ref/GP-NeRF/gpnerf/data_loaders/utils/base_utils.py

import math
import os

import cv2
import h5py
import torch

import numpy as np
import pickle

import yaml
from plyfile import PlyData
from skimage.io import imread

#######################io#########################################
from transforms3d.axangles import mat2axangle
from transforms3d.euler import euler2mat


def read_pickle(pkl_path):
    with open(pkl_path, 'rb') as f:
        return pickle.load(f)


def save_pickle(data, pkl_path):
    os.system('mkdir -p {}'.format(os.path.dirname(pkl_path)))
    with open(pkl_path, 'wb') as f:
        pickle.dump(data, f)


#####################depth and image###############################

def mask_zbuffer_to_pts(mask, zbuffer, K):
    ys, xs = np.nonzero(mask)
    zbuffer = zbuffer[ys, xs]
    u, v, f = K[0, 2], K[1, 2], K[0, 0]
    depth = zbuffer / np.sqrt((xs - u + 0.5) ** 2 + (ys - v + 0.5) ** 2 + f ** 2) * f

    pts = np.asarray([xs, ys, depth], np.float32).transpose()
    pts[:, :2] *= pts[:, 2:]
    return np.dot(pts, np.linalg.inv(K).transpose())


def mask_depth_to_pts(mask, depth, K, rgb=None):
    hs, ws = np.nonzero(mask)
    depth = depth[hs, ws]
    pts = np.asarray([ws, hs, depth], np.float32).transpose()
    pts[:, :2] *= pts[:, 2:]
    if rgb is not None:
        return np.dot(pts, np.linalg.inv(K).transpose()), rgb[hs, ws]
    else:
        return np.dot(pts, np.linalg.inv(K).transpose())


def read_render_zbuffer(dpt_pth, max_depth, min_depth):
    zbuffer = imread(dpt_pth)
    mask = (zbuffer > 0) & (zbuffer < 5000)
    zbuffer = zbuffer.astype(np.float64) / 2 ** 16 * (max_depth - min_depth) + min_depth
    return mask, zbuffer


def zbuffer_to_depth(zbuffer, K):
    u, v, f = K[0, 2], K[1, 2], K[0, 0]
    x = np.arange(zbuffer.shape[1])
    y = np.arange(zbuffer.shape[0])
    x, y = np.meshgrid(x, y, indexing='xy')
    x = np.reshape(x, [-1, 1])
    y = np.reshape(y, [-1, 1])
    depth = np.reshape(zbuffer, [-1, 1])

    depth = depth / np.sqrt((x - u + 0.5) ** 2 + (y - v + 0.5) ** 2 + f ** 2) * f
    return np.reshape(depth, zbuffer.shape)


def project_points(pts, RT, K):
    pts = np.matmul(pts, RT[:, :3].transpose()) + RT[:, 3:].transpose()
    pts = np.matmul(pts, K.transpose())
    dpt = pts[:, 2]
    mask0 = (np.abs(dpt) < 1e-4) & (np.abs(dpt) > 0)
    if np.sum(mask0) > 0: dpt[mask0] = 1e-4
    mask1 = (np.abs(dpt) > -1e-4) & (np.abs(dpt) < 0)
    if np.sum(mask1) > 0: dpt[mask1] = -1e-4
    pts2d = pts[:, :2] / dpt[:, None]
    return pts2d, dpt


#######################image processing#############################

def grey_repeats(img_raw):
    if len(img_raw.shape) == 2: img_raw = np.repeat(img_raw[:, :, None], 3, axis=2)
    if img_raw.shape[2] > 3: img_raw = img_raw[:, :, :3]
    return img_raw


def normalize_image(img, mask=None):
    if mask is not None: img[np.logical_not(mask.astype(np.bool))] = 127
    img = (img.transpose([2, 0, 1]).astype(np.float32) - 127.0) / 128.0
    return torch.tensor(img, dtype=torch.float32)


def tensor_to_image(tensor):
    return (tensor * 128 + 127).astype(np.uint8).transpose(1, 2, 0)


