论文中分析了边界框的回归过程，指出了IoU损失的局限性，它对不同的检测任务没有很强的泛化能力。基于边界框回归问题的固有特点，提出了一种基于辅助边界框的边界框回归损失Inner-IoU。通过比例因子比率（scale factor ratio）控制辅助边界框的生成，计算损失，加速训练的收敛。它可以集成到现有的基于IoU的损失函数中。通过一系列的模拟和烧蚀消融实验验证，该方法优于现有方法。本文提出的方法不仅适用于一般的检测任务，而且对于非常小目标的检测任务也表现良好，证实了该方法的泛化性。

官方的代码给出了2种结合方式，文件如下图：

Inner-IoU的描述见下图：

Inner-IoU的实验效果

CIoU 方法, Inner-CIoU (ratio=0.7), Inner-CIoU (ratio=0.75) and Inner-CIoU (ratio=0.8)的检测效果如下图所示：

SIoU 方法, Inner-SIoU (ratio=0.7), Inner-SIoU (ratio=0.75) and Inner-SIoU (ratio=0.8)的检测效果如下图所示：

2 Focaler-IoU：更聚焦的IoU损失

官方论文地址：官方论文地址点击即可跳转

官方代码地址：官方代码地址点击即可跳转

论文中分析了难易样本的分布对目标检测的影响。当困难样品占主导地位时，需要关注困难样品以提高检测性能。当简单样本的比例较大时，则相反。论文中提出了Focaler-IoU方法，通过线性区间映射重建原始IoU损失，达到聚焦难易样本的目的。最后通过对比实验证明，该方法能够有效提高检测性能。

为了在不同的回归样本中关注不同的检测任务，使用线性间隔映射方法重构IoU损失，这有助于提高边缘回归。具体的公式如下所示：

将Focaler-IoU应用于现有的基于IoU的边界框回归损失函数中，如下所示：

实验结果如下：

GIoU、DIoU、CIoU、EIoU和MPDIou等的概述见使用MPDIou回归损失函数帮助YOLOv9模型更优秀 点击此处即可跳转

二改进YOLOv8的损失函数

1 总体修改

首先，我们现将后续会使用到的损失函数集成到项目中。

① ultralytics/utils/metrics.py文件

在utils/metrics.py文件中，使用下述代码（替换后的部分）替换掉bbox_iou（）函数，即将被替换的bbox_iou（）函数如下图所示：

使用下述的替换代码替换掉下述原始代码。

a 原始代码


# before
def bbox_iou(box1, box2, xywh=True, GIoU=False, DIoU=False, CIoU=False, eps=1e-7):
    """
    Calculate Intersection over Union (IoU) of box1(1, 4) to box2(n, 4).
    Args:
        box1 (torch.Tensor): A tensor representing a single bounding box with shape (1, 4).
        box2 (torch.Tensor): A tensor representing n bounding boxes with shape (n, 4).
        xywh (bool, optional): If True, input boxes are in (x, y, w, h) format. If False, input boxes are in
                               (x1, y1, x2, y2) format. Defaults to True.
        GIoU (bool, optional): If True, calculate Generalized IoU. Defaults to False.
        DIoU (bool, optional): If True, calculate Distance IoU. Defaults to False.
        CIoU (bool, optional): If True, calculate Complete IoU. Defaults to False.
        eps (float, optional): A small value to avoid division by zero. Defaults to 1e-7.
    Returns:
        (torch.Tensor): IoU, GIoU, DIoU, or CIoU values depending on the specified flags.
    """
 
    # 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 + eps
        w2, h2 = b2_x2 - b2_x1, b2_y2 - b2_y1 + 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
    if CIoU or DIoU or GIoU:
        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:  # Distance or Complete IoU https://arxiv.org/abs/1911.08287v1
            c2 = cw.pow(2) + ch.pow(2) + eps  # convex diagonal squared
            rho2 = (
                (b2_x1 + b2_x2 - b1_x1 - b1_x2).pow(2) + (b2_y1 + b2_y2 - b1_y1 - b1_y2).pow(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) * ((w2 / h2).atan() - (w1 / h1).atan()).pow(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
    return iou  # IoU

