bbox_utils.py

#   Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

import math
import paddle
import numpy as np


def bbox2delta(src_boxes, tgt_boxes, weights=[1.0, 1.0, 1.0, 1.0]):
    """Encode bboxes to deltas.
    """
    src_w = src_boxes[:, 2] - src_boxes[:, 0]
    src_h = src_boxes[:, 3] - src_boxes[:, 1]
    src_ctr_x = src_boxes[:, 0] + 0.5 * src_w
    src_ctr_y = src_boxes[:, 1] + 0.5 * src_h

    tgt_w = tgt_boxes[:, 2] - tgt_boxes[:, 0]
    tgt_h = tgt_boxes[:, 3] - tgt_boxes[:, 1]
    tgt_ctr_x = tgt_boxes[:, 0] + 0.5 * tgt_w
    tgt_ctr_y = tgt_boxes[:, 1] + 0.5 * tgt_h

    wx, wy, ww, wh = weights
    dx = wx * (tgt_ctr_x - src_ctr_x) / src_w
    dy = wy * (tgt_ctr_y - src_ctr_y) / src_h
    dw = ww * paddle.log(tgt_w / src_w)
    dh = wh * paddle.log(tgt_h / src_h)

    deltas = paddle.stack((dx, dy, dw, dh), axis=1)
    return deltas


def delta2bbox(deltas, boxes, weights=[1.0, 1.0, 1.0, 1.0], max_shape=None):
    """Decode deltas to boxes. Used in RCNNBox,CascadeHead,RCNNHead,RetinaHead.
    Note: return tensor shape [n,1,4]
        If you want to add a reshape, please add after the calling code instead of here.
    """
    clip_scale = math.log(1000.0 / 16)

    widths = boxes[:, 2] - boxes[:, 0]
    heights = boxes[:, 3] - boxes[:, 1]
    ctr_x = boxes[:, 0] + 0.5 * widths
    ctr_y = boxes[:, 1] + 0.5 * heights

    wx, wy, ww, wh = weights
    dx = deltas[:, 0::4] / wx
    dy = deltas[:, 1::4] / wy
    dw = deltas[:, 2::4] / ww
    dh = deltas[:, 3::4] / wh
    # Prevent sending too large values into paddle.exp()
    dw = paddle.clip(dw, max=clip_scale)
    dh = paddle.clip(dh, max=clip_scale)

    pred_ctr_x = dx * widths.unsqueeze(1) + ctr_x.unsqueeze(1)
    pred_ctr_y = dy * heights.unsqueeze(1) + ctr_y.unsqueeze(1)
    pred_w = paddle.exp(dw) * widths.unsqueeze(1)
    pred_h = paddle.exp(dh) * heights.unsqueeze(1)

    pred_boxes = []
    pred_boxes.append(pred_ctr_x - 0.5 * pred_w)
    pred_boxes.append(pred_ctr_y - 0.5 * pred_h)
    pred_boxes.append(pred_ctr_x + 0.5 * pred_w)
    pred_boxes.append(pred_ctr_y + 0.5 * pred_h)
    pred_boxes = paddle.stack(pred_boxes, axis=-1)

    if max_shape is not None:
        pred_boxes[..., 0::2] = pred_boxes[..., 0::2].clip(
            min=0, max=max_shape[1])
        pred_boxes[..., 1::2] = pred_boxes[..., 1::2].clip(
            min=0, max=max_shape[0])
    return pred_boxes


def bbox2delta_v2(src_boxes,
                  tgt_boxes,
                  delta_mean=[0.0, 0.0, 0.0, 0.0],
                  delta_std=[1.0, 1.0, 1.0, 1.0]):
    """Encode bboxes to deltas.
    Modified from bbox2delta() which just use weight parameters to multiply deltas.
    """
    src_w = src_boxes[:, 2] - src_boxes[:, 0]
    src_h = src_boxes[:, 3] - src_boxes[:, 1]
    src_ctr_x = src_boxes[:, 0] + 0.5 * src_w
    src_ctr_y = src_boxes[:, 1] + 0.5 * src_h