def equal_hist(img):
    if len(img.shape) == 3:
        img0 = cv2.equalizeHist(img[:, :, 0])
        img1 = cv2.equalizeHist(img[:, :, 1])
        img2 = cv2.equalizeHist(img[:, :, 2])
        img = np.concatenate([img0[..., None], img1[..., None], img2[..., None]], 2)
    else:
        img = cv2.equalizeHist(img)
    return img


def resize_large_image(img, resize_max):
    h, w = img.shape[:2]
    max_side = max(h, w)
    if max_side > resize_max:
        ratio = resize_max / max_side
        if ratio <= 0.5: img = cv2.GaussianBlur(img, (5, 5), 1.5)
        img = cv2.resize(img, (int(round(ratio * w)), int(round(ratio * h))), interpolation=cv2.INTER_LINEAR)
        return img, ratio
    else:
        return img, 1.0


def downsample_gaussian_blur(img, ratio):
    sigma = (1 / ratio) / 3
    # ksize=np.ceil(2*sigma)
    ksize = int(np.ceil(((sigma - 0.8) / 0.3 + 1) * 2 + 1))
    ksize = ksize + 1 if ksize % 2 == 0 else ksize
    img = cv2.GaussianBlur(img, (ksize, ksize), sigma, borderType=cv2.BORDER_REFLECT101)
    return img


def resize_small_image(img, resize_min):
    h, w = img.shape[:2]
    min_side = min(h, w)
    if min_side < resize_min:
        ratio = resize_min / min_side
        img = cv2.resize(img, (int(round(ratio * w)), int(round(ratio * h))), interpolation=cv2.INTER_LINEAR)
        return img, ratio
    else:
        return img, 1.0


############################geometry######################################
def round_coordinates(coord, h, w):
    coord = np.round(coord).astype(np.int32)
    coord[coord[:, 0] < 0, 0] = 0
    coord[coord[:, 0] >= w, 0] = w - 1
    coord[coord[:, 1] < 0, 1] = 0
    coord[coord[:, 1] >= h, 1] = h - 1
    return coord


def get_img_patch(img, pt, size):
    if isinstance(size, list) or isinstance(size, tuple) or isinstance(size, np.ndarray):
        size_h, size_w = size
    else:
        size_h, size_w = size, size
    h, w = img.shape[:2]
    x, y = pt.astype(np.int32)
    xmin = max(0, x - size_w)
    xmax = min(w - 1, x + size_w)
    ymin = max(0, y - size_h)
    ymax = min(h - 1, y + size_h)
    patch = np.full([size_h * 2, size_w * 2, 3], 127, np.uint8)
    patch[ymin - y + size_h:ymax - y + size_h, xmin - x + size_w:xmax - x + size_w] = img[ymin:ymax, xmin:xmax]
    return patch


def perspective_transform(pts, H):
    tpts = np.concatenate([pts, np.ones([pts.shape[0], 1])], 1) @ H.transpose()
    tpts = tpts[:, :2] / np.abs(tpts[:, 2:])
    return tpts


def get_rot_m(angle):
    return np.asarray([[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]], np.float32)  # rn+1,3,3


def get_rot_m_batch(angle):
    return np.asarray([[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]], np.float32).transpose(
        [2, 0, 1])


def compute_F(K1, K2, R, t):
    """

    :param K1: [3,3]
    :param K2: [3,3]
    :param R:  [3,3]
    :param t:  [3,1]
    :return:
    """
    A = K1 @ R.T @ t  # [3,1]
    C = np.asarray([[0, -A[2, 0], A[1, 0]],
                    [A[2, 0], 0, -A[0, 0]],
                    [-A[1, 0], A[0, 0], 0]])
    F = (np.linalg.inv(K2)).T @ R @ K1.T @ C
    return F


def compute_relative_transformation(Rt0, Rt1):
    """
    x1=Rx0+t
    :param Rt0: x0=R0x+t0
    :param Rt1: x1=R1x+t1
    :return:
        R1R0.T(x0-t0)+t1
    """
    R = Rt1[:, :3] @ Rt0[:, :3].T
    t = Rt1[:, 3] - R @ Rt0[:, 3]
    return np.concatenate([R, t[:, None]], 1)


def compute_angle(rotation_diff):
    trace = np.trace(rotation_diff)
    trace = trace if trace <= 3 else 3
    angular_distance = np.rad2deg(np.arccos((trace - 1.) / 2.))
    return angular_distance


