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目标检测: 一文读懂 YOLOV5 Loss 正样本采样_yolov5 loss公式

作者：小丑西瓜9 | 2024-06-12 18:58:56

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yolov5 loss公式

前言

YoloV5中loss由正样本和负样本两部分loss组成，负样本对应着图像的背景，如果负样本远多于正样本，则负样本会淹没正样本的损失，从而降低网络收敛的效率与检测精度。这就是目标检测中常见的正负样本不均衡问题，解决方案之一是增加正样本数。

Yolo anchor_based 系列使用的loss公式如下：

公式中：

$S$ ： $S \times S$ 个网格；

$B$ ：每个网格产生 $B$ 个候选框anchor box；

$1_{i,j}^{obj}$ ：如果在 $i, j$ 处的box有目标（正样本），其值为1，否则为0；

$1_{i,j}^{noobj}$ ：如果在 $i, j$ 处的box没有目标（负样本），其值为1，否则为0；

$l^{box}_{i,j}$ : 在 $i, j$ 处的box损失函数；

$l^{cls}_{i,j}$ :在 $i, j$ 处的cls 损失函数；

$l^{obj}_{i,j}$ :在 $i, j$ 处的obj损失函数

正样本采样

Yolov5算法使用如下3种方式增加正样本个数：

(1) 跨`anchor`预测

假设一个GT框落在了某个预测分支的某个网格内，该网格具有3种不同大小anchor，若GT可以和这3种anchor中的多种anchor匹配，则这些匹配的anchor都可以来预测该GT框，即一个GT框可以使用多种anchor来预测。

具体方法：
不同于IOU匹配，yolov5采用基于宽高比例的匹配策略，GT的宽高与anchors的宽高对应相除得到ratio1，anchors的宽高与GT的宽高对应相除得到ratio2，取ratio1和ratio2的最大值作为最后的宽高比，该宽高比和设定阈值（默认为4）比较，小于设定阈值的anchor则为匹配到的anchor。

计算例子：

anchor_boxes=torch.tensor([[1.25000, 1.62500],[2.00000, 3.75000],[4.12500, 2.87500]])
gt_box=torch.tensor([5,4])

ratio1=gt_box/anchor_boxes
ratio2=anchor_boxes/gt_box
ratio=torch.max(ratio1, ratio2).max(1)[0]
print(ratio)

anchor_t=4
res=ratio<anchor_t
print(res)
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输出：

tensor([4.0000, 2.5000, 1.3913])
tensor([False,  True,  True])
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与GT相匹配的的anchor为anchor 2和anchor3。

图1 匹配 anchor

(2) 跨`grid`预测

假设一个GT框落在了某个预测分支的某个网格内，则该网格有左、上、右、下4个邻域网格，根据GT框的中心位置，将最近的2个邻域网格也作为预测网格，也即一个GT框可以由3个网格来预测。

计算例子：
GT box中心点处于grid1中，grid1被选中，为了增加增样本，grid1的上下左右grid为候选网格，因为GT中心点更靠近grid2和grid3，grid2和grid3也作为匹配到的网格，根据上步的anchor匹配结果，GT与anchor2、anchor3相匹配，因此GT在当前层匹配到的正样本有6个，分别为：grid1_anchor2，grid1_anchor3，grid2_anchor2，grid2_anchor3，grid3_anchor2，grid3_anchor3。

图2 匹配 grid

(3) 跨分支预测

假设一个GT框可以和2个甚至3个预测分支上的anchor匹配，则这2个或3个预测分支都可以预测该GT框，即一个GT框可以由多个预测分支来预测，重复anchor匹配和grid匹配的步骤，可以得到某个GT 匹配到的所有正样本。

debug 代码

上述正样本采样过程在yolov5通过函数build_targets实现，为了方便理解上述代码，对每一步进行debug，具体如下：

def build_targets(self, p, targets):
    # Build targets for compute_loss(), input targets(image,class,x,y,w,h)
    na, nt = self.na, targets.shape[0]  # number of anchors, targets
    tcls, tbox, indices, anch = [], [], [], []
    gain = torch.ones(7, device=targets.device)  # normalized to gridspace gain
    