    tgt_w = tgt_boxes[:, 2] - tgt_boxes[:, 0]
    tgt_h = tgt_boxes[:, 3] - tgt_boxes[:, 1]
    tgt_ctr_x = tgt_boxes[:, 0] + 0.5 * tgt_w
    tgt_ctr_y = tgt_boxes[:, 1] + 0.5 * tgt_h

    dx = (tgt_ctr_x - src_ctr_x) / src_w
    dy = (tgt_ctr_y - src_ctr_y) / src_h
    dw = paddle.log(tgt_w / src_w)
    dh = paddle.log(tgt_h / src_h)

    deltas = paddle.stack((dx, dy, dw, dh), axis=1)
    deltas = (
        deltas - paddle.to_tensor(delta_mean)) / paddle.to_tensor(delta_std)
    return deltas


def delta2bbox_v2(deltas,
                  boxes,
                  delta_mean=[0.0, 0.0, 0.0, 0.0],
                  delta_std=[1.0, 1.0, 1.0, 1.0],
                  max_shape=None,
                  ctr_clip=32.0):
    """Decode deltas to bboxes.
    Modified from delta2bbox() which just use weight parameters to be divided by deltas.
    Used in YOLOFHead.
    Note: return tensor shape [n,1,4]
        If you want to add a reshape, please add after the calling code instead of here.
    """
    clip_scale = math.log(1000.0 / 16)

    widths = boxes[:, 2] - boxes[:, 0]
    heights = boxes[:, 3] - boxes[:, 1]
    ctr_x = boxes[:, 0] + 0.5 * widths
    ctr_y = boxes[:, 1] + 0.5 * heights

    deltas = deltas * paddle.to_tensor(delta_std) + paddle.to_tensor(delta_mean)
    dx = deltas[:, 0::4]
    dy = deltas[:, 1::4]
    dw = deltas[:, 2::4]
    dh = deltas[:, 3::4]

    # Prevent sending too large values into paddle.exp()
    dx = dx * widths.unsqueeze(1)
    dy = dy * heights.unsqueeze(1)
    if ctr_clip is not None:
        dx = paddle.clip(dx, max=ctr_clip, min=-ctr_clip)
        dy = paddle.clip(dy, max=ctr_clip, min=-ctr_clip)
        dw = paddle.clip(dw, max=clip_scale)
        dh = paddle.clip(dh, max=clip_scale)
    else:
        dw = dw.clip(min=-ctr_clip, max=ctr_clip)
        dh = dh.clip(min=-ctr_clip, max=ctr_clip)

    pred_ctr_x = dx + ctr_x.unsqueeze(1)
    pred_ctr_y = dy + ctr_y.unsqueeze(1)
    pred_w = paddle.exp(dw) * widths.unsqueeze(1)
    pred_h = paddle.exp(dh) * heights.unsqueeze(1)

    pred_boxes = []
    pred_boxes.append(pred_ctr_x - 0.5 * pred_w)
    pred_boxes.append(pred_ctr_y - 0.5 * pred_h)
    pred_boxes.append(pred_ctr_x + 0.5 * pred_w)
    pred_boxes.append(pred_ctr_y + 0.5 * pred_h)
    pred_boxes = paddle.stack(pred_boxes, axis=-1)

    if max_shape is not None:
        pred_boxes[..., 0::2] = pred_boxes[..., 0::2].clip(
            min=0, max=max_shape[1])
        pred_boxes[..., 1::2] = pred_boxes[..., 1::2].clip(
            min=0, max=max_shape[0])
    return pred_boxes


def expand_bbox(bboxes, scale):
    w_half = (bboxes[:, 2] - bboxes[:, 0]) * .5
    h_half = (bboxes[:, 3] - bboxes[:, 1]) * .5
    x_c = (bboxes[:, 2] + bboxes[:, 0]) * .5
    y_c = (bboxes[:, 3] + bboxes[:, 1]) * .5