def load_h5(filename):
    dict_to_load = {}
    with h5py.File(filename, 'r') as f:
        keys = [key for key in f.keys()]
        for key in keys:
            dict_to_load[key] = f[key][()]  # .value
    return dict_to_load


def save_h5(dict_to_save, filename):
    with h5py.File(filename, 'w') as f:
        for key in dict_to_save:
            f.create_dataset(key, data=dict_to_save[key])


def pts_to_hpts(pts):
    return np.concatenate([pts, np.ones([pts.shape[0], 1])], 1)


def hpts_to_pts(hpts):
    return hpts[:, :-1] / hpts[:, -1:]


def np_skew_symmetric(v):
    M = np.asarray([
        [0, -v[2], v[1], ],
        [v[2], 0, -v[0], ],
        [-v[1], v[0], 0, ],
    ])

    return M


def point_line_dist(hpts, lines):
    """
    :param hpts: n,3 or n,2
    :param lines: n,3
    :return:
    """
    if hpts.shape[1] == 2:
        hpts = np.concatenate([hpts, np.ones([hpts.shape[0], 1])], 1)
    return np.abs(np.sum(hpts * lines, 1)) / np.linalg.norm(lines[:, :2], 2, 1)


def epipolar_distance(x0, x1, F):
    """

    :param x0: [n,2]
    :param x1: [n,2]
    :param F:  [3,3]
    :return:
    """

    hkps0 = np.concatenate([x0, np.ones([x0.shape[0], 1])], 1)
    hkps1 = np.concatenate([x1, np.ones([x1.shape[0], 1])], 1)

    lines1 = hkps0 @ F.T
    lines0 = hkps1 @ F

    dist10 = point_line_dist(hkps0, lines0)
    dist01 = point_line_dist(hkps1, lines1)

    return dist10, dist01


def epipolar_distance_mean(x0, x1, F):
    return np.mean(np.stack(epipolar_distance(x0, x1, F), 1), 1)


def compute_dR_dt(R0, t0, R1, t1):
    # Compute dR, dt
    dR = np.dot(R1, R0.T)
    dt = t1 - np.dot(dR, t0)
    return dR, dt


def compute_precision_recall_np(pr, gt, eps=1e-5):
    tp = np.sum(gt & pr)
    fp = np.sum((~gt) & pr)
    fn = np.sum(gt & (~pr))
    precision = (tp + eps) / (fp + tp + eps)
    recall = (tp + eps) / (tp + fn + eps)
    if precision < 1e-3 or recall < 1e-3:
        f1 = 0.0
    else:
        f1 = (2 * precision * recall + eps) / (precision + recall + eps)

    return precision, recall, f1


def load_cfg(path):
    with open(path, 'r') as f:
        return yaml.load(f, Loader=yaml.FullLoader)


def get_stem(path, suffix_len=5):
    return os.path.basename(path)[:-suffix_len]


def load_component(component_func, component_cfg_fn):
    component_cfg = load_cfg(component_cfg_fn)
    return component_func[component_cfg['type']](component_cfg)


def interpolate_image_points(img, pts, interpolation=cv2.INTER_LINEAR):
    # img [h,w,k] pts [n,2]
    if len(pts) < 32767:
        pts = pts.astype(np.float32)
        return cv2.remap(img, pts[:, None, 0], pts[:, None, 1], borderMode=cv2.BORDER_CONSTANT, borderValue=0,
                         interpolation=interpolation)[:, 0]
        # pn=len(pts)
        # sl=int(np.ceil(np.sqrt(pn)))
        # tmp_img=np.zeros([sl*sl,2],np.float32)
        # tmp_img[:pn]=pts
        # tmp_img=tmp_img.reshape([sl,sl,2])
        # tmp_img=cv2.remap(img,tmp_img[:,:,0],tmp_img[:,:,1],borderMode=cv2.BORDER_CONSTANT,borderValue=0,interpolation=interpolation)
        # return tmp_img.flatten()[:pn]
    else:
        results = []
        for k in range(0, len(pts), 30000):
            results.append(interpolate_image_points(img, pts[k:k + 30000], interpolation))
        return np.concatenate(results, 0)


def transform_points_Rt(pts, R, t):
    t = t.flatten()
    return pts @ R.T + t[None, :]


def transform_points_pose(pts, pose):
    R, t = pose[:, :3], pose[:, 3]
    return pts @ R.T + t[None, :]


def quaternion_from_matrix(matrix, isprecise=False):
    '''Return quaternion from rotation matrix.