    ## 前置处理
    # same as .repeat_interleave(nt)
    ai = torch.arange(na, device=targets.device).float().view(na, 1).repeat(1, nt)  
    targets = torch.cat((targets.repeat(na, 1, 1), ai[:, :, None]), 2)  # append anchor indices
    g = 0.5  # bias
    off = torch.tensor([[0, 0],
                        [1, 0], [0, 1], [-1, 0], [0, -1],  # j,k,l,m
                        # [1, 1], [1, -1], [-1, 1], [-1, -1],  # jk,jm,lk,lm
                       ], device=targets.device).float() * g  # offsets

    for i in range(self.nl):
        ## target映射到当前层的尺度
        anchors = self.anchors[i]
        gain[2:6] = torch.tensor(p[i].shape)[[3, 2, 3, 2]]  # xyxy gain
        # Match targets to anchors
        t = targets * gain
        if nt:
            # Matches
            r = t[:, :, 4:6] / anchors[:, None]  # wh ratio
            j = torch.max(r, 1 / r).max(2)[0] < self.hyp['anchor_t']  # compare
            t = t[j]  # filter

            # Offsets
            gxy = t[:, 2:4]  # grid xy
            gxi = gain[[2, 3]] - gxy  # inverse
            j, k = ((gxy % 1 < g) & (gxy > 1)).T
            l, m = ((gxi % 1 < g) & (gxi > 1)).T
            j = torch.stack((torch.ones_like(j), j, k, l, m))
            t = t.repeat((5, 1, 1))[j]
            offsets = (torch.zeros_like(gxy)[None] + off[:, None])[j]
            else:
                t = targets[0]
                offsets = 0

                # Define
                b, c = t[:, :2].long().T  # image, class
                gxy = t[:, 2:4]  # grid xy
                gwh = t[:, 4:6]  # grid wh
                gij = (gxy - offsets).long()
                gi, gj = gij.T  # grid xy indices

                # Append
                a = t[:, 6].long()  # anchor indices
                indices.append((b, a, gj.clamp_(0, gain[3] - 1), gi.clamp_(0, gain[2] - 1)))  # image, anchor, grid indices
                tbox.append(torch.cat((gxy - gij, gwh), 1))  # box
                anch.append(anchors[a])  # anchors
                tcls.append(c)  # class

                return tcls, tbox, indices, anch
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输入：targets: shape (7，6)，其中7是一个batch的bbox数量，6代表 (image_id, class, x, y, w, h)：

tensor([[[0.00000, 2.00000, 0.23471, 0.63425, 0.30464, 0.16110],
         [0.00000, 3.00000, 0.08736, 0.64150, 0.11682, 0.21073],
         [0.00000, 3.00000, 0.86652, 0.63158, 0.10384, 0.19088],
         [0.00000, 2.00000, 0.69091, 0.65983, 0.21684, 0.24738],
         [0.00000, 2.00000, 0.95464, 0.64647, 0.09072, 0.13514],
         [0.00000, 2.00000, 0.69473, 0.98720, 0.17866, 0.02560],
         [0.00000, 3.00000, 0.87034, 0.98758, 0.13743, 0.02484]]], device='cuda:0')
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前置处理

ai = torch.arange(na, device=targets.device).float().view(na, 1).repeat(1, nt)  
targets = torch.cat((targets.repeat(na, 1, 1), ai[:, :, None]), 2)

g = 0.5  # bias
off = torch.tensor([[0, 0],[1, 0], [0, 1], [-1, 0], [0, -1]], 
                   device=targets.device).float() * g
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将target复制3份，shape变成(3,7,7)，7代表 (image_id, class, x, y, w, h, anchor_id)，复制的目的是为了进行anchor匹配，对应3个anchor:

# targets
tensor([[[0.00000, 2.00000, 0.23471, 0.63425, 0.30464, 0.16110, 0.00000],
         [0.00000, 3.00000, 0.08736, 0.64150, 0.11682, 0.21073, 0.00000],
         [0.00000, 3.00000, 0.86652, 0.63158, 0.10384, 0.19088, 0.00000],
         [0.00000, 2.00000, 0.69091, 0.65983, 0.21684, 0.24738, 0.00000],
         [0.00000, 2.00000, 0.95464, 0.64647, 0.09072, 0.13514, 0.00000],
         [0.00000, 2.00000, 0.69473, 0.98720, 0.17866, 0.02560, 0.00000],
         [0.00000, 3.00000, 0.87034, 0.98758, 0.13743, 0.02484, 0.00000]],

        [[0.00000, 2.00000, 0.23471, 0.63425, 0.30464, 0.16110, 1.00000],
         [0.00000, 3.00000, 0.08736, 0.64150, 0.11682, 0.21073, 1.00000],
         [0.00000, 3.00000, 0.86652, 0.63158, 0.10384, 0.19088, 1.00000],
         [0.00000, 2.00000, 0.69091, 0.65983, 0.21684, 0.24738, 1.00000],
         [0.00000, 2.00000, 0.95464, 0.64647, 0.09072, 0.13514, 1.00000],
         [0.00000, 2.00000, 0.69473, 0.98720, 0.17866, 0.02560, 1.00000],
         [0.00000, 3.00000, 0.87034, 0.98758, 0.13743, 0.02484, 1.00000]],

        [[0.00000, 2.00000, 0.23471, 0.63425, 0.30464, 0.16110, 2.00000],
         [0.00000, 3.00000, 0.08736, 0.64150, 0.11682, 0.21073, 2.00000],
         [0.00000, 3.00000, 0.86652, 0.63158, 0.10384, 0.19088, 2.00000],
         [0.00000, 2.00000, 0.69091, 0.65983, 0.21684, 0.24738, 2.00000],
         [0.00000, 2.00000, 0.95464, 0.64647, 0.09072, 0.13514, 2.00000],
         [0.00000, 2.00000, 0.69473, 0.98720, 0.17866, 0.02560, 2.00000],
         [0.00000, 3.00000, 0.87034, 0.98758, 0.13743, 0.02484, 2.00000]]], device='cuda:0')

# off
tensor([[ 0.00000,  0.00000],
        [ 0.50000,  0.00000],
        [ 0.00000,  0.50000],
        [-0.50000,  0.00000],
        [ 0.00000, -0.50000]], device='cuda:0')
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target坐标映射到当前层的尺度

输入的target坐标值为归一化的值，当前层尺寸为80，target坐标值乘以80则可将target坐标值映射到当前层的尺度：

# anchors
anchors = self.anchors[i]

# gain
gain = torch.ones(7, device=targets.device)
gain[2:6] = torch.tensor(p[i].shape)[[3, 2, 3, 2]]

t = targets * gain
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# anchors(anchor在当前层的尺寸)
tensor([[1.25000, 1.62500],
        [2.00000, 3.75000],
        [4.12500, 2.87500]], device='cuda:0')

# gain (当前层尺寸为80)
tensor([ 1.,  1., 80., 80., 80., 80.,  1.], device='cuda:0')

# t(target 在当前层的尺寸)
# shape:(3,7,7)
tensor([[[ 0.00000,  2.00000, 18.77713, 50.73999, 24.37135, 12.88811,  0.00000],
         [ 0.00000,  3.00000,  6.98848, 51.32027,  9.34541, 16.85838,  0.00000],
         [ 0.00000,  3.00000, 69.32172, 50.52621,  8.30702, 15.27027,  0.00000],
         [ 0.00000,  2.00000, 55.27307, 52.78621, 17.34703, 19.79027,  0.00000],
         [ 0.00000,  2.00000, 76.37107, 51.71729,  7.25761, 10.81135,  0.00000],
         [ 0.00000,  2.00000, 55.57848, 78.97575, 14.29298,  2.04826,  0.00000],
         [ 0.00000,  3.00000, 69.62713, 79.00629, 10.99460,  1.98718,  0.00000]],

