ViTPose/mmpose/core/evaluation/top_down_eval.py

# Copyright (c) OpenMMLab. All rights reserved.
import warnings

import cv2
import numpy as np

from mmpose.core.post_processing import transform_preds


def _calc_distances(preds, targets, mask, normalize):
    """Calculate the normalized distances between preds and target.

    Note:
        batch_size: N
        num_keypoints: K
        dimension of keypoints: D (normally, D=2 or D=3)

    Args:
        preds (np.ndarray[N, K, D]): Predicted keypoint location.
        targets (np.ndarray[N, K, D]): Groundtruth keypoint location.
        mask (np.ndarray[N, K]): Visibility of the target. False for invisible
            joints, and True for visible. Invisible joints will be ignored for
            accuracy calculation.
        normalize (np.ndarray[N, D]): Typical value is heatmap_size

    Returns:
        np.ndarray[K, N]: The normalized distances. \
            If target keypoints are missing, the distance is -1.
    """
    N, K, _ = preds.shape
    # set mask=0 when normalize==0
    _mask = mask.copy()
    _mask[np.where((normalize == 0).sum(1))[0], :] = False
    distances = np.full((N, K), -1, dtype=np.float32)
    # handle invalid values
    normalize[np.where(normalize <= 0)] = 1e6
    distances[_mask] = np.linalg.norm(
        ((preds - targets) / normalize[:, None, :])[_mask], axis=-1)
    return distances.T


def _distance_acc(distances, thr=0.5):
    """Return the percentage below the distance threshold, while ignoring
    distances values with -1.

    Note:
        batch_size: N
    Args:
        distances (np.ndarray[N, ]): The normalized distances.
        thr (float): Threshold of the distances.

    Returns:
        float: Percentage of distances below the threshold. \
            If all target keypoints are missing, return -1.
    """
    distance_valid = distances != -1
    num_distance_valid = distance_valid.sum()
    if num_distance_valid > 0:
        return (distances[distance_valid] < thr).sum() / num_distance_valid
    return -1


def _get_max_preds(heatmaps):
    """Get keypoint predictions from score maps.

    Note:
        batch_size: N
        num_keypoints: K
        heatmap height: H
        heatmap width: W

    Args:
        heatmaps (np.ndarray[N, K, H, W]): model predicted heatmaps.

    Returns:
        tuple: A tuple containing aggregated results.

        - preds (np.ndarray[N, K, 2]): Predicted keypoint location.
        - maxvals (np.ndarray[N, K, 1]): Scores (confidence) of the keypoints.
    """
    assert isinstance(heatmaps,
                      np.ndarray), ('heatmaps should be numpy.ndarray')
    assert heatmaps.ndim == 4, 'batch_images should be 4-ndim'

    N, K, _, W = heatmaps.shape
    heatmaps_reshaped = heatmaps.reshape((N, K, -1))
    idx = np.argmax(heatmaps_reshaped, 2).reshape((N, K, 1))
    maxvals = np.amax(heatmaps_reshaped, 2).reshape((N, K, 1))

    preds = np.tile(idx, (1, 1, 2)).astype(np.float32)
    preds[:, :, 0] = preds[:, :, 0] % W
    preds[:, :, 1] = preds[:, :, 1] // W

    preds = np.where(np.tile(maxvals, (1, 1, 2)) > 0.0, preds, -1)
    return preds, maxvals


def _get_max_preds_3d(heatmaps):
    """Get keypoint predictions from 3D score maps.

    Note:
        batch size: N
        num keypoints: K
        heatmap depth size: D
        heatmap height: H
        heatmap width: W

    Args:
        heatmaps (np.ndarray[N, K, D, H, W]): model predicted heatmaps.

    Returns:
        tuple: A tuple containing aggregated results.

        - preds (np.ndarray[N, K, 3]): Predicted keypoint location.
        - maxvals (np.ndarray[N, K, 1]): Scores (confidence) of the keypoints.
    """
    assert isinstance(heatmaps, np.ndarray), \
        ('heatmaps should be numpy.ndarray')
    assert heatmaps.ndim == 5, 'heatmaps should be 5-ndim'

    N, K, D, H, W = heatmaps.shape
    heatmaps_reshaped = heatmaps.reshape((N, K, -1))
    idx = np.argmax(heatmaps_reshaped, 2).reshape((N, K, 1))
    maxvals = np.amax(heatmaps_reshaped, 2).reshape((N, K, 1))

    preds = np.zeros((N, K, 3), dtype=np.float32)
    _idx = idx[..., 0]
    preds[..., 2] = _idx // (H * W)
    preds[..., 1] = (_idx // W) % H
    preds[..., 0] = _idx % W

    preds = np.where(maxvals > 0.0, preds, -1)
    return preds, maxvals


def pose_pck_accuracy(output, target, mask, thr=0.05, normalize=None):
    """Calculate the pose accuracy of PCK for each individual keypoint and the
    averaged accuracy across all keypoints from heatmaps.