    If isprecise is True, the input matrix is assumed to be a precise rotation
    matrix and a faster algorithm is used.

    >>> q = quaternion_from_matrix(numpy.identity(4), True)
    >>> numpy.allclose(q, [1, 0, 0, 0])
    True
    >>> q = quaternion_from_matrix(numpy.diag([1, -1, -1, 1]))
    >>> numpy.allclose(q, [0, 1, 0, 0]) or numpy.allclose(q, [0, -1, 0, 0])
    True
    >>> R = rotation_matrix(0.123, (1, 2, 3))
    >>> q = quaternion_from_matrix(R, True)
    >>> numpy.allclose(q, [0.9981095, 0.0164262, 0.0328524, 0.0492786])
    True
    >>> R = [[-0.545, 0.797, 0.260, 0], [0.733, 0.603, -0.313, 0],
    ...      [-0.407, 0.021, -0.913, 0], [0, 0, 0, 1]]
    >>> q = quaternion_from_matrix(R)
    >>> numpy.allclose(q, [0.19069, 0.43736, 0.87485, -0.083611])
    True
    >>> R = [[0.395, 0.362, 0.843, 0], [-0.626, 0.796, -0.056, 0],
    ...      [-0.677, -0.498, 0.529, 0], [0, 0, 0, 1]]
    >>> q = quaternion_from_matrix(R)
    >>> numpy.allclose(q, [0.82336615, -0.13610694, 0.46344705, -0.29792603])
    True
    >>> R = random_rotation_matrix()
    >>> q = quaternion_from_matrix(R)
    >>> is_same_transform(R, quaternion_matrix(q))
    True
    >>> R = euler_matrix(0.0, 0.0, numpy.pi/2.0)
    >>> numpy.allclose(quaternion_from_matrix(R, isprecise=False),
    ...                quaternion_from_matrix(R, isprecise=True))
    True

    '''

    M = np.array(matrix, dtype=np.float64, copy=False)[:4, :4]
    if isprecise:
        q = np.empty((4,))
        t = np.trace(M)
        if t > M[3, 3]:
            q[0] = t
            q[3] = M[1, 0] - M[0, 1]
            q[2] = M[0, 2] - M[2, 0]
            q[1] = M[2, 1] - M[1, 2]
        else:
            i, j, k = 1, 2, 3
            if M[1, 1] > M[0, 0]:
                i, j, k = 2, 3, 1
            if M[2, 2] > M[i, i]:
                i, j, k = 3, 1, 2
            t = M[i, i] - (M[j, j] + M[k, k]) + M[3, 3]
            q[i] = t
            q[j] = M[i, j] + M[j, i]
            q[k] = M[k, i] + M[i, k]
            q[3] = M[k, j] - M[j, k]
        q *= 0.5 / math.sqrt(t * M[3, 3])
    else:
        m00 = M[0, 0]
        m01 = M[0, 1]
        m02 = M[0, 2]
        m10 = M[1, 0]
        m11 = M[1, 1]
        m12 = M[1, 2]
        m20 = M[2, 0]
        m21 = M[2, 1]
        m22 = M[2, 2]

        # symmetric matrix K
        K = np.array([[m00 - m11 - m22, 0.0, 0.0, 0.0],
                      [m01 + m10, m11 - m00 - m22, 0.0, 0.0],
                      [m02 + m20, m12 + m21, m22 - m00 - m11, 0.0],
                      [m21 - m12, m02 - m20, m10 - m01, m00 + m11 + m22]])
        K /= 3.0

