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 ```