    Note:
        PCK metric measures accuracy of the localization of the body joints.
        The distances between predicted positions and the ground-truth ones
        are typically normalized by the bounding box size.
        The threshold (thr) of the normalized distance is commonly set
        as 0.05, 0.1 or 0.2 etc.

        - batch_size: N
        - num_keypoints: K
        - heatmap height: H
        - heatmap width: W

    Args:
        output (np.ndarray[N, K, H, W]): Model output heatmaps.
        target (np.ndarray[N, K, H, W]): Groundtruth heatmaps.
        mask (np.ndarray[N, K]): Visibility of the target. False for invisible
            joints, and True for visible. Invisible joints will be ignored for
            accuracy calculation.
        thr (float): Threshold of PCK calculation. Default 0.05.
        normalize (np.ndarray[N, 2]): Normalization factor for H&W.

    Returns:
        tuple: A tuple containing keypoint accuracy.

        - np.ndarray[K]: Accuracy of each keypoint.
        - float: Averaged accuracy across all keypoints.
        - int: Number of valid keypoints.
    """
    N, K, H, W = output.shape
    if K == 0:
        return None, 0, 0
    if normalize is None:
        normalize = np.tile(np.array([[H, W]]), (N, 1))

    pred, _ = _get_max_preds(output)
    gt, _ = _get_max_preds(target)
    return keypoint_pck_accuracy(pred, gt, mask, thr, normalize)


def keypoint_pck_accuracy(pred, gt, mask, thr, normalize):
    """Calculate the pose accuracy of PCK for each individual keypoint and the
    averaged accuracy across all keypoints for coordinates.

    Note:
        PCK metric measures accuracy of the localization of the body joints.
        The distances between predicted positions and the ground-truth ones
        are typically normalized by the bounding box size.
        The threshold (thr) of the normalized distance is commonly set
        as 0.05, 0.1 or 0.2 etc.

        - batch_size: N
        - num_keypoints: K

    Args:
        pred (np.ndarray[N, K, 2]): Predicted keypoint location.
        gt (np.ndarray[N, K, 2]): Groundtruth keypoint location.
        mask (np.ndarray[N, K]): Visibility of the target. False for invisible
            joints, and True for visible. Invisible joints will be ignored for
            accuracy calculation.
        thr (float): Threshold of PCK calculation.
        normalize (np.ndarray[N, 2]): Normalization factor for H&W.

    Returns:
        tuple: A tuple containing keypoint accuracy.

        - acc (np.ndarray[K]): Accuracy of each keypoint.
        - avg_acc (float): Averaged accuracy across all keypoints.
        - cnt (int): Number of valid keypoints.
    """
    distances = _calc_distances(pred, gt, mask, normalize)

    acc = np.array([_distance_acc(d, thr) for d in distances])
    valid_acc = acc[acc >= 0]
    cnt = len(valid_acc)
    avg_acc = valid_acc.mean() if cnt > 0 else 0
    return acc, avg_acc, cnt


def keypoint_auc(pred, gt, mask, normalize, num_step=20):
    """Calculate the pose accuracy of PCK for each individual keypoint and the
    averaged accuracy across all keypoints for coordinates.

    Note:
        - batch_size: N
        - num_keypoints: K

    Args:
        pred (np.ndarray[N, K, 2]): Predicted keypoint location.
        gt (np.ndarray[N, K, 2]): Groundtruth keypoint location.
        mask (np.ndarray[N, K]): Visibility of the target. False for invisible
            joints, and True for visible. Invisible joints will be ignored for
            accuracy calculation.
        normalize (float): Normalization factor.