        [[ 0.00000,  2.00000, 18.77713, 50.73999, 24.37135, 12.88811,  1.00000],
         [ 0.00000,  3.00000,  6.98848, 51.32027,  9.34541, 16.85838,  1.00000],
         [ 0.00000,  3.00000, 69.32172, 50.52621,  8.30702, 15.27027,  1.00000],
         [ 0.00000,  2.00000, 55.27307, 52.78621, 17.34703, 19.79027,  1.00000],
         [ 0.00000,  2.00000, 76.37107, 51.71729,  7.25761, 10.81135,  1.00000],
         [ 0.00000,  2.00000, 55.57848, 78.97575, 14.29298,  2.04826,  1.00000],
         [ 0.00000,  3.00000, 69.62713, 79.00629, 10.99460,  1.98718,  1.00000]],

        [[ 0.00000,  2.00000, 18.77713, 50.73999, 24.37135, 12.88811,  2.00000],
         [ 0.00000,  3.00000,  6.98848, 51.32027,  9.34541, 16.85838,  2.00000],
         [ 0.00000,  3.00000, 69.32172, 50.52621,  8.30702, 15.27027,  2.00000],
         [ 0.00000,  2.00000, 55.27307, 52.78621, 17.34703, 19.79027,  2.00000],
         [ 0.00000,  2.00000, 76.37107, 51.71729,  7.25761, 10.81135,  2.00000],
         [ 0.00000,  2.00000, 55.57848, 78.97575, 14.29298,  2.04826,  2.00000],
         [ 0.00000,  3.00000, 69.62713, 79.00629, 10.99460,  1.98718,  2.00000]]], device='cuda:0')
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匹配 anchor

step1：对每一个GT框，分别计算它与9种anchor的宽与宽的比值、高与高的比值；

step2：在宽比值、高比值这2个比值中，取最极端的一个比值，作为GT框和anchor的比值，具体实现的伪代码为：max(anchor / GT, GT / anchor )；

step3：得到GT框和anchor的比值后，若这个比值小于设定的比值阈值，那么这个anchor就负责预测GT框，这个anchor的预测框就被称为正样本，所有其它的预测框都是负样本。

得到当前层需要检测的GT以及其对应的anchor_id。

# step1
r = t[:, :, 4:6] / anchors[:, None]

# step2
j = torch.max(r, 1 / r).max(2)[0] < self.hyp['anchor_t']

# step3
t = t[j]
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输出：

# r
# shape:(3,7,2)
tensor([[[19.49708,  7.93114],
         [ 7.47632, 10.37439],
         [ 6.64562,  9.39709],
         [13.87762, 12.17863],
         [ 5.80609,  6.65314],
         [11.43438,  1.26047],
         [ 8.79568,  1.22288]],

        [[12.18568,  3.43683],
         [ 4.67270,  4.49557],
         [ 4.15351,  4.07207],
         [ 8.67351,  5.27741],
         [ 3.62881,  2.88303],
         [ 7.14649,  0.54620],
         [ 5.49730,  0.52992]],

        [[ 5.90821,  4.48282],
         [ 2.26555,  5.86378],
         [ 2.01382,  5.31140],
         [ 4.20534,  6.88357],
         [ 1.75942,  3.76047],
         [ 3.46496,  0.71244],
         [ 2.66536,  0.69119]]], device='cuda:0')
# j
tensor([[False, False, False, False, False, False, False],
        [False, False, False, False,  True, False, False],
        [False, False, False, False,  True,  True,  True]], device='cuda:0')