    w_half *= scale
    h_half *= scale

    bboxes_exp = np.zeros(bboxes.shape, dtype=np.float32)
    bboxes_exp[:, 0] = x_c - w_half
    bboxes_exp[:, 2] = x_c + w_half
    bboxes_exp[:, 1] = y_c - h_half
    bboxes_exp[:, 3] = y_c + h_half

    return bboxes_exp


def clip_bbox(boxes, im_shape):
    h, w = im_shape[0], im_shape[1]
    x1 = boxes[:, 0].clip(0, w)
    y1 = boxes[:, 1].clip(0, h)
    x2 = boxes[:, 2].clip(0, w)
    y2 = boxes[:, 3].clip(0, h)
    return paddle.stack([x1, y1, x2, y2], axis=1)


def nonempty_bbox(boxes, min_size=0, return_mask=False):
    w = boxes[:, 2] - boxes[:, 0]
    h = boxes[:, 3] - boxes[:, 1]
    mask = paddle.logical_and(h > min_size, w > min_size)
    if return_mask:
        return mask
    keep = paddle.nonzero(mask).flatten()
    return keep


def bbox_area(boxes):
    return (boxes[:, 2] - boxes[:, 0]) * (boxes[:, 3] - boxes[:, 1])


def bbox_overlaps(boxes1, boxes2):
    """
    Calculate overlaps between boxes1 and boxes2

    Args:
        boxes1 (Tensor): boxes with shape [M, 4]
        boxes2 (Tensor): boxes with shape [N, 4]

    Return:
        overlaps (Tensor): overlaps between boxes1 and boxes2 with shape [M, N]
    """
    M = boxes1.shape[0]
    N = boxes2.shape[0]
    if M * N == 0:
        return paddle.zeros([M, N], dtype='float32')
    area1 = bbox_area(boxes1)
    area2 = bbox_area(boxes2)

    xy_max = paddle.minimum(
        paddle.unsqueeze(boxes1, 1)[:, :, 2:], boxes2[:, 2:])
    xy_min = paddle.maximum(
        paddle.unsqueeze(boxes1, 1)[:, :, :2], boxes2[:, :2])
    width_height = xy_max - xy_min
    width_height = width_height.clip(min=0)
    inter = width_height.prod(axis=2)

    overlaps = paddle.where(inter > 0, inter /
                            (paddle.unsqueeze(area1, 1) + area2 - inter),
                            paddle.zeros_like(inter))
    return overlaps


def batch_bbox_overlaps(bboxes1,
                        bboxes2,
                        mode='iou',
                        is_aligned=False,
                        eps=1e-6):
    """Calculate overlap between two set of bboxes.
    If ``is_aligned `` is ``False``, then calculate the overlaps between each
    bbox of bboxes1 and bboxes2, otherwise the overlaps between each aligned
    pair of bboxes1 and bboxes2.
    Args:
        bboxes1 (Tensor): shape (B, m, 4) in <x1, y1, x2, y2> format or empty.
        bboxes2 (Tensor): shape (B, n, 4) in <x1, y1, x2, y2> format or empty.
            B indicates the batch dim, in shape (B1, B2, ..., Bn).
            If ``is_aligned `` is ``True``, then m and n must be equal.
        mode (str): "iou" (intersection over union) or "iof" (intersection over
            foreground).
        is_aligned (bool, optional): If True, then m and n must be equal.
            Default False.
        eps (float, optional): A value added to the denominator for numerical
            stability. Default 1e-6.
    Returns:
        Tensor: shape (m, n) if ``is_aligned `` is False else shape (m,)
    """
    assert mode in ['iou', 'iof', 'giou'], 'Unsupported mode {}'.format(mode)
    # Either the boxes are empty or the length of boxes's last dimenstion is 4
    assert (bboxes1.shape[-1] == 4 or bboxes1.shape[0] == 0)
    assert (bboxes2.shape[-1] == 4 or bboxes2.shape[0] == 0)