    Returns:
        float: Area under curve.
    """
    nor = np.tile(np.array([[normalize, normalize]]), (pred.shape[0], 1))
    x = [1.0 * i / num_step for i in range(num_step)]
    y = []
    for thr in x:
        _, avg_acc, _ = keypoint_pck_accuracy(pred, gt, mask, thr, nor)
        y.append(avg_acc)

    auc = 0
    for i in range(num_step):
        auc += 1.0 / num_step * y[i]
    return auc


def keypoint_nme(pred, gt, mask, normalize_factor):
    """Calculate the normalized mean error (NME).

    Note:
        - batch_size: N
        - num_keypoints: K

    Args:
        pred (np.ndarray[N, K, 2]): Predicted keypoint location.
        gt (np.ndarray[N, K, 2]): Groundtruth keypoint location.
        mask (np.ndarray[N, K]): Visibility of the target. False for invisible
            joints, and True for visible. Invisible joints will be ignored for
            accuracy calculation.
        normalize_factor (np.ndarray[N, 2]): Normalization factor.

    Returns:
        float: normalized mean error
    """
    distances = _calc_distances(pred, gt, mask, normalize_factor)
    distance_valid = distances[distances != -1]
    return distance_valid.sum() / max(1, len(distance_valid))


def keypoint_epe(pred, gt, mask):
    """Calculate the end-point error.

    Note:
        - batch_size: N
        - num_keypoints: K

    Args:
        pred (np.ndarray[N, K, 2]): Predicted keypoint location.
        gt (np.ndarray[N, K, 2]): Groundtruth keypoint location.
        mask (np.ndarray[N, K]): Visibility of the target. False for invisible
            joints, and True for visible. Invisible joints will be ignored for
            accuracy calculation.

    Returns:
        float: Average end-point error.
    """

    distances = _calc_distances(
        pred, gt, mask,
        np.ones((pred.shape[0], pred.shape[2]), dtype=np.float32))
    distance_valid = distances[distances != -1]
    return distance_valid.sum() / max(1, len(distance_valid))


def _taylor(heatmap, coord):
    """Distribution aware coordinate decoding method.

    Note:
        - heatmap height: H
        - heatmap width: W

    Args:
        heatmap (np.ndarray[H, W]): Heatmap of a particular joint type.
        coord (np.ndarray[2,]): Coordinates of the predicted keypoints.

    Returns:
        np.ndarray[2,]: Updated coordinates.
    """
    H, W = heatmap.shape[:2]
    px, py = int(coord[0]), int(coord[1])
    if 1 < px < W - 2 and 1 < py < H - 2:
        dx = 0.5 * (heatmap[py][px + 1] - heatmap[py][px - 1])
        dy = 0.5 * (heatmap[py + 1][px] - heatmap[py - 1][px])
        dxx = 0.25 * (
            heatmap[py][px + 2] - 2 * heatmap[py][px] + heatmap[py][px - 2])
        dxy = 0.25 * (
            heatmap[py + 1][px + 1] - heatmap[py - 1][px + 1] -
            heatmap[py + 1][px - 1] + heatmap[py - 1][px - 1])
        dyy = 0.25 * (
            heatmap[py + 2 * 1][px] - 2 * heatmap[py][px] +
            heatmap[py - 2 * 1][px])
        derivative = np.array([[dx], [dy]])
        hessian = np.array([[dxx, dxy], [dxy, dyy]])
        if dxx * dyy - dxy**2 != 0:
            hessianinv = np.linalg.inv(hessian)
            offset = -hessianinv @ derivative
            offset = np.squeeze(np.array(offset.T), axis=0)
            coord += offset
    return coord


def post_dark_udp(coords, batch_heatmaps, kernel=3):
    """DARK post-pocessing. Implemented by udp. Paper ref: Huang et al. The
    Devil is in the Details: Delving into Unbiased Data Processing for Human
    Pose Estimation (CVPR 2020). Zhang et al. Distribution-Aware Coordinate
    Representation for Human Pose Estimation (CVPR 2020).

    Note:
        - batch size: B
        - num keypoints: K
        - num persons: N
        - height of heatmaps: H
        - width of heatmaps: W

        B=1 for bottom_up paradigm where all persons share the same heatmap.
        B=N for top_down paradigm where each person has its own heatmaps.

    Args:
        coords (np.ndarray[N, K, 2]): Initial coordinates of human pose.
        batch_heatmaps (np.ndarray[B, K, H, W]): batch_heatmaps
        kernel (int): Gaussian kernel size (K) for modulation.

