分都是黑色背景。这显然是不合理的。
因此作者提出了一种learning-to-match的方法，即在训练过程中让模型自己去学习挑选合适的anchor作为正负样本，抛弃基于IoU的这种hand-crafted方法。这种方法从三个方面来优化目标检测模型的学习过程。
-
高召回率
对于每个gt，保证至少有一个anchor去匹配该gt，即至少有一个anchor作为正样本，其proposal负责预测该gt。 -
高精度
对于定位差的anchor，模型要将其分类为背景。 -
兼容NMS
即分类优先，分类score越高，其定位也应该越准。否则定位很好但分类score低的结果就被去除了。
为了同时满足这三个方面，作者将object-anchor matching设计成极大似然估计问题，在训练过程中使用模型的预测结果去寻找合适的anchor，反过来再推断模型的参数。
对于一张输入图片\(I\)，gt annotations定义为\(B\)，其中一个gt box \(b_{i}\in B\)由类别标签\(b_{i}^{cls}\)和位置标签\(b_{i}^{loc}\)组成。在前向传播过程中，每个anchor \(a_{j}\in A\)在sigmoid函数后得到一个类别预测结果\(a_{j}^{cls}\in \mathbb{R}^{k}\)，\(k\)是类别个数，在边框回归后得到一个位置的预测结果\(a_{j}^{loc}=\left \{ x,y,w,h \right \}\)。
训练过程中，基于IoU的分配规则会生成一个矩阵\(C_{ij}\in \left \{ 0,1 \right \}\)来定义gt \(b_{i}\)是否与anchor \(a_{j}\)匹配，当\(b_{i}\)和\(a_{j}\)的IoU大于设定阈值时，\(b_{i}\)和\(a_{j}\)匹配且\(C_{ij}=1\)，否则\(C_{ij}=0\)。当一个anchor和多个gt的IoU都大于设定阈值时，取IoU最大的gt与该anchor匹配，即要保证每个anchor至多和一个gt匹配，即 \(\sum_{i}C_{ij}\in \left \{ 0,1 \right \},\forall a_{j}\in A\)。
定义\(A_{+}\subseteq A\)为\(\left \{ a_{j}|\sum _{i}C_{ij}=1 \right \}\)，\(A_{-}\subseteq A\)为\(\left \{ a_{j}|\sum _{i}C_{ij}=0 \right \}\)，目标检测模型的Loss通常定义成如下形式
其中\(\theta\)是待学习的模型参数，\(L_{ij}^{cls}(\theta )=BCE(a_{j}^{cls},b_{i}^{cls},\theta)\)，\(L_{ij}^{loc}(\theta )=SmoothL1(a_{j}^{loc},b_{i}^{loc},\theta)\)，\(L_{j}^{bg}(\theta )=BCE(a_{j}^{cls},\vec{0},\theta)\)，\(\beta\)是正则化因子，\(bg\)指背景。
将上式Loss转换成似然概率，如下
其中\(P_{ij}^{cls}(\theta)\)和\(P_{j}^{bg}(\theta)\)表示分类置信度，\(P_{ij}^{loc}(\theta)\)代表定位置信度。减小(1)式中的loss等价于增大(2)式中的似然概率。
注意，式(2)中第一项本应如\(\prod _{a_{j}\in A_{+}}(e^{-\sum _{b_{i}\in B}C_{ij}L_{ij}^{cls}(\theta)}))\)所示，因为\(\sum_{b_{i}\in B}C_{ij}\)在\(j\)确定的情况下，只有一项等于1，其它都为0，因此可以将其移到\(e\)前面。
式(2)从MLE的角度同时考虑到了分类和定位的优化，但忽视了如何学习匹配矩阵\(C_{ij}\)。
Detection Customized Likelihood
因此作者提出了针对检测的似然概率Detection Customized Likelihood。首先，对于每个目标\(b_{i}\)，挑选\(n\)个IoU最大的anchor \(A_{i}\subset A\)作为候选正样本，然后在maximizing detection customized likelihood的同时去学习匹配最优的anchor。
为了优化召回率，对于每个目标\(b_{i} \subset B\)，需要保证至少有一个anchor \(a_{j}\subset A_{i}\)，它的预测\(a_{j}^{cls}\)和\(a_{j}^{loc}\)和ground truth较为接近，然后去负责预测该gt。优化召回率对应的似然函数如下所示
这个公式的含义是，对于每个目标\(i\)，取anchor候选集\(A_{i}\)中分类和定位置信度乘积最大的那个，然后去优化这个anchor，即最大化这个乘积。
为了优化精度，需要把定位差的anchor分类为背景。对应的似然函数如下
其中\(P\left \{ a_{j}\in A_{-} \right \}=1-max_{i}P\left \{ a_{j}\rightarrow b_{i} \right \}\)是\(a_{j}\)没有和任一个gt匹配上的概率，\(P\left \{ a_{j}\rightarrow b_{i} \right \}\)是\(a_{j}\)正确预测\(b_{i}\)的概率。