    # Batch dim must be the same
    # Batch dim: (B1, B2, ... Bn)
    assert bboxes1.shape[:-2] == bboxes2.shape[:-2]
    batch_shape = bboxes1.shape[:-2]

    rows = bboxes1.shape[-2] if bboxes1.shape[0] > 0 else 0
    cols = bboxes2.shape[-2] if bboxes2.shape[0] > 0 else 0
    if is_aligned:
        assert rows == cols

    if rows * cols == 0:
        if is_aligned:
            return paddle.full(batch_shape + (rows, ), 1)
        else:
            return paddle.full(batch_shape + (rows, cols), 1)

    area1 = (bboxes1[:, 2] - bboxes1[:, 0]) * (bboxes1[:, 3] - bboxes1[:, 1])
    area2 = (bboxes2[:, 2] - bboxes2[:, 0]) * (bboxes2[:, 3] - bboxes2[:, 1])

    if is_aligned:
        lt = paddle.maximum(bboxes1[:, :2], bboxes2[:, :2])  # [B, rows, 2]
        rb = paddle.minimum(bboxes1[:, 2:], bboxes2[:, 2:])  # [B, rows, 2]

        wh = (rb - lt).clip(min=0)  # [B, rows, 2]
        overlap = wh[:, 0] * wh[:, 1]

        if mode in ['iou', 'giou']:
            union = area1 + area2 - overlap
        else:
            union = area1
        if mode == 'giou':
            enclosed_lt = paddle.minimum(bboxes1[:, :2], bboxes2[:, :2])
            enclosed_rb = paddle.maximum(bboxes1[:, 2:], bboxes2[:, 2:])
    else:
        lt = paddle.maximum(bboxes1[:, :2].reshape([rows, 1, 2]),
                            bboxes2[:, :2])  # [B, rows, cols, 2]
        rb = paddle.minimum(bboxes1[:, 2:].reshape([rows, 1, 2]),
                            bboxes2[:, 2:])  # [B, rows, cols, 2]

        wh = (rb - lt).clip(min=0)  # [B, rows, cols, 2]
        overlap = wh[:, :, 0] * wh[:, :, 1]

        if mode in ['iou', 'giou']:
            union = area1.reshape([rows,1]) \
                    + area2.reshape([1,cols]) - overlap
        else:
            union = area1[:, None]
        if mode == 'giou':
            enclosed_lt = paddle.minimum(bboxes1[:, :2].reshape([rows, 1, 2]),
                                         bboxes2[:, :2])
            enclosed_rb = paddle.maximum(bboxes1[:, 2:].reshape([rows, 1, 2]),
                                         bboxes2[:, 2:])

    eps = paddle.to_tensor([eps])
    union = paddle.maximum(union, eps)
    ious = overlap / union
    if mode in ['iou', 'iof']:
        return ious
    # calculate gious
    enclose_wh = (enclosed_rb - enclosed_lt).clip(min=0)
    enclose_area = enclose_wh[:, :, 0] * enclose_wh[:, :, 1]
    enclose_area = paddle.maximum(enclose_area, eps)
    gious = ious - (enclose_area - union) / enclose_area
    return 1 - gious


def xywh2xyxy(box):
    x, y, w, h = box
    x1 = x - w * 0.5
    y1 = y - h * 0.5
    x2 = x + w * 0.5
    y2 = y + h * 0.5
    return [x1, y1, x2, y2]


def make_grid(h, w, dtype):
    yv, xv = paddle.meshgrid([paddle.arange(h), paddle.arange(w)])
    return paddle.stack((xv, yv), 2).cast(dtype=dtype)


def decode_yolo(box, anchor, downsample_ratio):
    """decode yolo box

    Args:
        box (list): [x, y, w, h], all have the shape [b, na, h, w, 1]
        anchor (list): anchor with the shape [na, 2]
        downsample_ratio (int): downsample ratio, default 32
        scale (float): scale, default 1.

