前言

损失函数的改进一直是涨点的重要技巧，本篇博客将使用六个不同损失函数对算法进行改进，并绘制出改进结果对比图~

往期回顾

YOLOv5-7.0改进（一）MobileNetv3替换主干网络

YOLOv5-7.0改进（二）BiFPN替换Neck网络

一、IoU损失介绍

不同IoU的区别：

1、IoU Loss：主要考虑检测框和目标框重叠面积
2、GIoU Loss：在IoU的基础上，解决边界框不相交时loss等于0的情况
3、DIoU Loss：在IoU和GIoU的基础上，考虑边界框中心点距离的信息
4、CIoU Loss：在DIoU的基础上，考虑边界框宽高比的尺度信息
5、EIoU Loss：在CIoU的基础上，解决纵横比的模糊定义，并添加Focal Loss解决BBox回归中的样本不平衡问题
6、alpha IoU Loss：通过调节a,使探测器更灵活地实现不同水平的bbox回归精度
7、SIoU Loss：在EIoU的基础上，加入了类别信息的权重因子，以提高检测模型的分类准确率
8、WIoU Loss：解决质量较好和质量较差的样本间的BBR的平衡问题
9、MPDIoU：包含了现有损失函数中考虑的所有相关因素，即重叠或非重叠区域、中心点距离、宽高偏差，同时简化计算过程。
10、NWD：一种新的度量方法计算框与框之间的相似度，就是把框建成高斯分布，然后用Wasserstein距离来度量这两个分布之间的相似度，来代替IoU

二、GIoU、DIoU、CIoU

1、YOLOv5-7.0版本中的代码中已经提供这三种损失函数，源代码如下：

bbox_iou函数用于计算矩阵框间的IoU

2、bbox损失计算

在__call__函数下默认用的是CIoU

三、EIoU、AlphaIoU、SIoU改进

第一步：添加损失函数

在utils/metric.py中将bbox_iou函数替换成以下代码：

def bbox_iou(box1, box2, xywh=True, GIoU=False, DIoU=False, CIoU=False, SIoU=False, EIoU=False, Focal=False, alpha=1, gamma=0.5, eps=1e-7):
    # Returns Intersection over Union (IoU) of box1(1,4) to box2(n,4)

    # Get the coordinates of bounding boxes
    if xywh:  # transform from xywh to xyxy
        (x1, y1, w1, h1), (x2, y2, w2, h2) = box1.chunk(4, -1), box2.chunk(4, -1)
        w1_, h1_, w2_, h2_ = w1 / 2, h1 / 2, w2 / 2, h2 / 2
        b1_x1, b1_x2, b1_y1, b1_y2 = x1 - w1_, x1 + w1_, y1 - h1_, y1 + h1_
        b2_x1, b2_x2, b2_y1, b2_y2 = x2 - w2_, x2 + w2_, y2 - h2_, y2 + h2_
    else:  # x1, y1, x2, y2 = box1
        b1_x1, b1_y1, b1_x2, b1_y2 = box1.chunk(4, -1)
        b2_x1, b2_y1, b2_x2, b2_y2 = box2.chunk(4, -1)
        w1, h1 = b1_x2 - b1_x1, (b1_y2 - b1_y1).clamp(eps)
        w2, h2 = b2_x2 - b2_x1, (b2_y2 - b2_y1).clamp(eps)

    # Intersection area
    inter = (b1_x2.minimum(b2_x2) - b1_x1.maximum(b2_x1)).clamp(0) * \
            (b1_y2.minimum(b2_y2) - b1_y1.maximum(b2_y1)).clamp(0)