        # quaternion is eigenvector of K that corresponds to largest eigenvalue
        w, V = np.linalg.eigh(K)
        q = V[[3, 0, 1, 2], np.argmax(w)]

    if q[0] < 0.0:
        np.negative(q, q)

    return q


def compute_rotation_angle_diff(R_gt, R):
    eps = 1e-15
    q_gt = quaternion_from_matrix(R_gt)
    q = quaternion_from_matrix(R)
    q = q / (np.linalg.norm(q) + eps)
    q_gt = q_gt / (np.linalg.norm(q_gt) + eps)
    loss_q = np.maximum(eps, (1.0 - np.sum(q * q_gt) ** 2))
    err_q = np.arccos(1 - 2 * loss_q)
    return np.rad2deg(np.abs(err_q))


def compute_translation_angle_diff(t_gt, t):
    eps = 1e-15
    t = t / (np.linalg.norm(t) + eps)
    t_gt = t_gt / (np.linalg.norm(t_gt) + eps)
    loss_t = np.maximum(eps, (1.0 - np.sum(t * t_gt) ** 2))
    err_t = np.arccos(np.sqrt(1 - loss_t))
    return np.rad2deg(np.abs(err_t))


def bbox2corners(bbox):
    return np.asarray([
        [bbox[0], bbox[1]],
        [bbox[0] + bbox[2], bbox[1]],
        [bbox[0] + bbox[2], bbox[1] + bbox[3]],
        [bbox[0], bbox[1] + bbox[3]],
    ])


def get_identity_pose():
    return np.concatenate([np.identity(3), np.zeros([3, 1])], 1).astype(np.float32)


def angular_difference(R0, R1):
    return np.rad2deg(mat2axangle(R0 @ R1.T)[1])


def load_ply_model(model_path):
    ply = PlyData.read(model_path)
    data = ply.elements[0].data
    x = data['x']
    y = data['y']
    z = data['z']
    return np.stack([x, y, z], axis=-1)


def color_map_forward(rgb):
    return rgb.astype(np.float32) / 255


def color_map_backward(rgb):
    rgb = rgb * 255
    rgb = np.clip(rgb, a_min=0, a_max=255).astype(np.uint8)
    return rgb


def rotate_image(rot, pose, K, img, mask):
    if isinstance(rot, np.ndarray):
        R = rot
    else:
        R = np.array([[np.cos(rot), -np.sin(rot), 0.0],
                      [np.sin(rot), np.cos(rot), 0.0],
                      [0, 0, 1]], dtype=np.float32)

    # adjust pose
    pose_adj = np.copy(pose)
    pose_adj[:, :3] = R @ pose_adj[:, :3]
    pose_adj[:, 3:] = R @ pose_adj[:, 3:]

    # adjust image
    transform = K @ R @ np.linalg.inv(K)  # transform original
    h, w, _ = img.shape

    ys, xs = np.nonzero(mask)
    coords = np.stack([xs, ys], -1).astype(np.float32)
    coords_new = cv2.perspectiveTransform(coords[:, None, :], transform)[:, 0, :]
    x_min, y_min = np.floor(np.min(coords_new, 0)).astype(np.int32)
    x_max, y_max = np.ceil(np.max(coords_new, 0)).astype(np.int32)
    th, tw = y_max - y_min, x_max - x_min
    translation = np.identity(3)
    translation[0, 2] = -x_min
    translation[1, 2] = -y_min
    K = translation @ K

    transform = translation @ transform
    img = cv2.warpPerspective(img, transform, (tw, th), flags=cv2.INTER_LINEAR)
    return img, pose_adj, K


def resize_img(img, ratio):
    # if ratio>=1.0: return img
    h, w, _ = img.shape
    hn, wn = int(np.round(h * ratio)), int(np.round(w * ratio))
    img_out = cv2.resize(downsample_gaussian_blur(img, ratio), (wn, hn), cv2.INTER_LINEAR)
    return img_out


def pad_img(img, padding_interval=8):
    h, w = img.shape[:2]
    hp = (padding_interval - (h % padding_interval)) % padding_interval
    wp = (padding_interval - (w % padding_interval)) % padding_interval
    if hp != 0 or wp != 0:
        img = np.pad(img, ((0, hp), (0, wp), (0, 0)), 'edge')
    return img


