About the principle and code implementation of Siou (review IOU, giou, Diou, CIO)

The paper ：https://arxiv.org/pdf/2205.12740.pdf
Code implementation （ unofficial ）：https://github.com/xialuxi/yolov5-car-plate/commit/aa41d1819b1fb03b4dc73e8a3e0000c46cfc370b
Pictures from video tutorials （ This big guy video tutorial yyds）：https://www.bilibili.com/video/BV1yi4y1g7ro?p=4

principle ：

From the earliest IoU To GIoU, Until then DIoU and CIoU, Now there is SIoU

L2 Loss and IoU Comparison of losses

GIoU Loss

A Represents the blue box , The largest rectangle .u representative GT Union with the prediction box .

DIoU Loss

On the left side of picture 1 is GIoU, The following is DIoU： Black stands for anchor, Blue represents the prediction box , The green one is GT box

CIoU Loss

SIoU Loss

On the basis of the above, the angle is considered
The paper also redefines the distance cost and shape cost,
angle cost The definition is as follows ：

The strange thing I see here is , This α Why bring into sin, And brought into the negative sin, Isn't that an unnecessary move ？σ Is the distance between the centers of the two boxes .

distance cost The definition is as follows ：

shape cost The definition is as follows ：

Whole lost Definition ：

There are still many details not analyzed 、 mining 、 discuss , Here is just a cursory sharing , Record .

Code implementation ：

！！！ Important things are to be repeated for 3 times , I didn't realize , I didn't realize , I didn't realize . From the big guy at the beginning of the link ：

        if SIoU:    # SIoU Loss https://arxiv.org/pdf/2205.12740.pdf
            sigma = torch.pow(cw ** 2 + ch ** 2, 0.5)
            sin_alpha_1 = ch / sigma
            sin_alpha_2 = cw / sigma
            threshold = pow(2, 0.5) / 2
            sin_alpha = torch.where(sin_alpha_1 > threshold, sin_alpha_2, sin_alpha_1)
            # angle_cost = 1 - 2 * torch.pow( torch.sin(torch.arcsin(sin_alpha) - np.pi/4), 2)
            angle_cost = torch.cos(torch.arcsin(sin_alpha) * 2 - np.pi / 2)
            rho_x = ((b2_x1 + b2_x2 - b1_x1 - b1_x2) / cw) ** 2
            rho_y = ((b2_y1 + b2_y2 - b1_y1 - b1_y2) / ch) ** 2
            gamma = 2 - angle_cost
            distance_cost = 2 - torch.exp(-1 * gamma * rho_x) - torch.exp(-1 * 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)
            return iou - 0.5 * (distance_cost + shape_cost)