    # Union Area
    union = w1 * h1 + w2 * h2 - inter + eps

    # IoU
    # iou = inter / union # ori iou
    iou = torch.pow(inter/(union + eps), alpha) # alpha iou
    if CIoU or DIoU or GIoU or EIoU or SIoU:
        cw = b1_x2.maximum(b2_x2) - b1_x1.minimum(b2_x1)  # convex (smallest enclosing box) width
        ch = b1_y2.maximum(b2_y2) - b1_y1.minimum(b2_y1)  # convex height
        if CIoU or DIoU or EIoU or SIoU:  # Distance or Complete IoU https://arxiv.org/abs/1911.08287v1
            c2 = (cw ** 2 + ch ** 2) ** alpha + eps  # convex diagonal squared
            rho2 = (((b2_x1 + b2_x2 - b1_x1 - b1_x2) ** 2 + (b2_y1 + b2_y2 - b1_y1 - b1_y2) ** 2) / 4) ** alpha  # center dist ** 2
            if CIoU:  # https://github.com/Zzh-tju/DIoU-SSD-pytorch/blob/master/utils/box/box_utils.py#L47
                v = (4 / math.pi ** 2) * (torch.atan(w2 / h2) - torch.atan(w1 / h1)).pow(2)
                with torch.no_grad():
                    alpha_ciou = v / (v - iou + (1 + eps))
                if Focal:
                    return iou - (rho2 / c2 + torch.pow(v * alpha_ciou + eps, alpha)), torch.pow(inter/(union + eps), gamma)  # Focal_CIoU
                else:
                    return iou - (rho2 / c2 + torch.pow(v * alpha_ciou + eps, alpha))  # CIoU
            elif EIoU:
                rho_w2 = ((b2_x2 - b2_x1) - (b1_x2 - b1_x1)) ** 2
                rho_h2 = ((b2_y2 - b2_y1) - (b1_y2 - b1_y1)) ** 2
                cw2 = torch.pow(cw ** 2 + eps, alpha)
                ch2 = torch.pow(ch ** 2 + eps, alpha)
                if Focal:
                    return iou - (rho2 / c2 + rho_w2 / cw2 + rho_h2 / ch2), torch.pow(inter/(union + eps), gamma) # Focal_EIou
                else:
                    return iou - (rho2 / c2 + rho_w2 / cw2 + rho_h2 / ch2) # EIou
            elif SIoU:
                # SIoU Loss https://arxiv.org/pdf/2205.12740.pdf
                s_cw = (b2_x1 + b2_x2 - b1_x1 - b1_x2) * 0.5 + eps
                s_ch = (b2_y1 + b2_y2 - b1_y1 - b1_y2) * 0.5 + eps
                sigma = torch.pow(s_cw ** 2 + s_ch ** 2, 0.5)
                sin_alpha_1 = torch.abs(s_cw) / sigma
                sin_alpha_2 = torch.abs(s_ch) / sigma
                threshold = pow(2, 0.5) / 2
                sin_alpha = torch.where(sin_alpha_1 > threshold, sin_alpha_2, sin_alpha_1)
                angle_cost = torch.cos(torch.arcsin(sin_alpha) * 2 - math.pi / 2)
                rho_x = (s_cw / cw) ** 2
                rho_y = (s_ch / ch) ** 2
                gamma = angle_cost - 2
                distance_cost = 2 - torch.exp(gamma * rho_x) - torch.exp(gamma * rho_y)
                omiga_w = torch.abs(w1 - w2) / torch.max(w1, w2)
                omiga_h = torch.abs(h1 - h2) / torch.max(h1, h2)
                shape_cost = torch.pow(1 - torch.exp(-1 * omiga_w), 4) + torch.pow(1 - torch.exp(-1 * omiga_h), 4)
                if Focal:
                    return iou - torch.pow(0.5 * (distance_cost + shape_cost) + eps, alpha), torch.pow(inter/(union + eps), gamma) # Focal_SIou
                else:
                    return iou - torch.pow(0.5 * (distance_cost + shape_cost) + eps, alpha) # SIou
            if Focal:
                return iou - rho2 / c2, torch.pow(inter/(union + eps), gamma)  # Focal_DIoU
            else:
                return iou - rho2 / c2  # DIoU
        c_area = cw * ch + eps  # convex area
        if Focal:
            return iou - torch.pow((c_area - union) / c_area + eps, alpha), torch.pow(inter/(union + eps), gamma)  # Focal_GIoU https://arxiv.org/pdf/1902.09630.pdf
        else:
            return iou - torch.pow((c_area - union) / c_area + eps, alpha)  # GIoU https://arxiv.org/pdf/1902.09630.pdf
    if Focal:
        return iou, torch.pow(inter/(union + eps), gamma)  # Focal_IoU
    else:
        return iou  # IoU