    Returns:
        np.ndarray([N, K, 2]): Refined coordinates.
    """
    if not isinstance(batch_heatmaps, np.ndarray):
        batch_heatmaps = batch_heatmaps.cpu().numpy()
    B, K, H, W = batch_heatmaps.shape
    N = coords.shape[0]
    assert (B == 1 or B == N)
    for heatmaps in batch_heatmaps:
        for heatmap in heatmaps:
            cv2.GaussianBlur(heatmap, (kernel, kernel), 0, heatmap)
    np.clip(batch_heatmaps, 0.001, 50, batch_heatmaps)
    np.log(batch_heatmaps, batch_heatmaps)

    batch_heatmaps_pad = np.pad(
        batch_heatmaps, ((0, 0), (0, 0), (1, 1), (1, 1)),
        mode='edge').flatten()

    index = coords[..., 0] + 1 + (coords[..., 1] + 1) * (W + 2)
    index += (W + 2) * (H + 2) * np.arange(0, B * K).reshape(-1, K)
    index = index.astype(int).reshape(-1, 1)
    i_ = batch_heatmaps_pad[index]
    ix1 = batch_heatmaps_pad[index + 1]
    iy1 = batch_heatmaps_pad[index + W + 2]
    ix1y1 = batch_heatmaps_pad[index + W + 3]
    ix1_y1_ = batch_heatmaps_pad[index - W - 3]
    ix1_ = batch_heatmaps_pad[index - 1]
    iy1_ = batch_heatmaps_pad[index - 2 - W]

    dx = 0.5 * (ix1 - ix1_)
    dy = 0.5 * (iy1 - iy1_)
    derivative = np.concatenate([dx, dy], axis=1)
    derivative = derivative.reshape(N, K, 2, 1)
    dxx = ix1 - 2 * i_ + ix1_
    dyy = iy1 - 2 * i_ + iy1_
    dxy = 0.5 * (ix1y1 - ix1 - iy1 + i_ + i_ - ix1_ - iy1_ + ix1_y1_)
    hessian = np.concatenate([dxx, dxy, dxy, dyy], axis=1)
    hessian = hessian.reshape(N, K, 2, 2)
    hessian = np.linalg.inv(hessian + np.finfo(np.float32).eps * np.eye(2))
    coords -= np.einsum('ijmn,ijnk->ijmk', hessian, derivative).squeeze()
    return coords


def _gaussian_blur(heatmaps, kernel=11):
    """Modulate heatmap distribution with Gaussian.
     sigma = 0.3*((kernel_size-1)*0.5-1)+0.8
     sigma~=3 if k=17
     sigma=2 if k=11;
     sigma~=1.5 if k=7;
     sigma~=1 if k=3;

    Note:
        - batch_size: N
        - num_keypoints: K
        - heatmap height: H
        - heatmap width: W

    Args:
        heatmaps (np.ndarray[N, K, H, W]): model predicted heatmaps.
        kernel (int): Gaussian kernel size (K) for modulation, which should
            match the heatmap gaussian sigma when training.
            K=17 for sigma=3 and k=11 for sigma=2.

    Returns:
        np.ndarray ([N, K, H, W]): Modulated heatmap distribution.
    """
    assert kernel % 2 == 1

    border = (kernel - 1) // 2
    batch_size = heatmaps.shape[0]
    num_joints = heatmaps.shape[1]
    height = heatmaps.shape[2]
    width = heatmaps.shape[3]
    for i in range(batch_size):
        for j in range(num_joints):
            origin_max = np.max(heatmaps[i, j])
            dr = np.zeros((height + 2 * border, width + 2 * border),
                          dtype=np.float32)
            dr[border:-border, border:-border] = heatmaps[i, j].copy()
            dr = cv2.GaussianBlur(dr, (kernel, kernel), 0)
            heatmaps[i, j] = dr[border:-border, border:-border].copy()
            heatmaps[i, j] *= origin_max / np.max(heatmaps[i, j])
    return heatmaps


def keypoints_from_regression(regression_preds, center, scale, img_size):
    """Get final keypoint predictions from regression vectors and transform
    them back to the image.

    Note:
        - batch_size: N
        - num_keypoints: K

    Args:
        regression_preds (np.ndarray[N, K, 2]): model prediction.
        center (np.ndarray[N, 2]): Center of the bounding box (x, y).
        scale (np.ndarray[N, 2]): Scale of the bounding box
            wrt height/width.
        img_size (list(img_width, img_height)): model input image size.

