Various IoU descriptions in target detection

1. Description

IoU loss is the most common loss function in target detection, which represents the intersection ratio of the real box and the predicted box.

2. Code implementation

import math

def bbox_iou(box1, box2, xywh=True, GIoU=False, DIoU=False, CIoU=False, eps=1e-7):
    # Returns Intersection over Union IoU(n,1) of box1(n,4) to box2(n,4)
    # Get the coordinates of bounding boxes
    if xywh:  # transform from xywh to xyxy
        x1, y1, w1, h1 = box1.chunk(4, -1)  # n*4 --> n*1, n*1, n*1, n*1
        x2, y2, w2, h2 = box2.chunk(4, -1)
        b1_x1, b1_x2, b1_y1, b1_y2 = x1 - w1 / 2, x1 + w1 / 2, y1 - h1 / 2, y1 + h1 / 2
        b2_x1, b2_x2, b2_y1, b2_y2 = x2 - w2 / 2, x2 + w2 / 2, y2 - h2 / 2, y2 + h2 / 2
    else:  # x1, y1, x2, y2 = box
        b1_x1, b1_y1, b1_x2, b1_y2 = box1.chunk(4, -1)  # n*4 --> n*1, n*1, n*1, n*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   n*1
    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   n*1
    union = w1 * h1 + w2 * h2 - inter + eps

    # IoU  n*1
    iou = inter / union
    if CIoU or DIoU or GIoU:
        cw = b1_x2.maximum(b2_x2) - b1_x1.minimum(b2_x1)  # convex width
        ch = b1_y2.maximum(b2_y2) - b1_y1.minimum(b2_y1)  # convex height
        if CIoU or DIoU:  # Distance or Complete IoU
            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:
                v = (4 / math.pi ** 2) * (torch.atan(w2 / h2) - torch.atan(w1 / h1)).pow(2)
                with torch.no_grad():
                    alpha = v / (v - iou + (1 + eps))
                return iou - (rho2 / c2 + v * alpha)  # CIoU = IoU - center_dist / diagonal_dist - length_width_ratio
            return iou - rho2 / c2  # DIoU = IoU - center_dist / diagonal_dist
        c_area = cw * ch + eps  # convex area
        return iou - (c_area - union) / c_area  # GIoU = IoU - (area_convex - area_union) / area_convex
    return iou  # IoU