效果如下：

第二步：重新配置utils/loss.py

将__call__函数中计算IoU的代码换成以下内容：

• 如果使用EIoU:

iou = bbox_iou(pbox, tbox[i], EIoU=True)  # iou(prediction, target)
if type(iou) is tuple:
    lbox += (iou[1].detach().squeeze() * (1 - iou[0].squeeze())).mean()
    iou = iou[0].squeeze()
else:
    lbox += (1.0 - iou.squeeze()).mean()  # iou loss
    iou = iou.squeeze()

• 如果使用Focal_EIoU:

iou = bbox_iou(pbox, tbox[i], EIoU=True, Focal=True)  # iou(prediction, target)
if type(iou) is tuple:
    lbox += (iou[1].detach().squeeze() * (1 - iou[0].squeeze())).mean()
    iou = iou[0].squeeze()
else:
    lbox += (1.0 - iou.squeeze()).mean()  # iou loss
    iou = iou.squeeze()

• 如果使用Alpha IoU，更改alpha参数值即可：

iou = bbox_iou(pbox, tbox[i], CIoU=True,alpha=3)  # iou(prediction, target)
if type(iou) is tuple:
    lbox += (iou[1].detach().squeeze() * (1 - iou[0].squeeze())).mean()
    iou = iou[0].squeeze()
else:
    lbox += (1.0 - iou.squeeze()).mean()  # iou loss
    iou = iou.squeeze()

• 如果使用SIoU:

iou = bbox_iou(pbox, tbox[i], CIoU=True)  # iou(prediction, target)
if type(iou) is tuple:
    lbox += (iou[1].detach().squeeze() * (1 - iou[0].squeeze())).mean()
    iou = iou[0].squeeze()
else:
    lbox += (1.0 - iou.squeeze()).mean()  # iou loss
    iou = iou.squeeze()

最终效果取决于当前的数据集和模型，多次尝试可以挑选出适合自己数据集的最优改进方法~

四、WIOU改进

第一步：添加损失函数

在utils/metric.py中将bbox_iou函数替换成以下代码：

class WIoU_Scale:
    ''' monotonous: {
            None: origin v1
            True: monotonic FM v2
            False: non-monotonic FM v3
        }
        momentum: The momentum of running mean'''
    
    iou_mean = 1.
    monotonous = False
    _momentum = 1 - 0.5 ** (1 / 7000)
    _is_train = True
 
    def __init__(self, iou):
        self.iou = iou
        self._update(self)
    
    @classmethod
    def _update(cls, self):
        if cls._is_train: cls.iou_mean = (1 - cls._momentum) * cls.iou_mean + \
                                         cls._momentum * self.iou.detach().mean().item()
    
    @classmethod
    def _scaled_loss(cls, self, gamma=1.9, delta=3):
        if isinstance(self.monotonous, bool):
            if self.monotonous:
                return (self.iou.detach() / self.iou_mean).sqrt()
            else:
                beta = self.iou.detach() / self.iou_mean
                alpha = delta * torch.pow(gamma, beta - delta)
                return beta / alpha
        return 1
    
 
def bbox_iou(box1, box2, xywh=True, GIoU=False, DIoU=False, CIoU=False, SIoU=False, EIoU=False, WIoU=False, Focal=False, alpha=1, gamma=0.5, scale=False, eps=1e-7):
    # Returns Intersection over Union (IoU) of box1(1,4) to box2(n,4)
 
