YOLOV5代码详解之损失函数的计算

摘要：

神经网络的训练的主要流程包括图像输入神经网络, 得到模型的输出结果,计算模型的输出与真实值的损失, 计算损失值的梯度,最后用梯度下降算法更新模型参数。损失函数值的计算是非常关键的一个步骤。

本博客将对yolov5损失值的计算过程代码的实现做简要的理解。

def compute_loss(p, targets, model):  # predictions, targets, model
   device = targets.device
   lcls, lbox, lobj = torch.zeros(1, device=device), torch.zeros(1, device=device), torch.zeros(1, device=device)
   tcls, tbox, indices, anchors = build_targets(p, targets, model)  # targets
   h = model.hyp  # hyperparameters

# Define criteria
   BCEcls = nn.BCEWithLogitsLoss(pos_weight=torch.Tensor([h['cls_pw']])).to(device)
   BCEobj = nn.BCEWithLogitsLoss(pos_weight=torch.Tensor([h['obj_pw']])).to(device)

# Class label smoothing https://arxiv.org/pdf/1902.04103.pdf eqn 3
   cp, cn = smooth_BCE(eps=0.0)

# Focal loss
   g = h['fl_gamma']  # focal loss gamma
   if g > 0:
       BCEcls, BCEobj = FocalLoss(BCEcls, g), FocalLoss(BCEobj, g)
  。。。。。。

yolov5代码用IOU指标评价目标框和预测框的位置损失损失。yolov5代码用nn.BCEWithLogitsLoss或FocalLoss评价目标框和预测框的类损失和置信度损失 .

yolov5代码用宽高比选择对应真实框的预测框,且每一个真实框对应三个预测框 。

1、位置损失

yolov5代码用IOU值评价预测框和真实框的位置损失, 本文介绍CIoU指标.

公式如下截图:

公式中参数代表的意义如下:

IOU: 预测框和真实框的叫并比

v是衡量长宽比一致性的参数，我们也可以定义为:

代码实现：

iou = bbox_iou(pbox.T, tbox[i], x1y1x2y2=False, CIoU=True)  # iou(prediction, target)
           lbox += (1.0 - iou).mean()  # iou loss

def bbox_iou(box1, box2, x1y1x2y2=True, GIoU=False, DIoU=False, CIoU=False, eps=1e-9):
   # Returns the IoU of box1 to box2. box1 is 4, box2 is nx4
   box2 = box2.T

# Get the coordinates of bounding boxes
   if x1y1x2y2:  # x1, y1, x2, y2 = box1
       b1_x1, b1_y1, b1_x2, b1_y2 = box1[0], box1[1], box1[2], box1[3]
       b2_x1, b2_y1, b2_x2, b2_y2 = box2[0], box2[1], box2[2], box2[3]
   else:  # transform from xywh to xyxy
       b1_x1, b1_x2 = box1[0] - box1[2] / 2, box1[0] + box1[2] / 2
       b1_y1, b1_y2 = box1[1] - box1[3] / 2, box1[1] + box1[3] / 2
       b2_x1, b2_x2 = box2[0] - box2[2] / 2, box2[0] + box2[2] / 2
       b2_y1, b2_y2 = box2[1] - box2[3] / 2, box2[1] + box2[3] / 2

# Intersection area
   inter = (torch.min(b1_x2, b2_x2) - torch.max(b1_x1, b2_x1)).clamp(0) * \
           (torch.min(b1_y2, b2_y2) - torch.max(b1_y1, b2_y1)).clamp(0)