# t（在当前层只检测这4个target）
tensor([[ 0.00000,  2.00000, 76.37107, 51.71729,  7.25761, 10.81135,  1.00000],
        [ 0.00000,  2.00000, 76.37107, 51.71729,  7.25761, 10.81135,  2.00000],
        [ 0.00000,  2.00000, 55.57848, 78.97575, 14.29298,  2.04826,  2.00000],
        [ 0.00000,  3.00000, 69.62713, 79.00629, 10.99460,  1.98718,  2.00000]], device='cuda:0')
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匹配 grid
为了扩展正样本数量，将上下左右的gird作为候选grid，更靠近GT 所在的grid的则为匹配到的grid。

gxy = t[:, 2:4]
gxi = gain[[2, 3]] - gxy
j, k = ((gxy % 1 < g) & (gxy > 1)).T # (左，下)，gxy > 1排除超出边界的部分
l, m = ((gxi % 1 < g) & (gxi > 1)).T # (右，上)，gxi > 1排除超出边界的部分
j = torch.stack((torch.ones_like(j), j, k, l, m))
t = t.repeat((5, 1, 1))[j]
offsets = (torch.zeros_like(gxy)[None] + off[:, None])[j]
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输出：

# gxy
tensor([[76.37107, 51.71729],
        [76.37107, 51.71729],
        [55.57848, 78.97575],
        [69.62713, 79.00629]], device='cuda:0')

# gxi
tensor([[ 3.62893, 28.28271],
        [ 3.62893, 28.28271],
        [24.42152,  1.02425],
        [10.37287,  0.99371]], device='cuda:0')
# j, k
j: tensor([ True,  True, False, False], device='cuda:0')
k: tensor([False, False, False,  True], device='cuda:0')
    
# l, m
l: tensor([False, False,  True,  True], device='cuda:0')
m: tensor([ True,  True,  True, False], device='cuda:0')
    
# j
tensor([[ True,  True,  True,  True],
        [ True,  True, False, False],
        [False, False, False,  True],
        [False, False,  True,  True],
        [ True,  True,  True, False]], device='cuda:0')
# t
tensor([[ 0.00000,  2.00000, 76.37107, 51.71729,  7.25761, 10.81135,  1.00000],
        [ 0.00000,  2.00000, 76.37107, 51.71729,  7.25761, 10.81135,  2.00000],
        [ 0.00000,  2.00000, 55.57848, 78.97575, 14.29298,  2.04826,  2.00000],
        [ 0.00000,  3.00000, 69.62713, 79.00629, 10.99460,  1.98718,  2.00000],
        [ 0.00000,  2.00000, 76.37107, 51.71729,  7.25761, 10.81135,  1.00000],
        [ 0.00000,  2.00000, 76.37107, 51.71729,  7.25761, 10.81135,  2.00000],
        [ 0.00000,  3.00000, 69.62713, 79.00629, 10.99460,  1.98718,  2.00000],
        [ 0.00000,  2.00000, 55.57848, 78.97575, 14.29298,  2.04826,  2.00000],
        [ 0.00000,  3.00000, 69.62713, 79.00629, 10.99460,  1.98718,  2.00000],
        [ 0.00000,  2.00000, 76.37107, 51.71729,  7.25761, 10.81135,  1.00000],
        [ 0.00000,  2.00000, 76.37107, 51.71729,  7.25761, 10.81135,  2.00000],
        [ 0.00000,  2.00000, 55.57848, 78.97575, 14.29298,  2.04826,  2.00000]], device='cuda:0')

# offsets
tensor([[ 0.00000,  0.00000],
        [ 0.00000,  0.00000],
        [ 0.00000,  0.00000],
        [ 0.00000,  0.00000],
        [ 0.50000,  0.00000],
        [ 0.50000,  0.00000],
        [ 0.00000,  0.50000],
        [-0.50000,  0.00000],
        [-0.50000,  0.00000],
        [ 0.00000, -0.50000],
        [ 0.00000, -0.50000],
        [ 0.00000, -0.50000]], device='cuda:0')
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grid坐标

计算匹配到的grid左上坐标点：

b, c = t[:, :2].long().T  # image, class
gxy = t[:, 2:4]  # grid xy
gwh = t[:, 4:6]  # grid wh
gij = (gxy - offsets).long()
gi, gj = gij.T  # grid 
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输出：

