总结下LovaszSoftmax损失函数（pytorch版）_lovasz-softmax loss

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0.开始是想把自己遇到的损失函数都总结一下，结果第一个unet++的损失函数就卡住了。发现自己理解的还远远不够啊。那就先总结它吧。

1.这个算法出自论文《The Lovasz-Softmax loss: A tractable surrogate for the optimization of the ´ intersection-over-union measure in neural networks》。粗看就是IOU方法的一个优化方法。

先是提出了loss的最基础形式：公式3 和4 

然后说这个有啥啥啥问题。将它变个形：就是公式5  6 

变完了形还是不满意,再转成具有凸解形式： 就是公式8  9 

 8就是最终变形的loss函数形式。

然后专门讲了公式9的实现过程：

里面的理论一大堆，没咋看懂。后来就直接看pytorch代码了。有些地方实现的过程还是懵懵懂懂啊。在网上找相关资料发现翻译的我能看明白的也基本木有啊，那贴上自己的理解吧。

2.贴代码加注释：

"""
Lovasz-Softmax and Jaccard hinge loss in PyTorch
Maxim Berman 2018 ESAT-PSI KU Leuven (MIT License)
"""
 
from __future__ import print_function, division
 
import torch
from torch.autograd import Variable
import torch.nn.functional as F
import numpy as np
try:
    from itertools import  ifilterfalse
except ImportError: # py3k
    from itertools import  filterfalse as ifilterfalse
 
 
#函数输入是一个排过序的 标签组  越靠近前面的标签 表示这个像素点与真值的误差越大
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)
    print("p = ", p)
    print("gt_sorted = ", gt_sorted)
    gts = gt_sorted.sum()#求个和
    #gt_sorted.float().cumsum(0) 1维的 计算的是累加和 例如 【1 2 3 4 5】 做完后就是【1 3 6 10 15】
    #这个intersection是用累加和的值按维度减 累加数组的值，目的是做啥呢  看字面是取交集
    intersection = gts - gt_sorted.float().cumsum(0) #对应论文Algorithm 1的第3行
    union = gts + (1 - gt_sorted).float().cumsum(0) #对应论文Algorithm 1的第4行
    jaccard = 1. - intersection / union #对应论文Algorithm 1的第5行
    if p > 1: # cover 1-pixel case
        jaccard[1:p] = jaccard[1:p] - jaccard[0:-1]#对应论文Algorithm 1的第7行
    return jaccard
 
 
def iou_binary(preds, labels, EMPTY=1., ignore=None, per_image=True):
    """
    IoU for foreground class
    binary: 1 foreground, 0 background
    """
    if not per_image:
        preds, labels = (preds,), (labels,)
    ious = []
    for pred, label in zip(preds, labels):
        intersection = ((label == 1) & (pred == 1)).sum()
        union = ((label == 1) | ((pred == 1) & (label != ignore))).sum()
        if not union:
            iou = EMPTY
        else:
            iou = float(intersection) / float(union)
        ious.append(iou)
    iou = mean(ious)    # mean accross images if per_image
    return 100 * iou
 
 
def iou(preds, labels, C, EMPTY=1., ignore=None, per_image=False):
    """
    Array of IoU for each (non ignored) class
    """
    if not per_image:
        preds, labels = (preds,), (labels,)
    ious = []
    for pred, label in zip(preds, labels):
        iou = []    
        for i in range(C):
            if i != ignore: # The ignored label is sometimes among predicted classes (ENet - CityScapes)
                intersection = ((label == i) & (pred == i)).sum()
                union = ((label == i) | ((pred == i) & (label != ignore))).sum()
                if not union:
                    iou.append(EMPTY)
                else:
                    iou.append(float(intersection) / float(union))
        ious.append(iou)
    ious = [mean(iou) for iou in zip(*ious)] # mean accross images if per_image
    return 100 * np.array(ious)
 
 
# --------------------------- BINARY LOSSES ---------------------------
 
 
def lovasz_hinge(logits, labels, per_image=True, ignore=None):
    """
    Binary Lovasz hinge loss
      logits: [B, H, W] Variable, logits at each pixel (between -\infty and +\infty)
      labels: [B, H, W] Tensor, binary ground truth masks (0 or 1)
      per_image: compute the loss per image instead of per batch
      ignore: void class id
    """
    if per_image:
        loss = mean(lovasz_hinge_flat(*flatten_binary_scores(log.unsqueeze(0), lab.unsqueeze(0), ignore))
                          for log, lab in zip(logits, labels))
    else:
        loss = lovasz_hinge_flat(*flatten_binary_scores(logits, labels, ignore))
    return loss
 
 
def lovasz_hinge_flat(logits, labels):
    """
    Binary Lovasz hinge loss
      logits: [P] Variable, logits at each prediction (between -\infty and +\infty)
      labels: [P] Tensor, binary ground truth labels (0 or 1)
      ignore: label to ignore
    """
    if len(labels) == 0:
        # only void pixels, the gradients should be 0
        return logits.sum() * 0.
    signs = 2. * labels.float() - 1.
    errors = (1. - logits * Variable(signs))
    errors_sorted, perm = torch.sort(errors, dim=0, descending=True)
    perm = perm.data
    gt_sorted = labels[perm]
    grad = lovasz_grad(gt_sorted)
    loss = torch.dot(F.relu(errors_sorted), Variable(grad))
    return loss
 