# Union Area
   w1, h1 = b1_x2 - b1_x1, b1_y2 - b1_y1 + eps
   w2, h2 = b2_x2 - b2_x1, b2_y2 - b2_y1 + eps
   union = w1 * h1 + w2 * h2 - inter + eps

iou = inter / union
   if GIoU or DIoU or CIoU:
       cw = torch.max(b1_x2, b2_x2) - torch.min(b1_x1, b2_x1)  # convex (smallest enclosing box) width
       ch = torch.max(b1_y2, b2_y2) - torch.min(b1_y1, b2_y1)  # convex height
       if CIoU or DIoU:  # Distance or Complete IoU https://arxiv.org/abs/1911.08287v1
           c2 = cw ** 2 + ch ** 2 + eps  # convex diagonal squared
           rho2 = ((b2_x1 + b2_x2 - b1_x1 - b1_x2) ** 2 +
                   (b2_y1 + b2_y2 - b1_y1 - b1_y2) ** 2) / 4  # center distance squared
           if DIoU:
               return iou - rho2 / c2  # DIoU
           elif CIoU:  # https://github.com/Zzh-tju/DIoU-SSD-pytorch/blob/master/utils/box/box_utils.py#L47
               v = (4 / math.pi ** 2) * torch.pow(torch.atan(w2 / h2) - torch.atan(w1 / h1), 2)
               with torch.no_grad():
                   alpha = v / ((1 + eps) - iou + v)
               return iou - (rho2 / c2 + v * alpha)  # CIoU
       else:  # GIoU https://arxiv.org/pdf/1902.09630.pdf
           c_area = cw * ch + eps  # convex area
           return iou - (c_area - union) / c_area  # GIoU
   else:
       return iou  # IoU

2、置信度损失和类损失

yolov5代码用nn.BCEWithLogitsLoss或FocalLoss评价目标框和预测框的类损失和置信度损失,本节一一介绍这两个损失函数。

• nn.BCEWithLogitsLoss:

首先对预测输出作sigmoid变换,然后求变换后的结果与真实值的二值交叉熵.

假设预测输出是3分类,预测输出:

预测输出sigmoid变换:

假设真实输出是:

两者的二值交叉熵的计算方法:

接口函数验证下上面的结果:

• FocalLoss损失:

FocalLoss损失考虑的是:目标检测中正负样本严重不均衡的一种策略。该损失函数的设计思想类似于boosting，降低容易分类的样本对损失函数的影响，注重较难分类的样本的训练.

简而言之,FocalLoss更加关注的是比较难分的样本,何谓难分?若某一个真实类预测的概率只有0.2,我们认为它比较难分,相反若该真实类的预测概率是0.95,则容易分类.

FocalLoss通过提高难分类别的损失函数来实现,公式如下:

图像如下:

可以看出预测真实类概率越大,则损失函数越小,即实现了之前的想法.

为了能够平衡正负样本的重要性,我们可以给各个类别添加一个权重常数 α ,比如想使正样本初始权重为0.8，负样本就为0.2.
代码实现为:

class FocalLoss(nn.Module):
   # Wraps focal loss around existing loss_fcn(), i.e. criteria = FocalLoss(nn.BCEWithLogitsLoss(), gamma=1.5)
   def __init__(self, loss_fcn, gamma=1.5, alpha=0.25):
       super(FocalLoss, self).__init__()
       self.loss_fcn = loss_fcn  # must be nn.BCEWithLogitsLoss()
       self.gamma = gamma
       self.alpha = alpha
       self.reduction = loss_fcn.reduction
       self.loss_fcn.reduction = 'none'  # required to apply FL to each element

def forward(self, pred, true):
       loss = self.loss_fcn(pred, true)
       # p_t = torch.exp(-loss)
       # loss *= self.alpha * (1.000001 - p_t) ** self.gamma  # non-zero power for gradient stability

# TF implementation https://github.com/tensorflow/addons/blob/v0.7.1/tensorflow_addons/losses/focal_loss.py
       pred_prob = torch.sigmoid(pred)  # prob from logits
       p_t = true * pred_prob + (1 - true) * (1 - pred_prob)
       alpha_factor = true * self.alpha + (1 - true) * (1 - self.alpha)
       modulating_factor = (1.0 - p_t) ** self.gamma
       loss *= alpha_factor * modulating_factor

if self.reduction == 'mean':
           return loss.mean()
       elif self.reduction == 'sum':
           return loss.sum()
       else:  # 'none'
           return loss

其中成员函数loss_fcn为nn.BCEWithLogitsLoss。

来源：https://blog.csdn.net/l13022736018/article/details/118346085