b 替换代码


# after
class WIoU_Scale:
    ''' monotonous: {
            None: origin v1
            True: monotonic FM v2
            False: non-monotonic FM v3
        }
    '''
    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, ratio=1, GIoU=False, DIoU=False, CIoU=False,
             SIoU=False, EIoU=False, WIoU=False, MPDIoU=False, LMPDIoU=False,
             Inner=False, Focal=False, alpha=1, gamma=0.5, scale=False, eps=1e-7):
    # 计算box1与box2之间的Intersection over Union（IoU）
    # 获取bounding box的坐标
    if Inner:
        (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_ * ratio, x1 + w1_ * ratio, \
                                     y1 - h1_ * ratio, y1 + h1_ * ratio
        b2_x1, b2_x2, b2_y1, b2_y2 = x2 - w2_ * ratio, x2 + w2_ * ratio, \
                                     y2 - h2_ * ratio, y2 + h2_ * ratio
        # 计算交集面积
        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)
        # 计算并集面积
        union = w1 * ratio * h1 * ratio + w2 * ratio * h2 * ratio - inter + eps
 
        iou = inter / union  # inner_iou
 
    else:
        # Returns the IoU of box1 to box2. box1 is 4, box2 is nx4
        if xywh:  # xywh转换为xyxy格式
            (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 + eps
            w2, h2 = b2_x2 - b2_x1, b2_y2 - b2_y1 + eps
 
        # 计算交集面积
        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)
 
        # 计算并集面积
        union = w1 * h1 + w2 * h2 - inter + eps
 
        # 计算IoU值
        iou = inter / union
 
    if CIoU or DIoU or GIoU or EIoU or SIoU or WIoU or MPDIoU or LMPDIoU:
        cw = b1_x2.maximum(b2_x2) - b1_x1.minimum(b2_x1)  # 计算最小外接矩形的宽度
        ch = b1_y2.maximum(b2_y2) - b1_y1.minimum(b2_y1)  # 计算最小外接矩形的高度
        if CIoU or DIoU or EIoU or SIoU or WIoU or MPDIoU or LMPDIoU:  # Distance or Complete IoU
            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  # 中心点距离的平方
            if CIoU:
                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的计算
                else:
                    return iou - (rho2 / c2 + torch.pow(v * alpha_ciou + eps, alpha))  # CIoU
            elif MPDIoU:
                d1 = (b2_x1 - b1_x1) ** 2 + (b2_y1 - b1_y1) ** 2
                d2 = (b2_x2 - b1_x2) ** 2 + (b2_y2 - b1_y2) ** 2
                w = (b2_x2 - b2_x1)  # x2 - x1
                h = (b2_y2 - b2_y1)  # y2 - y1
                if Focal:
                    return iou - ((d1 + d2) / (w ** 2 + h ** 2)), torch.pow(inter / (union + eps), gamma)# Focal_MPDIoU
                else:
                    return iou - (d1 + d2) / (w ** 2 + h ** 2)
            elif LMPDIoU:
                d1 = (b2_x1 - b1_x1) ** 2 + (b2_y1 - b1_y1) ** 2
                d2 = (b2_x2 - b1_x2) ** 2 + (b2_y2 - b1_y2) ** 2
                w = (b2_x2 - b2_x1)  # x2 - x1
                h = (b2_y2 - b2_y1)  # y2 - y1
                if Focal:
                    return 1 - (iou - (d1 + d2) / (w ** 2 + h ** 2)), torch.pow(inter / (union + eps), gamma)# Focal_MPDIo  # MPDIoU
                else:
                    return 1 - iou + d1 / (w ** 2 + h ** 2) + d2 / (w ** 2 + h ** 2)
            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
                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的计算
                else:
                    return iou - torch.pow(0.5 * (distance_cost + shape_cost) + eps, alpha)  # SIou
            elif WIoU:
                self = WIoU_Scale(1 - (inter / union))
                dist = getattr(WIoU_Scale, '_scaled_loss')(self)
                return iou * dist  # WIoU
 
            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
        else:
            return iou - torch.pow((c_area - union) / c_area + eps, alpha) # GIoU
    if Focal:
        return iou, torch.pow(inter / (union + eps), gamma)  # Focal_IoU
    else:
        return iou  # IoU的值

② ultralytics/utils/loss.py文件

接下来，需要修改loss.py文件中的内容。

before

after

③ ultralytics/utils/tal.py文件

before

after

2 各种机制的使用

与上述内容类比，如果将对应机制设置为True则开启，否则关闭。之后，可以尝试多种组合方式去训练模型。

那么。接下来开始训练模型吧！！！

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【YOLOv8改进[损失函数]】使用结合InnerIoU和Focaler的各种损失函数助力YOLOv8更优秀

一 回归损失函数（Bounding Box Regression Loss）

1 Inner-IoU