写出Lovasz-Softmax Loss的代码

Lovasz-Softmax Loss是一种用于处理多类别分割任务的损失函数，尤其适用于那些类别不平衡的数据集。它结合了传统softmax交叉熵和Jaccard相似度的思想。以下是使用PyTorch实现 Lovasz-Softmax Loss的基本代码：

import torch
from scipy.special import softmax

def lovasz_grad(gt_sorted):
    """
    Computes gradient of the Lovasz extension w.r.t sorted errors
    See Alg. 1 in paper
    """
    p = len(gt_sorted)
    gts = gt_sorted.sum()
    intersection = gts - gt_sorted.float().cumsum(0)
    union = gts + (1 - gt_sorted).float().cumsum(0)
    jaccard = 1. - intersection / union
    if p > 1: # cover 1-pixel case
        jaccard[1:] = jaccard[1:] - jaccard[:-1]
    return jaccard

def lovasz_softmax_flat(probas, labels, classes='present', per_image=False, ignore=None):
    """
    Multi-class Lovasz-Softmax loss
    probas: [B, C, H, W] Variable, class probabilities at each prediction (between 0 and 1).
    labels: [B, H, W] Tensor, ground truth labels (between 0 and C - 1)
    classes: 'all' for all, 'present' for classes present in labels, or a list of classes to average.
    per_image: compute the loss per image instead of per batch
    ignore: void class id
    """
    if per_image:
        loss = mean(lovasz_softmax_flat(probas[i], labels[i], classes, ignore=ignore)
                    for i in range(labels.size(0)))
    else:
        losses = []
        C = probas.size(1)
        if ignore is not None:
            valid = (labels != ignore)
        else:
            valid = labels >= 0
        for c in range(C):
            fg = (labels == c) & valid
            if classes == 'present':
                fg_sum = fg.sum(dim=(1, 2))
                if fg_sum.item() > 0:
                    if classes == 'all':
                        if ignore is not None:
                            valid_c = (labels != (c + ignore)) & valid
                            fg = fg & valid_c
                    else:
                        fg = fg[labels == c]
            elif c not in classes:
                continue
            if fg.any():
                if permute:
                    fg = fg[:, :, None].expand_as(probas)
                    fg = fg.contiguous().view(-1)
                    probas_c = probas[:, c].contiguous().view(-1)
                else:
                    fg = fg.view(-1)
                    probas_c = probas[fg, c]
                lab_c = labels.new_full((probas_c.numel(),), c, dtype=torch.long)
                lab_c = lab_c[fg]
                loss = lovasz_loss(probas_c, lab_c, reduce=False)
                losses.append(loss.view(-1, 1))

        loss = sum(losses)

    return loss

# 使用示例
probas = torch.rand(5, 10, 28, 28)
labels = torch.randint(0, 9, (5, 28, 28))

loss = lovasz_softmax_flat(probas, labels)

注意，这个实现需要`scipy`库来进行softmax操作，以及一些额外的计算。如果你的环境中没有安装`scipy`，可以尝试其他开源库如`pylops`提供类似的功能。同时，`permute`变量在这里被假设为True，表示是否需要对输入概率分布进行维度转换。