语义分割中的度量标准

pixel accuracy (PA，像素精度)

标记正确的像素占总像素的比例

$$
PA=\frac{\sum_{i=1}^kp_{ii}}{\sum_{i=0}^k\sum_{j=0}^kp_{ij}}
$$

mean pixel accuracy (MPA, 均像素精度)

计算每个类中被正确分类像素的比例，然后平均

$$
MPA=\frac{1}{k+1}\sum_{i=0}^{k}\frac{p_{ii}}{\sum_{j=0}^kp_{ij}}
$$

Mean Intersection over Union(MIoU, 均交并比)

语义分割标准度量。计算两个集合的交集和并集之比。在semantic segmentation中，为真实值（ground truth）与预测值（predicted segmentation）的比值。这个比例变形为正真数（intersection）比上真正、假负、假正（并集）之和。在每个类上计算IoU，平均。

$$
MIoU=\frac{1}{k+1}\sum_{i=0}^k\frac{p_{ii}}{\sum_{j=0}^k p_{ij}+\sum_{j=0}^kp_{ji}-p_{ii}}
$$

Frequency Weight Intersection over Union(FWIoU, 频权交并比)

MIoU的提升。根据每个类出现的频率设置权重

$$
FWIoU=\frac{1}{\sum_{i=0}^k\sum_{j=0}^kp_{ij}}\sum_{i=0}^k\frac{p_{ii}}{\sum_{j=0}^k\sum_{j=0}^kp_{ji}-p_{ii}}
$$

#计算label_true和label_pred对应相同的就在矩阵中对应坐标加1。a和b保存着各个像素的分的类别
def _fast_hist(label_true, label_pred, n_class):
    #过滤掉多余的分类
    mask = (label_true >= 0) & (label_true < n_class)
    #bincount用于统计在范围内出现的个数，即直方图，如果不够n^2个，
    #那就填充到n^2，这样可以reshpe为n*n的矩阵，正好表示分割图和正确标记图在相同
    #类别上像素出现的个数
    hist = np.bincount(
        n_class * label_true[mask].astype(int) +
        label_pred[mask], minlength=n_class ** 2).reshape(n_class, n_class)
    return hist

def label_accuracy_score(label_trues, label_preds, n_class):
    """Returns accuracy score evaluation result.
      - overall accuracy
      - mean accuracy
      - mean IU
      - fwavacc
    """
    hist = np.zeros((n_class, n_class))
    for lt, lp in zip(label_trues, label_preds):
        hist += _fast_hist(lt.flatten(), lp.flatten(), n_class)
    acc = np.diag(hist).sum() / hist.sum()
    acc_cls = np.diag(hist) / hist.sum(axis=1)
    acc_cls = np.nanmean(acc_cls)
    iu = np.diag(hist) / (hist.sum(axis=1) + hist.sum(axis=0) - np.diag(hist))
    mean_iu = np.nanmean(iu)
    freq = hist.sum(axis=1) / hist.sum()
    fwavacc = (freq[freq > 0] * iu[freq > 0]).sum()
    return acc, acc_cls, mean_iu, fwavacc