    Return:
        box (list): decoded box, [x, y, w, h], all have the shape [b, na, h, w, 1]
    """
    x, y, w, h = box
    na, grid_h, grid_w = x.shape[1:4]
    grid = make_grid(grid_h, grid_w, x.dtype).reshape((1, 1, grid_h, grid_w, 2))
    x1 = (x + grid[:, :, :, :, 0:1]) / grid_w
    y1 = (y + grid[:, :, :, :, 1:2]) / grid_h

    anchor = paddle.to_tensor(anchor, dtype=x.dtype)
    anchor = anchor.reshape((1, na, 1, 1, 2))
    w1 = paddle.exp(w) * anchor[:, :, :, :, 0:1] / (downsample_ratio * grid_w)
    h1 = paddle.exp(h) * anchor[:, :, :, :, 1:2] / (downsample_ratio * grid_h)

    return [x1, y1, w1, h1]


def batch_iou_similarity(box1, box2, eps=1e-9):
    """Calculate iou of box1 and box2 in batch

    Args:
        box1 (Tensor): box with the shape [N, M1, 4]
        box2 (Tensor): box with the shape [N, M2, 4]

    Return:
        iou (Tensor): iou between box1 and box2 with the shape [N, M1, M2]
    """
    box1 = box1.unsqueeze(2)  # [N, M1, 4] -> [N, M1, 1, 4]
    box2 = box2.unsqueeze(1)  # [N, M2, 4] -> [N, 1, M2, 4]
    px1y1, px2y2 = box1[:, :, :, 0:2], box1[:, :, :, 2:4]
    gx1y1, gx2y2 = box2[:, :, :, 0:2], box2[:, :, :, 2:4]
    x1y1 = paddle.maximum(px1y1, gx1y1)
    x2y2 = paddle.minimum(px2y2, gx2y2)
    overlap = (x2y2 - x1y1).clip(0).prod(-1)
    area1 = (px2y2 - px1y1).clip(0).prod(-1)
    area2 = (gx2y2 - gx1y1).clip(0).prod(-1)
    union = area1 + area2 - overlap + eps
    return overlap / union


def bbox_iou(box1, box2, giou=False, diou=False, ciou=False, eps=1e-9):
    """calculate the iou of box1 and box2

    Args:
        box1 (list): [x, y, w, h], all have the shape [b, na, h, w, 1]
        box2 (list): [x, y, w, h], all have the shape [b, na, h, w, 1]
        giou (bool): whether use giou or not, default False
        diou (bool): whether use diou or not, default False
        ciou (bool): whether use ciou or not, default False
        eps (float): epsilon to avoid divide by zero

    Return:
        iou (Tensor): iou of box1 and box1, with the shape [b, na, h, w, 1]
    """
    px1, py1, px2, py2 = box1
    gx1, gy1, gx2, gy2 = box2
    x1 = paddle.maximum(px1, gx1)
    y1 = paddle.maximum(py1, gy1)
    x2 = paddle.minimum(px2, gx2)
    y2 = paddle.minimum(py2, gy2)

    overlap = ((x2 - x1).clip(0)) * ((y2 - y1).clip(0))

    area1 = (px2 - px1) * (py2 - py1)
    area1 = area1.clip(0)

    area2 = (gx2 - gx1) * (gy2 - gy1)
    area2 = area2.clip(0)

    union = area1 + area2 - overlap + eps
    iou = overlap / union

    if giou or ciou or diou:
        # convex w, h
        cw = paddle.maximum(px2, gx2) - paddle.minimum(px1, gx1)
        ch = paddle.maximum(py2, gy2) - paddle.minimum(py1, gy1)
        if giou:
            c_area = cw * ch + eps
            return iou - (c_area - union) / c_area
        else:
            # convex diagonal squared
            c2 = cw**2 + ch**2 + eps
            # center distance
            rho2 = ((px1 + px2 - gx1 - gx2)**2 + (py1 + py2 - gy1 - gy2)**2) / 4
            if diou:
                return iou - rho2 / c2
            else:
                w1, h1 = px2 - px1, py2 - py1 + eps
                w2, h2 = gx2 - gx1, gy2 - gy1 + eps
                delta = paddle.atan(w1 / h1) - paddle.atan(w2 / h2)
                v = (4 / math.pi**2) * paddle.pow(delta, 2)
                alpha = v / (1 + eps - iou + v)
                alpha.stop_gradient = True
                return iou - (rho2 / c2 + v * alpha)
    else:
        return iou


def bbox_iou_np_expand(box1, box2, x1y1x2y2=True, eps=1e-16):
    """
    Calculate the iou of box1 and box2 with numpy.