这个公式的含义是，从定位的角度来看，当一个anchor属于背景，那么\(P\left \{ a_{j}\rightarrow b_{i} \right \}\)就比较大。从分类的角度我们希望将其分类到背景，即\(P_{j}^{bg}(\theta)\)大，这样\(1-P_{j}^{bg}(\theta)\)才能小，\(P\left \{ a_{j}\subset A_{-} \right \}(1-P_{j}^{bg}(\theta))\)才能小，精度才能变大。
为了和NMS兼容，\(P\left \{ a_{j}\rightarrow b_{i} \right \}\)应该满足下面三个性质
- \(P\left \{ a_{j}\rightarrow b_{i} \right \}\)应该是\(a_{j}\)和\(b_{i}\)的IoU即\(IoU_{ij}^{loc}\)的单调递增函数
- 当\(IoU_{ij}^{loc}\)小于阈值\(t\)时，\(P\left \{ a_{j}\rightarrow b_{i} \right \}\)应该趋近于0
- 对于一个gt \(b_{i}\)，应该存在且仅存在一个\(a_{j}\)满足\(P\left \{ a_{j}\rightarrow b_{i} \right \}=1\)
饱和线性函数如下所示，可以满足上述3个性质
因此定义\(P\left \{ a_{j}\rightarrow b_{i} \right \}=Saturated\;linear(IoU_{ij}^{loc},t,max_{j}(IoU_{ij}^{loc}))\)
这样就满足上述优化召回率、优化精度、和NMS兼容三个条件，并且可以达到我们希望在训练过程中free object-anchor matching的要求。
Anchor Matching Mechanism
为了训练，再将上面的似然概率函数转换成Loss
其中max函数用来为每个目标\(b_{i}\)挑选最优的一个anchor，在训练过程中，从anchor候选正样本\(A_{i}\)中挑选出一个最优的用来更新模型权重\(\theta\)。
但在训练初期，所有anchor的置信度都比较小，置信度最高的anchor不一定是最匹配的。因此作者提出使用Mean-Max函数，定义如下
当训练不充分时，如下图所示，Mean-max类似于Mean函数，这意味着候选\(A_{i}\)中几乎所有anchor都参与训练了。随着训练的进行，某些anchor的置信度逐渐增加，Mean-max类似于Max函数，当训练充分时，最合适的一个anchor会从\(A_{i}\)中挑选出来匹配目标\(b_{i}\)。
把式(6)中的max函数替换为mean-max函数，添加权重因子\(w_{1},w_{2}\)，式中的第二项应用focal loss，FreeAnchor最终的loss如下所示
其中\(X_{i}=\left \{ P_{ij}^{cls}(\theta)P_{ij}^{loc}(\theta)|a_{j}\subset A_{i} \right \}\)是对应anchor候选集\(A_{i}\)的似然概率集和。使用focal loss中的参数\(\alpha,\gamma\)，设置\(w_{1}=\frac{\alpha}{\begin{Vmatrix}
B
\end{Vmatrix}}\)，\(w_{2}=\frac{1-\alpha}{n\begin{Vmatrix}
B
\end{Vmatrix}}\)，\(FL(x)=-x^{\gamma}log(1-x)\)。
定义好detection customized loss后，训练过程如下所示
代码
class FreeAnchorRetinaHead(RetinaHead):
"""FreeAnchor RetinaHead used in https://arxiv.org/abs/1909.02466.
Args:
num_classes (int): Number of categories excluding the background
category.
in_channels (int): Number of channels in the input feature map.
stacked_convs (int): Number of conv layers in cls and reg tower.
Default: 4.
conv_cfg (dict): dictionary to construct and config conv layer.
Default: None.
norm_cfg (dict): dictionary to construct and config norm layer.
Default: norm_cfg=dict(type='GN', num_groups=32,
requires_grad=True).
pre_anchor_topk (int): Number of boxes that be token in each bag.
bbox_thr (float): The threshold of the saturated linear function. It is
usually the same with the IoU threshold used in NMS.
gamma (float): Gamma parameter in focal loss.
alpha (float): Alpha parameter in focal loss.