# b
tensor([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], device='cuda:0')
# c
tensor([2, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 2], device='cuda:0')
# gxy 
tensor([[76.37107, 51.71729],
        [76.37107, 51.71729],
        [55.57848, 78.97575],
        [69.62713, 79.00629],
        [76.37107, 51.71729],
        [76.37107, 51.71729],
        [69.62713, 79.00629],
        [55.57848, 78.97575],
        [69.62713, 79.00629],
        [76.37107, 51.71729],
        [76.37107, 51.71729],
        [55.57848, 78.97575]], device='cuda:0')
# gwh
tensor([[ 7.25761, 10.81135],
        [ 7.25761, 10.81135],
        [14.29298,  2.04826],
        [10.99460,  1.98718],
        [ 7.25761, 10.81135],
        [ 7.25761, 10.81135],
        [10.99460,  1.98718],
        [14.29298,  2.04826],
        [10.99460,  1.98718],
        [ 7.25761, 10.81135],
        [ 7.25761, 10.81135],
        [14.29298,  2.04826]], device='cuda:0')
# gij
tensor([[76, 51],
        [76, 51],
        [55, 78],
        [69, 79],
        [75, 51],
        [75, 51],
        [69, 78],
        [56, 78],
        [70, 79],
        [76, 52],
        [76, 52],
        [55, 79]], device='cuda:0')

# gi
tensor([76, 76, 55, 69, 75, 75, 69, 56, 70, 76, 76, 55], device='cuda:0')

# gj
tensor([51, 51, 78, 79, 51, 51, 78, 78, 79, 52, 52, 79], device='cuda:0')
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结果放到列表中

a = t[:, 6].long()  # anchor indices
indices.append((b, a, gj.clamp_(0, gain[3] - 1), gi.clamp_(0, gain[2] - 1)))  # image, anchor, grid indices
tbox.append(torch.cat((gxy - gij, gwh), 1))  # box
anch.append(anchors[a])  # anchors
tcls.append(c)  # class
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输出：

tensor([1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2], device='cuda:0')

[(tensor([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], device='cuda:0'),               # image_id
  tensor([1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2], device='cuda:0'),               # anchor_id
  tensor([51, 51, 78, 79, 51, 51, 78, 78, 79, 52, 52, 79], device='cuda:0'),   # grid_indices
  tensor([76, 76, 55, 69, 75, 75, 69, 56, 70, 76, 76, 55], device='cuda:0'))]  

# tbox
[tensor([[ 3.71071e-01,  7.17293e-01,  7.25761e+00,  1.08114e+01],
        [ 3.71071e-01,  7.17293e-01,  7.25761e+00,  1.08114e+01],
        [ 5.78480e-01,  9.75746e-01,  1.42930e+01,  2.04826e+00],
        [ 6.27129e-01,  6.28662e-03,  1.09946e+01,  1.98718e+00],
        [ 1.37107e+00,  7.17293e-01,  7.25761e+00,  1.08114e+01],
        [ 1.37107e+00,  7.17293e-01,  7.25761e+00,  1.08114e+01],
        [ 6.27129e-01,  1.00629e+00,  1.09946e+01,  1.98718e+00],
        [-4.21520e-01,  9.75746e-01,  1.42930e+01,  2.04826e+00],
        [-3.72871e-01,  6.28662e-03,  1.09946e+01,  1.98718e+00],
        [ 3.71071e-01, -2.82707e-01,  7.25761e+00,  1.08114e+01],
        [ 3.71071e-01, -2.82707e-01,  7.25761e+00,  1.08114e+01],
        [ 5.78480e-01, -2.42538e-02,  1.42930e+01,  2.04826e+00]], device='cuda:0')]

# anch
[tensor([[2.00000, 3.75000],
        [4.12500, 2.87500],
        [4.12500, 2.87500],
        [4.12500, 2.87500],
        [2.00000, 3.75000],
        [4.12500, 2.87500],
        [4.12500, 2.87500],
        [4.12500, 2.87500],
        [4.12500, 2.87500],
        [2.00000, 3.75000],
        [4.12500, 2.87500],
        [4.12500, 2.87500]], device='cuda:0')]

# tcls
[tensor([2, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 2], device='cuda:0')]
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参考

YOLOV5: https://github.com/ultralytics/yolov5

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