    # Get the coordinates of bounding boxes
    if xywh:  # transform from xywh to xyxy
        (x1, y1, w1, h1), (x2, y2, w2, h2) = box1.chunk(4, -1), box2.chunk(4, -1)
        w1_, h1_, w2_, h2_ = w1 / 2, h1 / 2, w2 / 2, h2 / 2
        b1_x1, b1_x2, b1_y1, b1_y2 = x1 - w1_, x1 + w1_, y1 - h1_, y1 + h1_
        b2_x1, b2_x2, b2_y1, b2_y2 = x2 - w2_, x2 + w2_, y2 - h2_, y2 + h2_
    else:  # x1, y1, x2, y2 = box1
        b1_x1, b1_y1, b1_x2, b1_y2 = box1.chunk(4, -1)
        b2_x1, b2_y1, b2_x2, b2_y2 = box2.chunk(4, -1)
        w1, h1 = b1_x2 - b1_x1, (b1_y2 - b1_y1).clamp(eps)
        w2, h2 = b2_x2 - b2_x1, (b2_y2 - b2_y1).clamp(eps)
 
    # Intersection area
    inter = (b1_x2.minimum(b2_x2) - b1_x1.maximum(b2_x1)).clamp(0) * \
            (b1_y2.minimum(b2_y2) - b1_y1.maximum(b2_y1)).clamp(0)
 
    # Union Area
    union = w1 * h1 + w2 * h2 - inter + eps
    if scale:
        self = WIoU_Scale(1 - (inter / union))
 
    # IoU
    # iou = inter / union # ori iou
    iou = torch.pow(inter/(union + eps), alpha) # alpha iou
    if CIoU or DIoU or GIoU or EIoU or SIoU or WIoU:
        cw = b1_x2.maximum(b2_x2) - b1_x1.minimum(b2_x1)  # convex (smallest enclosing box) width
        ch = b1_y2.maximum(b2_y2) - b1_y1.minimum(b2_y1)  # convex height
        if CIoU or DIoU or EIoU or SIoU or WIoU:  # Distance or Complete IoU https://arxiv.org/abs/1911.08287v1
            c2 = (cw ** 2 + ch ** 2) ** alpha + eps  # convex diagonal squared
            rho2 = (((b2_x1 + b2_x2 - b1_x1 - b1_x2) ** 2 + (b2_y1 + b2_y2 - b1_y1 - b1_y2) ** 2) / 4) ** alpha  # center dist ** 2
            if CIoU:  # https://github.com/Zzh-tju/DIoU-SSD-pytorch/blob/master/utils/box/box_utils.py#L47
                v = (4 / math.pi ** 2) * (torch.atan(w2 / h2) - torch.atan(w1 / h1)).pow(2)
                with torch.no_grad():
                    alpha_ciou = v / (v - iou + (1 + eps))
                if Focal:
                    return iou - (rho2 / c2 + torch.pow(v * alpha_ciou + eps, alpha)), torch.pow(inter/(union + eps), gamma)  # Focal_CIoU
                else:
                    return iou - (rho2 / c2 + torch.pow(v * alpha_ciou + eps, alpha))  # CIoU
            elif EIoU:
                rho_w2 = ((b2_x2 - b2_x1) - (b1_x2 - b1_x1)) ** 2
                rho_h2 = ((b2_y2 - b2_y1) - (b1_y2 - b1_y1)) ** 2
                cw2 = torch.pow(cw ** 2 + eps, alpha)
                ch2 = torch.pow(ch ** 2 + eps, alpha)
                if Focal:
                    return iou - (rho2 / c2 + rho_w2 / cw2 + rho_h2 / ch2), torch.pow(inter/(union + eps), gamma) # Focal_EIou
