目标检测损失函数 yolos、DETR为例

yolos和DETR，除了yolos没有卷积层以外，几乎所有操作都一样。
HF官方文档

因为目标检测模型，实际会输出几百几千个“框”，所以损失函数计算比较复杂。损失函数为偶匹配损失 bipartite matching loss，参考此blog

target为class_label和box组成的字典。假设对于一张图片，我们有5个target框。
num_detection_tokens为模型对一张图最多可以产生的box的数量
简单阐述loss计算流程

1. vit 模型，输入经过预处理的图片，输出最后隐含层状态， 大小为 [batchsize，seq_len，hidden_size]

2. 取最后num_detection_tokens个token的隐藏状态，变为
   [batchsize，num_detection_tokens，hidden_size]

3. 由于输出了num_detection_tokens个box，而target为5个box，所以需要进行一对一的匹配，

4. 匹配过程：

   1. 先计算3个cost矩阵，shape均为【num_detection_tokens，num_target_box】，矩阵元素代表loss，矩阵代表对所有pred和target之间两两计算一次loss。
   2. 3个cost矩阵分别代表标签loss（交叉熵损失）、坐标loss（表示一个框的4个值的L1损失）、GIoU loss（框与框之间计算GIoU）
   3. 三个cost矩阵加权得到总体cost矩阵，大小为【num_detection_tokens，num_target_box】
   4. 对此矩阵进行linear_sum_assignment操作，得到一个匹配，此匹配下cost最小（即cost矩阵中找到不同行且不同列的5个元素，这5个元素之和最小）。匹配表示为长度为min(num_detection_tokens，num_target_box)的索引对。本例长度为5。

5. 根据此匹配，pred和target之间计算一次loss（本例中一共计算5次loss并求和），最重loss就是上面说的3种loss的加权和

6. 其实还有两种loss：

   1. “cardinality” loss，表示输出的num_detection_tokens个class_label中，class_label不为“无目标”的个数，与num_target_box的个数，的L1 loss. 说白了就是，除了5个框有实际的class以外，其他框应尽可能分类为“无目标”，避免检测出来目标过多。但之一loss不产生梯度，仅仅用于评估。
   2. mask loss:功能暂时不清楚

官方匹配函数，匈牙利算法

# Copied from transformers.models.detr.modeling_detr.DetrHungarianMatcher with Detr->Yolos
class YolosHungarianMatcher(nn.Module):"""This class computes an assignment between the targets and the predictions of the network.For efficiency reasons, the targets don't include the no_object. Because of this, in general, there are morepredictions than targets. In this case, we do a 1-to-1 matching of the best predictions, while the others areun-matched (and thus treated as non-objects).Args:class_cost:The relative weight of the classification error in the matching cost.bbox_cost:The relative weight of the L1 error of the bounding box coordinates in the matching cost.giou_cost:The relative weight of the giou loss of the bounding box in the matching cost."""def __init__(self, class_cost: float = 1, bbox_cost: float = 1, giou_cost: float = 1):super().__init__()requires_backends(self, ["scipy"])self.class_cost = class_costself.bbox_cost = bbox_costself.giou_cost = giou_costif class_cost == 0 and bbox_cost == 0 and giou_cost == 0:raise ValueError("All costs of the Matcher can't be 0")@torch.no_grad()def forward(self, outputs, targets):"""Args:outputs (`dict`):A dictionary that contains at least these entries:* "logits": Tensor of dim [batch_size, num_queries, num_classes] with the classification logits* "pred_boxes": Tensor of dim [batch_size, num_queries, 4] with the predicted box coordinates.targets (`List[dict]`):A list of targets (len(targets) = batch_size), where each target is a dict containing:* "class_labels": Tensor of dim [num_target_boxes] (where num_target_boxes is the number ofground-truthobjects in the target) containing the class labels* "boxes": Tensor of dim [num_target_boxes, 4] containing the target box coordinates.Returns:`List[Tuple]`: A list of size `batch_size`, containing tuples of (index_i, index_j) where:- index_i is the indices of the selected predictions (in order)- index_j is the indices of the corresponding selected targets (in order)For each batch element, it holds: len(index_i) = len(index_j) = min(num_queries, num_target_boxes)"""batch_size, num_queries = outputs["logits"].shape[:2]# We flatten to compute the cost matrices in a batchout_prob = outputs["logits"].flatten(0, 1).softmax(-1)  # [batch_size * num_queries, num_classes]out_bbox = outputs["pred_boxes"].flatten(0, 1)  # [batch_size * num_queries, 4]# Also concat the target labels and boxestarget_ids = torch.cat([v["class_labels"] for v in targets])target_bbox = torch.cat([v["boxes"] for v in targets])# Compute the classification cost. Contrary to the loss, we don't use the NLL,# but approximate it in 1 - proba[target class].# The 1 is a constant that doesn't change the matching, it can be ommitted.class_cost = -out_prob[:, target_ids]# Compute the L1 cost between boxesbbox_cost = torch.cdist(out_bbox, target_bbox, p=1)# Compute the giou cost between boxesgiou_cost = -generalized_box_iou(center_to_corners_format(out_bbox), center_to_corners_format(target_bbox))# Final cost matrixcost_matrix = self.bbox_cost * bbox_cost + self.class_cost * class_cost + self.giou_cost * giou_costcost_matrix = cost_matrix.view(batch_size, num_queries, -1).cpu()sizes = [len(v["boxes"]) for v in targets]indices = [linear_sum_assignment(c[i]) for i, c in enumerate(cost_matrix.split(sizes, -1))]return [(torch.as_tensor(i, dtype=torch.int64), torch.as_tensor(j, dtype=torch.int64)) for i, j in indices]

目标检测还有很多细节问题，以后更新