def pad_img_end(img, th, tw, padding_mode='edge', constant_values=0):
    h, w = img.shape[:2]
    hp = th - h
    wp = tw - w
    if hp != 0 or wp != 0:
        if padding_mode == 'constant':
            img = np.pad(img, ((0, hp), (0, wp), (0, 0)), padding_mode, constant_values=constant_values)
        else:
            img = np.pad(img, ((0, hp), (0, wp), (0, 0)), padding_mode)
    return img


def pad_img_target(img, th, tw, K=np.eye(3), background_color=0):
    h, w = img.shape[:2]
    hp = th - h
    wp = tw - w
    if hp != 0 or wp != 0:
        if len(img.shape) == 3:
            img = np.pad(img, ((hp // 2, hp - hp // 2), (wp // 2, wp - wp // 2), (0, 0)), 'constant',
                         constant_values=background_color)
        elif len(img.shape) == 2:
            img = np.pad(img, ((hp // 2, hp - hp // 2), (wp // 2, wp - wp // 2)), 'constant',
                         constant_values=background_color)
        else:
            print(f'image shape unknown {img.shape}')
            raise NotImplementedError
        translation = np.identity(3)
        translation[0, 2] = wp // 2
        translation[1, 2] = hp // 2
        K = translation @ K
    return img, K


def get_coords_mask(que_mask, train_ray_num, foreground_ratio):
    min_pos_num = int(train_ray_num * foreground_ratio)
    y0, x0 = np.nonzero(que_mask)
    y1, x1 = np.nonzero(~que_mask)
    xy0 = np.stack([x0, y0], 1).astype(np.float32)
    xy1 = np.stack([x1, y1], 1).astype(np.float32)
    idx = np.arange(xy0.shape[0])
    np.random.shuffle(idx)
    xy0 = xy0[idx]
    coords0 = xy0[:min_pos_num]
    # still remain pixels
    if min_pos_num < train_ray_num:
        xy1 = np.concatenate([xy1, xy0[min_pos_num:]], 0)
        idx = np.arange(xy1.shape[0])
        np.random.shuffle(idx)
        coords1 = xy1[idx[:(train_ray_num - min_pos_num)]]
        coords = np.concatenate([coords0, coords1], 0)
    else:
        coords = coords0
    return coords


def get_inverse_depth(depth_range, depth_num):
    near, far = depth_range
    interval = (1 / far - 1 / near) / (depth_num - 1)
    ticks = np.arange(1, depth_num - 1)
    ticks = 1 / (1 / near + ticks * interval)
    return np.concatenate([np.asarray([near]).reshape([1]), ticks, np.asarray(far).reshape([1])], 0)


def pose_inverse(pose):
    R = pose[:, :3].T
    t = - R @ pose[:, 3:]
    return np.concatenate([R, t], -1)


def pose_compose(pose0, pose1):
    """
    apply pose0 first, then pose1
    :param pose0:
    :param pose1:
    :return:
    """
    t = pose1[:, :3] @ pose0[:, 3:] + pose1[:, 3:]
    R = pose1[:, :3] @ pose0[:, :3]
    return np.concatenate([R, t], 1)


def make_dir(dir):
    if not os.path.exists(dir):
        os.system(f'mkdir -p {dir}')


def to_cuda(data):
    if type(data) == list:
        results = []
        for i, item in enumerate(data):
            results.append(to_cuda(item))
        return results
    elif type(data) == dict:
        results = {}
        for k, v in data.items():
            results[k] = to_cuda(v)
        return results
    elif type(data).__name__ == "Tensor" or type(data).__name__=="Parameter":
        return data.cuda()
    else:
        return data


def to_cpu_numpy(data):
    if type(data) == list:
        results = []
        for i, item in enumerate(data):
            results.append(to_cpu_numpy(item))
        return results
    elif type(data) == dict:
        results = {}
        for k, v in data.items():
            results[k] = to_cpu_numpy(v)
        return results
    elif type(data).__name__ == "Tensor" or type(data).__name__=="Parameter":
        return data.detach().cpu().numpy()
    else:
        return data


def sample_fps_points(points, sample_num, init_center=True, index_model=False, init_first=False, init_first_index=0,
                      init_point=None):
    sample_num = min(points.shape[0], sample_num)
    output_index = []
    if init_point is None:
        if init_center:
            init_point = np.mean(points, 0)
        else:
            if init_first:
                init_index = init_first_index
            else:
                init_index = np.random.randint(0, points.shape[0])
            init_point = points[init_index]
            output_index.append(init_index)