    Args:
        box1 (ndarray): [N, 4]
        box2 (ndarray): [M, 4], usually N != M
        x1y1x2y2 (bool): whether in x1y1x2y2 stype, default True
        eps (float): epsilon to avoid divide by zero
    Return:
        iou (ndarray): iou of box1 and box2, [N, M]
    """
    N, M = len(box1), len(box2)  # usually N != M
    if x1y1x2y2:
        b1_x1, b1_y1 = box1[:, 0], box1[:, 1]
        b1_x2, b1_y2 = box1[:, 2], box1[:, 3]
        b2_x1, b2_y1 = box2[:, 0], box2[:, 1]
        b2_x2, b2_y2 = box2[:, 2], box2[:, 3]
    else:
        # cxcywh style
        # Transform from center and width to exact coordinates
        b1_x1, b1_x2 = box1[:, 0] - box1[:, 2] / 2, box1[:, 0] + box1[:, 2] / 2
        b1_y1, b1_y2 = box1[:, 1] - box1[:, 3] / 2, box1[:, 1] + box1[:, 3] / 2
        b2_x1, b2_x2 = box2[:, 0] - box2[:, 2] / 2, box2[:, 0] + box2[:, 2] / 2
        b2_y1, b2_y2 = box2[:, 1] - box2[:, 3] / 2, box2[:, 1] + box2[:, 3] / 2

    # get the coordinates of the intersection rectangle
    inter_rect_x1 = np.zeros((N, M), dtype=np.float32)
    inter_rect_y1 = np.zeros((N, M), dtype=np.float32)
    inter_rect_x2 = np.zeros((N, M), dtype=np.float32)
    inter_rect_y2 = np.zeros((N, M), dtype=np.float32)
    for i in range(len(box2)):
        inter_rect_x1[:, i] = np.maximum(b1_x1, b2_x1[i])
        inter_rect_y1[:, i] = np.maximum(b1_y1, b2_y1[i])
        inter_rect_x2[:, i] = np.minimum(b1_x2, b2_x2[i])
        inter_rect_y2[:, i] = np.minimum(b1_y2, b2_y2[i])
    # Intersection area
    inter_area = np.maximum(inter_rect_x2 - inter_rect_x1, 0) * np.maximum(
        inter_rect_y2 - inter_rect_y1, 0)
    # Union Area
    b1_area = np.repeat(
        ((b1_x2 - b1_x1) * (b1_y2 - b1_y1)).reshape(-1, 1), M, axis=-1)
    b2_area = np.repeat(
        ((b2_x2 - b2_x1) * (b2_y2 - b2_y1)).reshape(1, -1), N, axis=0)

    ious = inter_area / (b1_area + b2_area - inter_area + eps)
    return ious


def bbox2distance(points, bbox, max_dis=None, eps=0.1):
    """Decode bounding box based on distances.
    Args:
        points (Tensor): Shape (n, 2), [x, y].
        bbox (Tensor): Shape (n, 4), "xyxy" format
        max_dis (float): Upper bound of the distance.
        eps (float): a small value to ensure target < max_dis, instead <=
    Returns:
        Tensor: Decoded distances.
    """
    left = points[:, 0] - bbox[:, 0]
    top = points[:, 1] - bbox[:, 1]
    right = bbox[:, 2] - points[:, 0]
    bottom = bbox[:, 3] - points[:, 1]
    if max_dis is not None:
        left = left.clip(min=0, max=max_dis - eps)
        top = top.clip(min=0, max=max_dis - eps)
        right = right.clip(min=0, max=max_dis - eps)
        bottom = bottom.clip(min=0, max=max_dis - eps)
    return paddle.stack([left, top, right, bottom], -1)


