时序动作分割中常用的评价指标（Acc,Segmental Edit Score, Segmental F1-Score）

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MS-TCN、MS-TCN++和BCN都使用了这三个评价指标，有必要深入一下。

1.frame-wise Accuracy

正确帧数/总帧数

"Acc: %.4f" % (100*float(correct)/total)

2.Segmental edit distance

编辑距离，又称为莱文斯坦距离，NLP中常用来衡量两个字符串之间的差异程度。Segmental edit distance考量了每两帧之间，从A帧替换到B帧所需的最小操作次数。即考量了两帧之间的差异性。Edit distance越大，两帧之间的差异就越大。Segmental edit distance也就是考量了每两帧之间的差异性。
以MS-TCN中的eval.py为例：

def get_labels_start_end_time(frame_wise_labels, bg_class=["background"]):
    labels = []
    starts = []
    ends = []
    last_label = frame_wise_labels[0]
    if frame_wise_labels[0] not in bg_class:
        labels.append(frame_wise_labels[0])
        starts.append(0)
    for i in range(len(frame_wise_labels)):
        if frame_wise_labels[i] != last_label:
            if frame_wise_labels[i] not in bg_class:
                labels.append(frame_wise_labels[i])
                starts.append(i)
            if last_label not in bg_class:
                ends.append(i)
            last_label = frame_wise_labels[i]
    if last_label not in bg_class:
        ends.append(i + 1)
    return labels, starts, ends


def levenstein(p, y, norm=False):
    m_row = len(p)    
    n_col = len(y)
    D = np.zeros([m_row+1, n_col+1], np.float)
    for i in range(m_row+1):
        D[i, 0] = i
    for i in range(n_col+1):
        D[0, i] = i

    for j in range(1, n_col+1):
        for i in range(1, m_row+1):
            if y[j-1] == p[i-1]:
                D[i, j] = D[i-1, j-1]
            else:
                D[i, j] = min(D[i-1, j] + 1,
                              D[i, j-1] + 1,
                              D[i-1, j-1] + 1)
    
    if norm:
        score = (1 - D[-1, -1]/max(m_row, n_col)) * 100
    else:
        score = D[-1, -1]

    return score


def edit_score(recognized, ground_truth, norm=True, bg_class=["background"]):
    P, _, _ = get_labels_start_end_time(recognized, bg_class)
    Y, _, _ = get_labels_start_end_time(ground_truth, bg_class)
    return levenstein(P, Y, norm)

3.Segmental F1-Score

分段重叠阈值的阈值是根据联合的IOU比率决定的

def f_score(recognized, ground_truth, overlap, bg_class=["background"]):
    p_label, p_start, p_end = get_labels_start_end_time(recognized, bg_class)
    y_label, y_start, y_end = get_labels_start_end_time(ground_truth, bg_class)

    tp = 0
    fp = 0

    hits = np.zeros(len(y_label))

    for j in range(len(p_label)):
        intersection = np.minimum(p_end[j], y_end) - np.maximum(p_start[j], y_start)
        union = np.maximum(p_end[j], y_end) - np.minimum(p_start[j], y_start)
        IoU = (1.0*intersection / union)*([p_label[j] == y_label[x] for x in range(len(y_label))])
        # Get the best scoring segment
        idx = np.array(IoU).argmax()

        if IoU[idx] >= overlap and not hits[idx]:
            tp += 1
            hits[idx] = 1
        else:
            fp += 1
    fn = len(y_label) - sum(hits)
    return float(tp), float(fp), float(fn)

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