    output_points = [init_point]
    cur_point = init_point
    distance = np.full(points.shape[0], 1e8)
    for k in range(sample_num - 1):
        cur_distance = np.linalg.norm(cur_point[None, :] - points, 2, 1)
        distance = np.min(np.stack([cur_distance, distance], 1), 1)
        cur_index = np.argmax(distance)
        cur_point = points[cur_index]
        output_points.append(cur_point)
        output_index.append(cur_index)

    if index_model:
        return np.asarray(output_index)
    else:
        return np.asarray(output_points)


def pnp(points_3d, points_2d, camera_matrix, method=cv2.SOLVEPNP_ITERATIVE):
    dist_coeffs = np.zeros(shape=[8, 1], dtype='float64')

    assert points_3d.shape[0] == points_2d.shape[0], 'points 3D and points 2D must have same number of vertices'
    if method == cv2.SOLVEPNP_EPNP:
        points_3d = np.expand_dims(points_3d, 0)
        points_2d = np.expand_dims(points_2d, 0)

    points_2d = np.ascontiguousarray(points_2d.astype(np.float64))
    points_3d = np.ascontiguousarray(points_3d.astype(np.float64))
    camera_matrix = camera_matrix.astype(np.float64)
    _, R_exp, t = cv2.solvePnP(points_3d,
                               points_2d,
                               camera_matrix,
                               dist_coeffs,
                               flags=method)

    R, _ = cv2.Rodrigues(R_exp)
    return np.concatenate([R, t], axis=-1)


def triangulate(kps0, kps1, pose0, pose1, K0, K1):
    kps0_ = hpts_to_pts(pts_to_hpts(kps0) @ np.linalg.inv(K0).T)
    kps1_ = hpts_to_pts(pts_to_hpts(kps1) @ np.linalg.inv(K1).T)
    pts3d = cv2.triangulatePoints(pose0.astype(np.float64), pose1.astype(np.float64),
                                  kps0_.T.astype(np.float64), kps1_.T.astype(np.float64)).T
    pts3d = pts3d[:, :3] / pts3d[:, 3:]
    return pts3d


def transformation_compose_2d(trans0, trans1):
    """
    @param trans0: [2,3]
    @param trans1: [2,3]
    @return: apply trans0 then trans1
    """
    t1 = trans1[:, 2]
    t0 = trans0[:, 2]
    R1 = trans1[:, :2]
    R0 = trans0[:, :2]
    R = R1 @ R0
    t = R1 @ t0 + t1
    return np.concatenate([R, t[:, None]], 1)


def transformation_apply_2d(trans, points):
    return points @ trans[:, :2].T + trans[:, 2:].T


def angle_to_rotation_2d(angle):
    return np.asarray([[np.cos(angle), -np.sin(angle)],
                       [np.sin(angle), np.cos(angle)]])


def transformation_offset_2d(x, y):
    return np.concatenate([np.eye(2), np.asarray([x, y])[:, None]], 1).astype(np.float32)


def transformation_scale_2d(scale):
    return np.concatenate([np.diag([scale, scale]), np.zeros([2, 1])], 1).astype(np.float32)


def transformation_rotation_2d(ang):
    return np.concatenate([angle_to_rotation_2d(ang), np.zeros([2, 1])], 1).astype(np.float32)


def look_at_rotation(point):
    """
    @param point: point in normalized image coordinate not in pixels
    @return: R
    R @ x_raw -> x_lookat
    """
    x, y = point
    R1 = euler2mat(-np.arctan2(x, 1), 0, 0, 'syxz')
    R2 = euler2mat(np.arctan2(y, 1), 0, 0, 'sxyz')
    return R2 @ R1


def save_depth(fn, depth, max_val=1000):
    import png
    depth = np.clip(depth, a_min=0, a_max=max_val) / max_val * 65535
    depth = depth.astype(np.uint16)
    with open(fn, 'wb') as f:
        writer = png.Writer(width=depth.shape[1], height=depth.shape[0], bitdepth=16, greyscale=True)
        zgray2list = depth.tolist()
        writer.write(f, zgray2list)