    Returns:
        tuple:

        - preds (np.ndarray[N, K, 2]): Predicted keypoint location in images.
        - maxvals (np.ndarray[N, K, 1]): Scores (confidence) of the keypoints.
    """
    N, K, _ = regression_preds.shape
    preds, maxvals = regression_preds, np.ones((N, K, 1), dtype=np.float32)

    preds = preds * img_size

    # Transform back to the image
    for i in range(N):
        preds[i] = transform_preds(preds[i], center[i], scale[i], img_size)

    return preds, maxvals


def keypoints_from_heatmaps(heatmaps,
                            center,
                            scale,
                            unbiased=False,
                            post_process='default',
                            kernel=11,
                            valid_radius_factor=0.0546875,
                            use_udp=False,
                            target_type='GaussianHeatmap'):
    """Get final keypoint predictions from heatmaps and transform them back to
    the image.

    Note:
        - batch size: N
        - num keypoints: K
        - heatmap height: H
        - heatmap width: W

    Args:
        heatmaps (np.ndarray[N, K, H, W]): model predicted heatmaps.
        center (np.ndarray[N, 2]): Center of the bounding box (x, y).
        scale (np.ndarray[N, 2]): Scale of the bounding box
            wrt height/width.
        post_process (str/None): Choice of methods to post-process
            heatmaps. Currently supported: None, 'default', 'unbiased',
            'megvii'.
        unbiased (bool): Option to use unbiased decoding. Mutually
            exclusive with megvii.
            Note: this arg is deprecated and unbiased=True can be replaced
            by post_process='unbiased'
            Paper ref: Zhang et al. Distribution-Aware Coordinate
            Representation for Human Pose Estimation (CVPR 2020).
        kernel (int): Gaussian kernel size (K) for modulation, which should
            match the heatmap gaussian sigma when training.
            K=17 for sigma=3 and k=11 for sigma=2.
        valid_radius_factor (float): The radius factor of the positive area
            in classification heatmap for UDP.
        use_udp (bool): Use unbiased data processing.
        target_type (str): 'GaussianHeatmap' or 'CombinedTarget'.
            GaussianHeatmap: Classification target with gaussian distribution.
            CombinedTarget: The combination of classification target
            (response map) and regression target (offset map).
            Paper ref: Huang et al. The Devil is in the Details: Delving into
            Unbiased Data Processing for Human Pose Estimation (CVPR 2020).

    Returns:
        tuple: A tuple containing keypoint predictions and scores.

        - preds (np.ndarray[N, K, 2]): Predicted keypoint location in images.
        - maxvals (np.ndarray[N, K, 1]): Scores (confidence) of the keypoints.
    """
    # Avoid being affected
    heatmaps = heatmaps.copy()

    # detect conflicts
    if unbiased:
        assert post_process not in [False, None, 'megvii']
    if post_process in ['megvii', 'unbiased']:
        assert kernel > 0
    if use_udp:
        assert not post_process == 'megvii'

    # normalize configs
    if post_process is False:
        warnings.warn(
            'post_process=False is deprecated, '
            'please use post_process=None instead', DeprecationWarning)
        post_process = None
    elif post_process is True:
        if unbiased is True:
            warnings.warn(
                'post_process=True, unbiased=True is deprecated,'
                " please use post_process='unbiased' instead",
                DeprecationWarning)
            post_process = 'unbiased'
        else:
            warnings.warn(
                'post_process=True, unbiased=False is deprecated, '
                "please use post_process='default' instead",
                DeprecationWarning)
            post_process = 'default'
    elif post_process == 'default':
        if unbiased is True:
            warnings.warn(
                'unbiased=True is deprecated, please use '
                "post_process='unbiased' instead", DeprecationWarning)
            post_process = 'unbiased'

