ciou损伤函数公式

### CIoU Loss Function Formula CIoU (Complete Intersection over Union) 是一种改进版的 IoU 损失函数，在计算机视觉和目标检测领域广泛应用。相比于传统的 IoU 和 GIoU，CIoU 不仅考虑了预测框与真实框之间的重叠面积比例，还加入了中心点距离以及宽高比的因素。 具体来说，CIoU 的定义如下： \[ \text{CIoU} = 1 - \left(\frac{\text{IOU}}{1+\alpha\cdot v}\right)-\alpha\cdot v \] 其中， - \( IOU \) 表示交并比； - \( d(c_{box},c_{gt})=\rho^{2}(c_{box}-c_{gt})/\rho^{2}_{diag}(bbox_{img}) \)，\( c_{box} \) 和 \( c_{gt} \) 分别代表预测框和真实框的中心坐标，而 \( bbox_{img} \) 则指代整个图片的最大外接矩形对角线长度平方； - \( v=(\frac{\pi}{4})(arctan(w_{gt}/h_{gt})-arctan(w_{pred}/h_{pred}))^2 \)，这里 \( w,h \) 对应宽度高度参数； - \( \alpha \) 定义为 \( \alpha=v/(1-\text{IOU}+v)\epsilon \)，用于调整权重因子使得当两个框形状相似时减少惩罚力度[^1]。 ```python import torch def ciou_loss(preds, targets): eps = 1e-7 # 获取边框的左上角和右下角坐标 preds_left_top = preds[:, :2] preds_right_bottom = preds[:, 2:] targets_left_top = targets[:, :2] targets_right_bottom = targets[:, 2:] # 计算交集部分 intersect_left_top = torch.max(preds_left_top, targets_left_top) intersect_right_bottom = torch.min(preds_right_bottom, targets_right_bottom) intersection_wh = (intersect_right_bottom - intersect_left_top).clamp(min=0.) intersection_area = intersection_wh[..., 0] * intersection_wh[..., 1] # 计算各自的面积 preds_area = ((preds_right_bottom - preds_left_top)[..., 0]) * \ ((preds_right_bottom - preds_left_top)[..., 1]) target_area = ((targets_right_bottom - targets_left_top)[..., 0]) * \ ((targets_right_bottom - targets_left_top)[..., 1]) union_area = preds_area + target_area - intersection_area + eps ious = intersection_area / union_area # 中心点距离 center_distance_squared = ( (preds_left_top + preds_right_bottom - targets_left_top - targets_right_bottom)**2).sum(dim=-1)/4. # 图片最大外接矩形对角线距离 enclosing_box_diag_squared = ( (torch.max(preds_right_bottom, targets_right_bottom) - torch.min(preds_left_top, targets_left_top))**2).sum(dim=-1)+eps u = center_distance_squared / enclosing_box_diag_squared # 宽高比一致性项 wh_ratio_clipped = torch.clamp( (preds_right_bottom - preds_left_top)/(targets_right_bottom-targets_left_top), min=0., max=1.) v = (4./math.pi ** 2)*(torch.atan(wh_ratio_clipped[:, 0])-torch.atan(wh_ratio_clipped[:, 1]))**2 alpha = v / (1.-ious+v+eps) ciou_term = u + alpha*v return 1. - ious + ciou_term ```