""" # noqa: W605
def __init__(self,
num_classes,
in_channels,
stacked_convs=4,
conv_cfg=None,
norm_cfg=None,
pre_anchor_topk=50,
bbox_thr=0.6,
gamma=2.0,
alpha=0.5,
**kwargs):
super(FreeAnchorRetinaHead,
self).__init__(num_classes, in_channels, stacked_convs, conv_cfg,
norm_cfg, **kwargs)
self.pre_anchor_topk = pre_anchor_topk
self.bbox_thr = bbox_thr
self.gamma = gamma
self.alpha = alpha # 0.5
def loss(self,
cls_scores,
bbox_preds,
gt_bboxes,
gt_labels,
img_metas,
gt_bboxes_ignore=None):
# cls_scores: [(1,180,38,38),(1,180,19,19),(1,180,10,10),(1,180,5,5),(1,180,3,3)]
# bbox_preds: [(1,36,38,38),(1,36,19,19),(1,36,10,10),(1,36,5,5),(1,36,3,3)]
# gt_bboxes: [tensor([[0.0000, 0.0000, 300.0000, 300.0000],
# [0.0000, 0.0000, 207.5188, 200.0000]], device='cuda:0')]
# gt_labels: [tensor([12, 14], device='cuda:0')]
# img_metas:
# gt_bboxes_ignore: None
"""Compute losses of the head.
Args:
cls_scores (list[Tensor]): Box scores for each scale level
Has shape (N, num_anchors * num_classes, H, W)
bbox_preds (list[Tensor]): Box energies / deltas for each scale
level with shape (N, num_anchors * 4, H, W)
gt_bboxes (list[Tensor]): each item are the truth boxes for each
image 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.
"""
featmap_sizes = [featmap.size()[-2:] for featmap in cls_scores] # [(38,38),(19,19),(10,10),(5,5),(3,3)]
assert len(featmap_sizes) == self.prior_generator.num_levels
anchor_list, _ = self.get_anchors(featmap_sizes, img_metas)
# len(anchor_list)=batch_size=1, len(anchor_list[0])=out_levels_num=5
# torch.Size([12996, 4]) 38*38*9
# torch.Size([3249, 4])
# torch.Size([900, 4])
# torch.Size([225, 4])
# torch.Size([81, 4])
anchors = [torch.cat(anchor) for anchor in anchor_list] # [(17451,4)]
# concatenate each level
cls_scores = [
cls.permute(0, 2, 3,
1).reshape(cls.size(0), -1, self.cls_out_channels)
for cls in cls_scores
]
# torch.Size([1, 12996, 20])
# torch.Size([1, 3249, 20])
# torch.Size([1, 900, 20])
# torch.Size([1, 225, 20])
# torch.Size([1, 81, 20])
bbox_preds = [
bbox_pred.permute(0, 2, 3, 1).reshape(bbox_pred.size(0), -1, 4)
for bbox_pred in bbox_preds
]
# torch.Size([1, 12996, 4])
# torch.Size([1, 3249, 4])
# torch.Size([1, 900, 4])
# torch.Size([1, 225, 4])
# torch.Size([1, 81, 4])
cls_scores = torch.cat(cls_scores, dim=1) # (1, 17451, 20)
bbox_preds = torch.cat(bbox_preds, dim=1) # (1, 17451, 4)
cls_prob = torch.sigmoid(cls_scores)
box_prob = []
num_pos = 0
positive_losses = []
for _, (anchors_, gt_labels_, gt_bboxes_, cls_prob_,
bbox_preds_) in enumerate(
zip(anchors, gt_labels, gt_bboxes, cls_prob, bbox_preds)):
with torch.no_grad(): # 注意这里要取消梯度
if len(gt_bboxes_) == 0:
image_box_prob = torch.zeros(
anchors_.size(0),
self.cls_out_channels).type_as(bbox_preds_)
else:
# box_localization: a_{j}^{loc}, shape: [j, 4]
pred_boxes = self.bbox_coder.decode(anchors_, bbox_preds_) # (17451,4),(17451,4) -> (17451,4)
# object_box_iou: IoU_{ij}^{loc}, shape: [i, j]
object_box_iou = bbox_overlaps(gt_bboxes_, pred_boxes) # (2,4),(17451,4) -> (2,17451)
# object_box_prob: P{a_{j} -> b_{i}}, shape: [i, j]
t1 = self.bbox_thr # 0.6
t2 = object_box_iou.max(