                else:
                    return iou - (rho2 / c2 + rho_w2 / cw2 + rho_h2 / ch2) # EIou
            elif SIoU:
                # SIoU Loss https://arxiv.org/pdf/2205.12740.pdf
                s_cw = (b2_x1 + b2_x2 - b1_x1 - b1_x2) * 0.5 + eps
                s_ch = (b2_y1 + b2_y2 - b1_y1 - b1_y2) * 0.5 + eps
                sigma = torch.pow(s_cw ** 2 + s_ch ** 2, 0.5)
                sin_alpha_1 = torch.abs(s_cw) / sigma
                sin_alpha_2 = torch.abs(s_ch) / sigma
                threshold = pow(2, 0.5) / 2
                sin_alpha = torch.where(sin_alpha_1 > threshold, sin_alpha_2, sin_alpha_1)
                angle_cost = torch.cos(torch.arcsin(sin_alpha) * 2 - math.pi / 2)
                rho_x = (s_cw / cw) ** 2
                rho_y = (s_ch / ch) ** 2
                gamma = angle_cost - 2
                distance_cost = 2 - torch.exp(gamma * rho_x) - torch.exp(gamma * rho_y)
                omiga_w = torch.abs(w1 - w2) / torch.max(w1, w2)
                omiga_h = torch.abs(h1 - h2) / torch.max(h1, h2)
                shape_cost = torch.pow(1 - torch.exp(-1 * omiga_w), 4) + torch.pow(1 - torch.exp(-1 * omiga_h), 4)
                if Focal:
                    return iou - torch.pow(0.5 * (distance_cost + shape_cost) + eps, alpha), torch.pow(inter/(union + eps), gamma) # Focal_SIou
                else:
                    return iou - torch.pow(0.5 * (distance_cost + shape_cost) + eps, alpha) # SIou
            elif WIoU:
                if Focal:
                    raise RuntimeError("WIoU do not support Focal.")
                elif scale:
                    return getattr(WIoU_Scale, '_scaled_loss')(self), (1 - iou) * torch.exp((rho2 / c2)), iou # WIoU https://arxiv.org/abs/2301.10051
                else:
                    return iou, torch.exp((rho2 / c2)) # WIoU v1
            if Focal:
                return iou - rho2 / c2, torch.pow(inter/(union + eps), gamma)  # Focal_DIoU
            else:
                return iou - rho2 / c2  # DIoU
        c_area = cw * ch + eps  # convex area
        if Focal:
            return iou - torch.pow((c_area - union) / c_area + eps, alpha), torch.pow(inter/(union + eps), gamma)  # Focal_GIoU https://arxiv.org/pdf/1902.09630.pdf
        else:
            return iou - torch.pow((c_area - union) / c_area + eps, alpha)  # GIoU https://arxiv.org/pdf/1902.09630.pdf
    if Focal:
        return iou, torch.pow(inter/(union + eps), gamma)  # Focal_IoU
    else:
        return iou  # IoU