    # start processing
    if post_process == 'megvii':
        heatmaps = _gaussian_blur(heatmaps, kernel=kernel)

    N, K, H, W = heatmaps.shape
    if use_udp:
        if target_type.lower() == 'GaussianHeatMap'.lower():
            preds, maxvals = _get_max_preds(heatmaps)
            preds = post_dark_udp(preds, heatmaps, kernel=kernel)
        elif target_type.lower() == 'CombinedTarget'.lower():
            for person_heatmaps in heatmaps:
                for i, heatmap in enumerate(person_heatmaps):
                    kt = 2 * kernel + 1 if i % 3 == 0 else kernel
                    cv2.GaussianBlur(heatmap, (kt, kt), 0, heatmap)
            # valid radius is in direct proportion to the height of heatmap.
            valid_radius = valid_radius_factor * H
            offset_x = heatmaps[:, 1::3, :].flatten() * valid_radius
            offset_y = heatmaps[:, 2::3, :].flatten() * valid_radius
            heatmaps = heatmaps[:, ::3, :]
            preds, maxvals = _get_max_preds(heatmaps)
            index = preds[..., 0] + preds[..., 1] * W
            index += W * H * np.arange(0, N * K / 3)
            index = index.astype(int).reshape(N, K // 3, 1)
            preds += np.concatenate((offset_x[index], offset_y[index]), axis=2)
        else:
            raise ValueError('target_type should be either '
                             "'GaussianHeatmap' or 'CombinedTarget'")
    else:
        preds, maxvals = _get_max_preds(heatmaps)
        if post_process == 'unbiased':  # alleviate biased coordinate
            # apply Gaussian distribution modulation.
            heatmaps = np.log(
                np.maximum(_gaussian_blur(heatmaps, kernel), 1e-10))
            for n in range(N):
                for k in range(K):
                    preds[n][k] = _taylor(heatmaps[n][k], preds[n][k])
        elif post_process is not None:
            # add +/-0.25 shift to the predicted locations for higher acc.
            for n in range(N):
                for k in range(K):
                    heatmap = heatmaps[n][k]
                    px = int(preds[n][k][0])
                    py = int(preds[n][k][1])
                    if 1 < px < W - 1 and 1 < py < H - 1:
                        diff = np.array([
                            heatmap[py][px + 1] - heatmap[py][px - 1],
                            heatmap[py + 1][px] - heatmap[py - 1][px]
                        ])
                        preds[n][k] += np.sign(diff) * .25
                        if post_process == 'megvii':
                            preds[n][k] += 0.5

    # Transform back to the image
    for i in range(N):
        preds[i] = transform_preds(
            preds[i], center[i], scale[i], [W, H], use_udp=use_udp)

    if post_process == 'megvii':
        maxvals = maxvals / 255.0 + 0.5

    return preds, maxvals


def keypoints_from_heatmaps3d(heatmaps, center, scale):
    """Get final keypoint predictions from 3d heatmaps and transform them back
    to the image.

    Note:
        - batch size: N
        - num keypoints: K
        - heatmap depth size: D
        - heatmap height: H
        - heatmap width: W

    Args:
        heatmaps (np.ndarray[N, K, D, H, W]): model predicted heatmaps.
        center (np.ndarray[N, 2]): Center of the bounding box (x, y).
        scale (np.ndarray[N, 2]): Scale of the bounding box
            wrt height/width.

    Returns:
        tuple: A tuple containing keypoint predictions and scores.

        - preds (np.ndarray[N, K, 3]): Predicted 3d keypoint location \
            in images.
        - maxvals (np.ndarray[N, K, 1]): Scores (confidence) of the keypoints.
    """
    N, K, D, H, W = heatmaps.shape
    preds, maxvals = _get_max_preds_3d(heatmaps)
    # Transform back to the image
    for i in range(N):
        preds[i, :, :2] = transform_preds(preds[i, :, :2], center[i], scale[i],
                                          [W, H])
    return preds, maxvals


def multilabel_classification_accuracy(pred, gt, mask, thr=0.5):
    """Get multi-label classification accuracy.

    Note:
        - batch size: N
        - label number: L

    Args:
        pred (np.ndarray[N, L, 2]): model predicted labels.
        gt (np.ndarray[N, L, 2]): ground-truth labels.
        mask (np.ndarray[N, 1] or np.ndarray[N, L] ): reliability of
        ground-truth labels.

    Returns:
        float: multi-label classification accuracy.
    """
    # we only compute accuracy on the samples with ground-truth of all labels.
    valid = (mask > 0).min(axis=1) if mask.ndim == 2 else (mask > 0)
    pred, gt = pred[valid], gt[valid]

    if pred.shape[0] == 0:
        acc = 0.0  # when no sample is with gt labels, set acc to 0.
    else:
        # The classification of a sample is regarded as correct
        # only if it's correct for all labels.
        acc = (((pred - thr) * (gt - thr)) > 0).all(axis=1).mean()
    return acc