dim=1, keepdim=True).values.clamp(min=t1 + 1e-12) # (2,1), tensor([[0.7288],[0.6268]])
object_box_prob = ((object_box_iou - t1) /
(t2 - t1)).clamp(
min=0, max=1) # (2,17451)
# object_cls_box_prob: P{a_{j} -> b_{i}}, shape: [i, c, j]
num_obj = gt_labels_.size(0) # 2
indices = torch.stack([
torch.arange(num_obj).type_as(gt_labels_), gt_labels_ # tensor([12,14],device='cuda:0')
],
dim=0) # (2,2), tensor([[0,1],[12,14]])
object_cls_box_prob = torch.sparse_coo_tensor(
indices, object_box_prob) # (2,15,17451)
# cj
# tmp = object_cls_box_prob.to_dense()
# import numpy as np
# for i in range(15):
# print(np.sum(tmp.cpu().numpy()[:, i, :]))
# exit()
# image_box_iou: P{a_{j} \in A_{+}}, shape: [c, j]
"""
from "start" to "end" implement:
image_box_iou = torch.sparse.max(object_cls_box_prob,
dim=0).t()
"""
# start
box_cls_prob = torch.sparse.sum(
object_cls_box_prob, dim=0).to_dense() # (15,17451)
# 若两个gt属于不同类别，相加时总有一个值为0。
# 若两个gt属于同一类别，但object_box_prob > 0的anchor完全错开，相加时也总有一个值为0。
# 只有当两个gt属于同一类别，并且同一个anchor与两个gt的object_box_prob都大于0时，相加时和才会发生变化。
# 但没有关系，因为这里是求object_box_prob > 0的anchor的位置。这个anchor可能与同一类别的两个gt的object_box_prob都大于0，也可能与不同类别的两个gt的object_box_prob都大于0。
indices = torch.nonzero(box_cls_prob, as_tuple=False).t_() # (23,2)->(2,23)
# tensor([[ 12, 12, 12, 14, 14, 14, 14, 14, 14, 14,
# 14],
# [16765, 16855, 16945, 13976, 14146, 14147, 14317, 14318, 14488, 14489,
# 16584]], device='cuda:0')
if indices.numel() == 0: # 2*23=46
image_box_prob = torch.zeros(
anchors_.size(0),
self.cls_out_channels).type_as(object_box_prob)
else:
nonzero_box_prob = torch.where(
(gt_labels_.unsqueeze(dim=-1) == indices[0]), # (2)->(2,1) == (15) -> (2,15)
object_box_prob[:, indices[1]], # (2,17451)[:,(15)] -> (2,15)
torch.tensor([
0
]).type_as(object_box_prob)).max(dim=0).values # (2,15)->(15)
# 取max是因为可能存在同一个anchor与两个gt的object_box_prob都大于0，取大的那个
# print(indices.flip([0]))
# tensor([[16655, 16664, 16745, 16748, 16754, 16757, 16835, 16838, 16847, 16486,
# 16564, 16572, 16573, 16575, 16576, 16663, 16666],
# [ 12, 12, 12, 12, 12, 12, 12, 12, 12, 14,
# 14, 14, 14, 14, 14, 14, 14]], device='cuda:0')
# upmap to shape [j, c]
image_box_prob = torch.sparse_coo_tensor(
indices.flip([0]),
nonzero_box_prob,
size=(anchors_.size(0),
self.cls_out_channels)).to_dense() # (17451,20)
# end
box_prob.append(image_box_prob)
# construct bags for objects
match_quality_matrix = bbox_overlaps(gt_bboxes_, anchors_) # (2,4),(17451,4) -> (2,17451)
_, matched = torch.topk(
match_quality_matrix,
self.pre_anchor_topk, # 50
dim=1,
sorted=False) # (2,50)
del match_quality_matrix
# matched_cls_prob: P_{ij}^{cls}
matched_cls_prob = torch.gather(
cls_prob_[matched], 2, # (17451,20)[(2,50)] -> (2,50,20)
gt_labels_.view(-1, 1, 1).repeat(1, self.pre_anchor_topk, # tensor([12,14]), (2)->(2,1,1)->(2,50,1)
1)).squeeze(2) # (2,50,1)->(2,50)
# exp(-BCE(matched_cls_prob))，这里exp和-BCE抵消了，所以还是matched_cls_prob
# matched_box_prob: P_{ij}^{loc}
matched_anchors = anchors_[matched] # (17451,4)[(2,50)] -> (2,50,4)
matched_object_targets = self.bbox_coder.encode(
matched_anchors,
gt_bboxes_.unsqueeze(dim=1).expand_as(matched_anchors)) # (2,4)->(2,1,4)->(2,50,4)
loss_bbox = self.loss_bbox( # SmoothL1Loss