• WIOU有三个版本，None表示v1版本，True表示v2版本，False表示v3版本

第二步：重新配置utils/loss.py

将__call__函数中计算IoU的代码换成以下内容：

iou = bbox_iou(pbox, tbox[i], WIoU=True, scale=True)  # iou(prediction, target)
if type(iou) is tuple:
    lbox += (iou[1].detach().squeeze() * (1 - iou[0].squeeze())).mean()
    iou = iou[0].squeeze()
else:
    lbox += (1.0 - iou.squeeze()).mean()  # iou loss
    iou = iou.squeeze()

效果如下：

五、MPDIOU改进

MPDIOU：一种基于最小点距离的新型边界框相似度比较度量标准，直接最小化预测边界框与实际标注边界框之间的左上角和右下角点距离。

第一步：添加损失函数

在utils/metric.py中将bbox_iou函数替换成以下代码：

def bbox_iou(box1, box2, xywh=True, GIoU=False, DIoU=False, CIoU=False, MDPIoU=False, hw=None, eps=1e-7):
    # Returns Intersection over Union (IoU) of box1(1,4) to box2(n,4)
    
    # Get the coordinates of bounding boxes
    if xywh:  # transform from xywh to xyxy
        (x1, y1, w1, h1), (x2, y2, w2, h2) = box1.chunk(4, 1), box2.chunk(4, 1)
        w1_, h1_, w2_, h2_ = w1 / 2, h1 / 2, w2 / 2, h2 / 2
        b1_x1, b1_x2, b1_y1, b1_y2 = x1 - w1_, x1 + w1_, y1 - h1_, y1 + h1_
        b2_x1, b2_x2, b2_y1, b2_y2 = x2 - w2_, x2 + w2_, y2 - h2_, y2 + h2_
    else:  # x1, y1, x2, y2 = box1
        b1_x1, b1_y1, b1_x2, b1_y2 = box1.chunk(4, 1)
        b2_x1, b2_y1, b2_x2, b2_y2 = box2.chunk(4, 1)
        w1, h1 = b1_x2 - b1_x1, b1_y2 - b1_y1
        w2, h2 = b2_x2 - b2_x1, b2_y2 - b2_y1

    # 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
    union = w1 * h1 + w2 * h2 - inter + eps

    # IoU
    iou = inter / union
    if CIoU or DIoU or GIoU:
        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 dist ** 2
            if 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 + eps)) - torch.atan(w1 / (h1 + eps)), 2)
                with torch.no_grad():
                    alpha = v / (v - iou + (1 + eps))
                return iou - (rho2 / c2 + v * alpha)  # CIoU
            return iou - rho2 / c2  # DIoU
        c_area = cw * ch + eps  # convex area
        return iou - (c_area - union) / c_area  # GIoU https://arxiv.org/pdf/1902.09630.pdf
    elif MDPIoU:
        d1 = (b2_x1 - b1_x1) ** 2 + (b2_y1 - b1_y1) ** 2
        d2 = (b2_x2 - b1_x2) ** 2 + (b2_y2 - b1_y2) ** 2
        return iou - d1 / hw - d2 / hw  # MPDIoU
    return iou  # IoU

第二步：重新配置utils/loss.py

将__call__函数中计算IoU的代码换成以下内容：

# MPDIoU
iou = bbox_iou(pbox, tbox[i], MDPIoU=True, hw=tobj.size()[2] * tobj.size()[3]).squeeze()

六、NWD改进(提升小目标检测能力)

第一步：添加损失函数

在utils/metrics.py文件中新增以下代码：

def wasserstein_loss(pred, target, eps=1e-7, constant=12.8):
    """`Implementation of paper `Enhancing Geometric Factors into
    Model Learning and Inference for Object Detection and Instance
    Segmentation <https://arxiv.org/abs/2005.03572>`_.
    Code is modified from https://github.com/Zzh-tju/CIoU.
    Args:
        pred (Tensor): Predicted bboxes of format (x_center, y_center, w, h),
            shape (n, 4).
        target (Tensor): Corresponding gt bboxes, shape (n, 4).
        eps (float): Eps to avoid log(0).
    Return:
        Tensor: Loss tensor.
    """

    center1 = pred[:, :2]
    center2 = target[:, :2]

    whs = center1[:, :2] - center2[:, :2]

    center_distance = whs[:, 0] * whs[:, 0] + whs[:, 1] * whs[:, 1] + eps #

    w1 = pred[:, 2]  + eps
    h1 = pred[:, 3]  + eps
    w2 = target[:, 2] + eps
    h2 = target[:, 3] + eps

    wh_distance = ((w1 - w2) ** 2 + (h1 - h2) ** 2) / 4

    wasserstein_2 = center_distance + wh_distance
    return torch.exp(-torch.sqrt(wasserstein_2) / constant)

效果如下：

第二步：将wasserstein_loss函数导入loss.py中

from utils.metrics import bbox_iou, wasserstein_loss

效果如下：

第三步：重新配置utils/loss.py

找到__call__函数下的Regression中部分，替换代码如下：

# NWD
nwd = wasserstein_loss(pbox, tbox[i]).squeeze()
iou_ratio = 0.5
lbox += (1 - iou_ratio) * (1.0 - nwd).mean() + iou_ratio * (1.0 - iou).mean()  # iou loss

# Objectness
iou = (iou.detach() * iou_ratio + nwd.detach() * (1 - iou_ratio)).clamp(0, 1).type(tobj.dtype)

如下图所示：

七、效果对比