focal eiou loss

### Focal EIOU Loss Implementation and Explanation in Object Detection In the context of object detection, loss functions play a crucial role in training models to accurately predict bounding boxes around objects. The focal EIOU (Extended Intersection over Union) loss function is an advanced variant that addresses some limitations found in traditional IoU-based losses. The standard IoU measures how well two bounding boxes overlap but does not account for other factors like scale or aspect ratio differences between predicted and ground truth boxes. To improve upon this, researchers introduced variants such as CIoU (Complete IoU), DIoU (Distance IoU), and finally EIoU which considers three aspects: - **Overlap**: Measures intersection area relative to union. - **Scale Difference**: Accounts for size discrepancy by penalizing predictions with different scales more heavily. - **Aspect Ratio Distortion**: Penalizes distortions along both axes independently rather than just considering overall shape similarity[^1]. Focal loss modifies cross entropy so it focuses on hard examples during training while reducing contribution from easy negatives. Combining these ideas leads us to define focal-EIoU as follows: \[ \text{FL}(p_t)=\alpha(1-p_t)^{\gamma}\log(p_t)\] Where \( p_t \) represents prediction confidence score after applying sigmoid activation. For regression part we use modified version of EIoU where weights are adjusted according to difficulty level indicated through classification branch output. Here's Python code implementing focal EIoU loss: ```python import torch from torch import nn class FocalEIoULoss(nn.Module): def __init__(self, alpha=0.25, gamma=2.0, eps=1e-7): super(FocalEIoULoss, self).__init__() self.alpha = alpha self.gamma = gamma self.eps = eps def forward(self, pred_boxes, target_boxes, labels): """ Args: pred_boxes: Predicted box coordinates [batch_size, num_anchors, 4]. target_boxes: Ground-truth box coordinates [batch_size, num_anchors, 4]. labels: Classification scores indicating positive/negative samples [batch_size, num_anchors]. Returns: Total loss value combining classification and localization components. """ # Compute pairwise distances between centers c_x_p, c_y_p = pred_boxes[:, :, :2].split([1, 1], dim=-1) c_x_g, c_y_g = target_boxes[:, :, :2].split([1, 1], dim=-1) dist_center = ((c_x_p - c_x_g)**2 + (c_y_p - c_y_g)**2).sqrt() w_pred, h_pred = pred_boxes[:, :, 2:].split([1, 1], dim=-1) w_gt, h_gt = target_boxes[:, :, 2:].split([1, 1], dim=-1) iou_loss_term = _compute_eiou(pred_boxes, target_boxes) cls_focal_loss = -(labels * (1-labels)**self.gamma * torch.log(torch.sigmoid(labels)+self.eps)).mean()[^2] total_loss = cls_focal_loss + iou_loss_term.mean() return total_loss def _compute_eiou(box_a, box_b): """Helper function computing Extended IOU.""" # Calculate center points distance squared rho_squared = ... # Width/height difference terms v_w = ... v_h = ... # Regular IoU component ious = ... eious = ious - (rho_squared / ...) - (...*(v_w+v_h)/(...)) return eious ```

Focal EIoU loss是一种用于目标检测任务的损失函数，它结合了Focal Loss和EIoU Loss的优点。下面是Focal EIoU loss的公式推导过程： 首先，我们回顾一下EIoU Loss的公式： $$ L_{EIoU} = 1 - IoU + E[IoU] $$ 其中，IoU是预测框和真实框的交并比，E[IoU]是IoU的期望值，可以通过计算真实框和预测框的中心点、长宽等信息得到。 接下来，我们考虑如何将Focal Loss和EIoU Loss结合起来。Focal Loss的公式如下： $$ L_{Focal} = -\alpha(1 - p_t)^\gamma log(p_t) $$ 其中，$p_t$是模型预测为正样本的概率，$\alpha$和$\gamma$是超参数，用于控制正负样本的权重。Focal Loss的主要思想是减少易分样本的权重，使难分样本的权重更大。 将Focal Loss和EIoU Loss结合起来，得到Focal EIoU Loss的公式如下： $$ L_{Focal\ EIoU} = -\alpha(1 - p_t)^\gamma log(p_t)(1 - IoU + E[IoU]) $$ 其中，$p_t$，$\alpha$，$\gamma$和E[IoU]的含义与上文相同。这个公式的含义是，在分类损失的基础上，引入IoU的因素，加强了对目标检测任务中难以分类的样本的重视。 至此，我们完成了Focal EIoU Loss的公式推导过程。