【Focal Loss】简单理解 及 Pytorch 代码 Focal Loss for Dense Object Detection

 

一、首先回顾下“交叉熵loss Cross Entropy Loss” 

      CE(Pi)=-log(Pi)

二、一般地说，我们数据集会存在类别不平衡问题，很多人会在loss上对应不同类别设置不同系数

                    

       loss就变成了上面的样子

三、Focal loss其实就是通过数学公式上的改变，扩大了不平衡因素在loss上的影响

                           

        这里的at 依然是和“二里面的”那个手动的一个意思！，这是他们文中的意思！我们来分析下！首先，这个的存在，无论为“预测器”分对分错，都会减小loss的值！！！

                        

          从上面一段话，我们可以看出，当某一个类别分类预测概率越来越高（分类准确的情况下），那么loss会因为的存在而被大大降低！这也是我们所希望的！！！当一个类别预测概率小于0.5，也就是基本上被判断到了别的类别去了！分错了！loss相对于“分对了”的情况而言最多只能减少4倍！！！loss减少量是“分对情况”下的“扩大”几十倍，百倍，千倍！

四、代码

这些，github上也有，那么怎么用呢？，顺边给大家lovasz_softmax loss的代码

使用小例子,图像分割为例子

#正常ce loss
loss  = F.bceloss(F.softmax(pred), target)

#Focal loss
loss  = FocalLoss2d(F.softmax(pred), target)

#lovasz_softmax
loss  = lovasz_softmax(F.softmax(pred1,dim=1), target)

class FocalLoss2d(torch.nn.Module):
    def __init__(self,  weight=None, size_average=True, ignore_index=255):
        super(FocalLoss2d, self).__init__()
        self.gamma = 2
        self.nll_loss = torch.nn.NLLLoss2d(weight, size_average)
    def forward(self, inputs, targets):
        return self.nll_loss((1 - F.softmax(inputs,1)) ** self.gamma * F.log_softmax(inputs,1), targets)

def softmax_focalloss(input, target, weight, size_average, ignore_index, reduce=True):
    return F.nll_loss((1 - F.softmax(inputs,1)) ** gamma * F.log_softmax(inputs,1), targets)

"""
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


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:p] = jaccard[1:p] - jaccard[0:-1]
    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) / 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) / union)
        ious.append(iou)
    ious = map(mean, 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, only_present=False, 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)
      only_present: average only on classes present in ground truth
      per_image: compute the loss per image instead of per batch
      ignore: void class labels
    """
    if per_image:
        loss = mean(lovasz_softmax_flat(*flatten_probas(prob.unsqueeze(0), lab.unsqueeze(0), ignore), only_present=only_present)
                          for prob, lab in zip(probas, labels))
    else:
        loss = lovasz_softmax_flat(*flatten_probas(probas, labels, ignore), only_present=only_present)
    return loss


def lovasz_softmax_flat(probas, labels, only_present=False):
    """
    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)
      only_present: average only on classes present in ground truth
    """
    C = probas.size(1)
    losses = []
    for c in range(C):
        fg = (labels == c).float() # foreground for class c
        if only_present and fg.sum() == 0:
            continue
        errors = (Variable(fg) - probas[:, c]).abs()
        errors_sorted, perm = torch.sort(errors, 0, descending=True)
        perm = perm.data
        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
    """
    B, C, H, W = probas.size()
    probas = probas.permute(0, 2, 3, 1).contiguous().view(-1, C)  # B * H * W, C = P, C
    labels = labels.view(-1)
    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 mean(l, ignore_nan=False, empty=0):
    """
    nanmean compatible with generators.
    """
    l = iter(l)
    if ignore_nan:
        l = ifilterfalse(np.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