 
def flatten_binary_scores(scores, labels, ignore=None):
    """
    Flattens predictions in the batch (binary case)
    Remove labels equal to 'ignore'
    """
    scores = scores.view(-1)
    labels = labels.view(-1)
    if ignore is None:
        return scores, labels
    valid = (labels != ignore)
    vscores = scores[valid]
    vlabels = labels[valid]
    return vscores, vlabels
 
 
class StableBCELoss(torch.nn.modules.Module):
    def __init__(self):
         super(StableBCELoss, self).__init__()
    def forward(self, input, target):
         neg_abs = - input.abs()
         loss = input.clamp(min=0) - input * target + (1 + neg_abs.exp()).log()
         return loss.mean()
 
 
def binary_xloss(logits, labels, ignore=None):
    """
    Binary Cross entropy loss
      logits: [B, H, W] Variable, logits at each pixel (between -\infty and +\infty)
      labels: [B, H, W] Tensor, binary ground truth masks (0 or 1)
      ignore: void class id
    """
    logits, labels = flatten_binary_scores(logits, labels, ignore)
    loss = StableBCELoss()(logits, Variable(labels.float()))
    return loss
 
 
# --------------------------- MULTICLASS LOSSES ---------------------------
 
 
def lovasz_softmax(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).
              Interpreted as binary (sigmoid) output with outputs of size [B, H, W].
      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 labels
    """
    print("probas.shape = ", probas.shape)
    if per_image:
        loss = mean(lovasz_softmax_flat(*flatten_probas(prob.unsqueeze(0), lab.unsqueeze(0), ignore), classes=classes)
                          for prob, lab in zip(probas, labels))
    else:
    	  #lovasz_softmax_flat的输入就是probas 【262144 2】  labels【262144】
        loss = lovasz_softmax_flat(*flatten_probas(probas, labels, ignore), classes=classes)
    return loss
 
 
#这个函数是计算损失函数的部位
def lovasz_softmax_flat(probas, labels, classes='present'):
    """
    Multi-class Lovasz-Softmax loss
      probas: [P, C] Variable, class probabilities at each prediction (between 0 and 1)
      labels: [P] 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.
    """
    #预测像素点个数，一张512*512的图
    if probas.numel() == 0:#返回数组中元素的个数
        # only void pixels, the gradients should be 0
        return probas * 0.
    C = probas.size(1)#获得通道数呗  就是预测几类
    losses = []
    #class_to_sum = [0 1]  类的种类总数 用list存储
    class_to_sum = list(range(C)) if classes in ['all', 'present'] else classes
    for c in class_to_sum:
        fg = (labels == c).float() # foreground for class c  如果语义标注数据与符合第c类，fg中存储1.0样数据
        if (classes is 'present' and fg.sum() == 0):
            continue
        if C == 1:
            if len(classes) > 1:
                raise ValueError('Sigmoid output possible only with 1 class')
            class_pred = probas[:, 0]
        else:
            class_pred = probas[:, c]#取出第c类预测值 是介于 0~1之间的float数
        #errors 是预测结果与标签结果差的绝对值
        errors = (Variable(fg) - class_pred).abs()
        #对误差排序 从大到小排   perm是下标值 errors_sorted 是排序后的预测值
        errors_sorted, perm = torch.sort(errors, 0, descending=True)
 
        perm = perm.data
        #排序后的标签值
        fg_sorted = fg[perm]
        
        losses.append(torch.dot(errors_sorted, Variable(lovasz_grad(fg_sorted))))
    return mean(losses)
 
 
def flatten_probas(probas, labels, ignore=None):
    """
    Flattens predictions in the batch
    """
    #在这维度为probas 【1 2 512 512】  labels维度为【1 1 512 512】
    if probas.dim() == 3:#dim()数组维度
        # assumes output of a sigmoid layer
        B, H, W = probas.size()
        probas = probas.view(B, 1, H, W)
    B, C, H, W = probas.size()#数组维度
    #维度交换并变形   将probas.permute(0, 2, 3, 1)变换后的前3维合并成1维，通道不变
    probas = probas.permute(0, 2, 3, 1).contiguous().view(-1, C)  # B * H * W, C = P, C
    #
    labels = labels.view(-1)
    #我的代码是用默认值 直接返回了 probas  labels  两个压缩完事的东西  
    #在这维度为probas 【262144 2】  labels维度为【262144】
    
    if ignore is None:
        return probas, labels
    valid = (labels != ignore)
    vprobas = probas[valid.nonzero().squeeze()]
    vlabels = labels[valid]
    return vprobas, vlabels
 
def xloss(logits, labels, ignore=None):
    """
    Cross entropy loss
    """
    return F.cross_entropy(logits, Variable(labels), ignore_index=255)
 
 
# --------------------------- HELPER FUNCTIONS ---------------------------
def isnan(x):
    return x != x
    
    
def mean(l, ignore_nan=False, empty=0):
    """
    nanmean compatible with generators.
    """
    l = iter(l)
    if ignore_nan:
        l = ifilterfalse(isnan, l)
    try:
        n = 1
        acc = next(l)
    except StopIteration:
        if empty == 'raise':
            raise ValueError('Empty mean')
        return empty
    for n, v in enumerate(l, 2):
        acc += v
    if n == 1:
        return acc
    return acc / n

3.论文中的某些地方与代码的对应。