NMS(Non-maximum suppression，非极大值抑制)算法

NMS广泛应用于目标检测算法中。其目的是为了消除多余的候选框，找到最佳的物体检测位置。

现在假设有有一个候选的boxes的集合B和其对应的scores集合S：

1. 找出分数最高的M；

2. 将M对应的box从B中删除；

3. 将删除的box添加到集合D中；

4. 从B中删除与M对应的box重叠区域大于阈值Nt的其他框；

5. 重复上述步骤1-4。

伪代码如下：

其中si可表述为：

Mask RCNN中的python实现：

def non_max_suppression(boxes, scores, threshold):
    """Performs non-maximum suppression and returns indices of kept boxes.
    boxes: [N, (y1, x1, y2, x2)]. Notice that (y2, x2) lays outside the box.
    scores: 1-D array of box scores.
    threshold: Float. IoU threshold to use for filtering.
    """
    assert boxes.shape[0] > 0
    if boxes.dtype.kind != "f":
        boxes = boxes.astype(np.float32)

    # Compute box areas
    y1 = boxes[:, 0]
    x1 = boxes[:, 1]
    y2 = boxes[:, 2]
    x2 = boxes[:, 3]
    area = (y2 - y1) * (x2 - x1)

    # Get indicies of boxes sorted by scores (highest first)
    ixs = scores.argsort()[::-1]

    pick = []
    while len(ixs) > 0:
        # Pick top box and add its index to the list
        i = ixs[0]
        pick.append(i)
        # Compute IoU of the picked box with the rest
        iou = compute_iou(boxes[i], boxes[ixs[1:]], area[i], area[ixs[1:]])
        # Identify boxes with IoU over the threshold. This
        # returns indices into ixs[1:], so add 1 to get
        # indices into ixs.
        remove_ixs = np.where(iou > threshold)[0] + 1
        # Remove indices of the picked and overlapped boxes.
        ixs = np.delete(ixs, remove_ixs)
        ixs = np.delete(ixs, 0)
    return np.array(pick, dtype=np.int32)