bbox_preds_[matched], # (17451,4)[(2,50)] -> (2,50,4)
matched_object_targets, # (2,50,4)
reduction_override='none').sum(-1) # (2,50,4)->(2,50)
matched_box_prob = torch.exp(-loss_bbox) # (2,50)
# positive_losses: {-log( Mean-max(P_{ij}^{cls} * P_{ij}^{loc}) )}
num_pos += len(gt_bboxes_) # 2
positive_losses.append(
self.positive_bag_loss(matched_cls_prob, matched_box_prob)) # (2,50),(2,50) -> (2)
positive_loss = torch.cat(positive_losses).sum() / max(1, num_pos) # 一个值，torch.Size([])
# box_prob: P{a_{j} \in A_{+}}
box_prob = torch.stack(box_prob, dim=0)
# negative_loss:
# \sum_{j}{ FL((1 - P{a_{j} \in A_{+}}) * (1 - P_{j}^{bg})) } / n||B||
# (1,17451,20),(1,17451,20)
negative_loss = self.negative_bag_loss(cls_prob, box_prob).sum() / max(
1, num_pos * self.pre_anchor_topk)
# avoid the absence of gradients in regression subnet
# when no ground-truth in a batch
if num_pos == 0:
positive_loss = bbox_preds.sum() * 0
losses = {
'positive_bag_loss': positive_loss,
'negative_bag_loss': negative_loss
}
return losses
def positive_bag_loss(self, matched_cls_prob, matched_box_prob):
"""Compute positive bag loss.
:math:`-log( Mean-max(P_{ij}^{cls} * P_{ij}^{loc}) )`.
:math:`P_{ij}^{cls}`: matched_cls_prob, classification probability of matched samples.
:math:`P_{ij}^{loc}`: matched_box_prob, box probability of matched samples.
Args:
matched_cls_prob (Tensor): Classification probability of matched
samples in shape (num_gt, pre_anchor_topk).
matched_box_prob (Tensor): BBox probability of matched samples,
in shape (num_gt, pre_anchor_topk).
Returns:
Tensor: Positive bag loss in shape (num_gt,).
""" # noqa: E501, W605
# bag_prob = Mean-max(matched_prob)
matched_prob = matched_cls_prob * matched_box_prob # (2,50)*(2,50)->(2,50)
weight = 1 / torch.clamp(1 - matched_prob, 1e-12, None) # (2,50)
weight /= weight.sum(dim=1).unsqueeze(dim=-1) # (2,50)->(2)->(2,1), (2,50)
bag_prob = (weight * matched_prob).sum(dim=1) # (2,50)->(2)
# positive_bag_loss = -self.alpha * log(bag_prob)
return self.alpha * F.binary_cross_entropy(
bag_prob, torch.ones_like(bag_prob), reduction='none')
def negative_bag_loss(self, cls_prob, box_prob):
"""Compute negative bag loss.
:math:`FL((1 - P_{a_{j} \in A_{+}}) * (1 - P_{j}^{bg}))`.
:math:`P_{a_{j} \in A_{+}}`: Box_probability of matched samples.
:math:`P_{j}^{bg}`: Classification probability of negative samples.
Args:
cls_prob (Tensor): Classification probability, in shape
(num_img, num_anchors, num_classes).
box_prob (Tensor): Box probability, in shape
(num_img, num_anchors, num_classes).
Returns:
Tensor: Negative bag loss in shape (num_img, num_anchors, num_classes).
""" # noqa: E501, W605
prob = cls_prob * (1 - box_prob) # cls_prob就是1-P_{j}^{bg}
# There are some cases when neg_prob = 0.
# This will cause the neg_prob.log() to be inf without clamp.
prob = prob.clamp(min=EPS, max=1 - EPS)
negative_bag_loss = prob**self.gamma * F.binary_cross_entropy(
prob, torch.zeros_like(prob), reduction='none')
return (1 - self.alpha) * negative_bag_loss参考
FreeAnchor：令anchor自由匹配标签的策略（附源码实现） - 简书
标签：box,gt,torch,prob,FreeAnchor,anchor,cls 来源： https://blog.csdn.net/ooooocj/article/details/122910932