def distance2bbox(points, distance, max_shape=None):
    """Decode distance prediction to bounding box.
        Args:
            points (Tensor): Shape (n, 2), [x, y].
            distance (Tensor): Distance from the given point to 4
                boundaries (left, top, right, bottom).
            max_shape (tuple): Shape of the image.
        Returns:
            Tensor: Decoded bboxes.
        """
    x1 = points[:, 0] - distance[:, 0]
    y1 = points[:, 1] - distance[:, 1]
    x2 = points[:, 0] + distance[:, 2]
    y2 = points[:, 1] + distance[:, 3]
    if max_shape is not None:
        x1 = x1.clip(min=0, max=max_shape[1])
        y1 = y1.clip(min=0, max=max_shape[0])
        x2 = x2.clip(min=0, max=max_shape[1])
        y2 = y2.clip(min=0, max=max_shape[0])
    return paddle.stack([x1, y1, x2, y2], -1)


def bbox_center(boxes):
    """Get bbox centers from boxes.
    Args:
        boxes (Tensor): boxes with shape (..., 4), "xmin, ymin, xmax, ymax" format.
    Returns:
        Tensor: boxes centers with shape (..., 2), "cx, cy" format.
    """
    boxes_cx = (boxes[..., 0] + boxes[..., 2]) / 2
    boxes_cy = (boxes[..., 1] + boxes[..., 3]) / 2
    return paddle.stack([boxes_cx, boxes_cy], axis=-1)


def batch_distance2bbox(points, distance, max_shapes=None):
    """Decode distance prediction to bounding box for batch.
    Args:
        points (Tensor): [B, ..., 2], "xy" format
        distance (Tensor): [B, ..., 4], "ltrb" format
        max_shapes (Tensor): [B, 2], "h,w" format, Shape of the image.
    Returns:
        Tensor: Decoded bboxes, "x1y1x2y2" format.
    """
    lt, rb = paddle.split(distance, 2, -1)
    # while tensor add parameters, parameters should be better placed on the second place
    x1y1 = -lt + points
    x2y2 = rb + points
    out_bbox = paddle.concat([x1y1, x2y2], -1)
    if max_shapes is not None:
        max_shapes = max_shapes.flip(-1).tile([1, 2])
        delta_dim = out_bbox.ndim - max_shapes.ndim
        for _ in range(delta_dim):
            max_shapes.unsqueeze_(1)
        out_bbox = paddle.where(out_bbox < max_shapes, out_bbox, max_shapes)
        out_bbox = paddle.where(out_bbox > 0, out_bbox,
                                paddle.zeros_like(out_bbox))
    return out_bbox


def iou_similarity(box1, box2, eps=1e-10):
    """Calculate iou of box1 and box2

    Args:
        box1 (Tensor): box with the shape [M1, 4]
        box2 (Tensor): box with the shape [M2, 4]

    Return:
        iou (Tensor): iou between box1 and box2 with the shape [M1, M2]
    """
    box1 = box1.unsqueeze(1)  # [M1, 4] -> [M1, 1, 4]
    box2 = box2.unsqueeze(0)  # [M2, 4] -> [1, M2, 4]
    px1y1, px2y2 = box1[:, :, 0:2], box1[:, :, 2:4]
    gx1y1, gx2y2 = box2[:, :, 0:2], box2[:, :, 2:4]
    x1y1 = paddle.maximum(px1y1, gx1y1)
    x2y2 = paddle.minimum(px2y2, gx2y2)
    overlap = (x2y2 - x1y1).clip(0).prod(-1)
    area1 = (px2y2 - px1y1).clip(0).prod(-1)
    area2 = (gx2y2 - gx1y1).clip(0).prod(-1)
    union = area1 + area2 - overlap + eps
    return overlap / union