recon/volumetric_rendering/renderer_next3d.py

# SPDX-FileCopyrightText: Copyright (c) 2021-2022 NVIDIA CORPORATION & AFFILIATES. All rights reserved.
# SPDX-License-Identifier: LicenseRef-NvidiaProprietary
#
# NVIDIA CORPORATION, its affiliates and licensors retain all intellectual
# property and proprietary rights in and to this material, related
# documentation and any modifications thereto. Any use, reproduction,
# disclosure or distribution of this material and related documentation
# without an express license agreement from NVIDIA CORPORATION or
# its affiliates is strictly prohibited.

"""
The renderer is a module that takes in rays, decides where to sample along each
ray, and computes pixel colors using the volume rendering equation.
"""

import math
import torch
import torch.nn as nn
import numpy as np

from training_avatar_texture.volumetric_rendering.ray_marcher import MipRayMarcher2
from training_avatar_texture.volumetric_rendering import math_utils

global Meshes, load_obj, rasterize_meshes
from pytorch3d.structures import Meshes
from pytorch3d.io import load_obj
from pytorch3d.renderer.mesh import rasterize_meshes


def generate_planes():
    """
    Defines planes by the three vectors that form the "axes" of the
    plane. Should work with arbitrary number of planes and planes of
    arbitrary orientation.
    """
    return torch.tensor([[[1, 0, 0],
                          [0, 1, 0],
                          [0, 0, 1]],
                         [[1, 0, 0],
                          [0, 0, 1],
                          [0, 1, 0]],
                         [[0, 0, 1],
                          [0, 1, 0],
                          [1, 0, 0]]], dtype=torch.float32)


def project_onto_planes(planes, coordinates):
    """
    Does a projection of a 3D point onto a batch of 2D planes,
    returning 2D plane coordinates.

    Takes plane axes of shape n_planes, 3, 3
    # Takes coordinates of shape N, M, 3
    # returns projections of shape N*n_planes, M, 2
    """
    N, M, C = coordinates.shape
    n_planes, _, _ = planes.shape
    coordinates = coordinates.unsqueeze(1).expand(-1, n_planes, -1, -1).reshape(N * n_planes, M, 3)
    inv_planes = torch.linalg.inv(planes).unsqueeze(0).expand(N, -1, -1, -1).reshape(N * n_planes, 3, 3)
    projections = torch.bmm(coordinates, inv_planes)
    return projections[..., :2]


def sample_from_planes(plane_axes, plane_features, coordinates, mode='bilinear', padding_mode='zeros', box_warp=None):
    assert padding_mode == 'zeros'
    N, n_planes, C, H, W = plane_features.shape
    _, M, _ = coordinates.shape
    plane_features = plane_features.view(N * n_planes, C, H, W)

    coordinates = (2 / box_warp) * coordinates  # TODO: add specific box bounds

    projected_coordinates = project_onto_planes(plane_axes, coordinates).unsqueeze(1)
    output_features = torch.nn.functional.grid_sample(plane_features, projected_coordinates.float(), mode=mode, padding_mode=padding_mode,
                                                      align_corners=False).permute(0, 3, 2, 1).reshape(N, n_planes, M, C)
    return output_features


def sample_from_3dgrid(grid, coordinates):
    """
    Expects coordinates in shape (batch_size, num_points_per_batch, 3)
    Expects grid in shape (1, channels, H, W, D)
    (Also works if grid has batch size)
    Returns sampled features of shape (batch_size, num_points_per_batch, feature_channels)
    """
    batch_size, n_coords, n_dims = coordinates.shape
    sampled_features = torch.nn.functional.grid_sample(grid.expand(batch_size, -1, -1, -1, -1),
                                                       coordinates.reshape(batch_size, 1, 1, -1, n_dims),
                                                       mode='bilinear', padding_mode='zeros', align_corners=False)
    N, C, H, W, D = sampled_features.shape
    sampled_features = sampled_features.permute(0, 4, 3, 2, 1).reshape(N, H * W * D, C)
    return sampled_features


class ImportanceRenderer(torch.nn.Module):
    def __init__(self):
        super().__init__()
        self.ray_marcher = MipRayMarcher2()
        self.plane_axes = generate_planes()

    def forward(self, planes, decoder, ray_origins, ray_directions, rendering_options):
        self.plane_axes = self.plane_axes.to(ray_origins.device)

        if rendering_options['ray_start'] == rendering_options['ray_end'] == 'auto':
            ray_start, ray_end = math_utils.get_ray_limits_box(ray_origins, ray_directions, box_side_length=rendering_options['box_warp'])
            is_ray_valid = ray_end > ray_start
            if torch.any(is_ray_valid).item():
                ray_start[~is_ray_valid] = ray_start[is_ray_valid].min()
                ray_end[~is_ray_valid] = ray_start[is_ray_valid].max()
            depths_coarse = self.sample_stratified(ray_origins, ray_start, ray_end, rendering_options['depth_resolution'],
                                                   rendering_options['disparity_space_sampling'])
        else:
            # Create stratified depth samples
            depths_coarse = self.sample_stratified(ray_origins, rendering_options['ray_start'], rendering_options['ray_end'],
                                                   rendering_options['depth_resolution'], rendering_options['disparity_space_sampling'])

        batch_size, num_rays, samples_per_ray, _ = depths_coarse.shape

        # Coarse Pass
        sample_coordinates = (ray_origins.unsqueeze(-2) + depths_coarse * ray_directions.unsqueeze(-2)).reshape(batch_size, -1, 3)
        sample_directions = ray_directions.unsqueeze(-2).expand(-1, -1, samples_per_ray, -1).reshape(batch_size, -1, 3)

        out = self.run_model(planes, decoder, sample_coordinates, sample_directions, rendering_options)
        colors_coarse = out['rgb']
        densities_coarse = out['sigma']
        colors_coarse = colors_coarse.reshape(batch_size, num_rays, samples_per_ray, colors_coarse.shape[-1])
        densities_coarse = densities_coarse.reshape(batch_size, num_rays, samples_per_ray, 1)

        # Fine Pass
        N_importance = rendering_options['depth_resolution_importance']
        if N_importance > 0:
            _, _, weights = self.ray_marcher(colors_coarse, densities_coarse, depths_coarse, rendering_options)

            depths_fine = self.sample_importance(depths_coarse, weights, N_importance)

            sample_directions = ray_directions.unsqueeze(-2).expand(-1, -1, N_importance, -1).reshape(batch_size, -1, 3)
            sample_coordinates = (ray_origins.unsqueeze(-2) + depths_fine * ray_directions.unsqueeze(-2)).reshape(batch_size, -1, 3)

            out = self.run_model(planes, decoder, sample_coordinates, sample_directions, rendering_options)
            colors_fine = out['rgb']
            densities_fine = out['sigma']
            colors_fine = colors_fine.reshape(batch_size, num_rays, N_importance, colors_fine.shape[-1])
            densities_fine = densities_fine.reshape(batch_size, num_rays, N_importance, 1)

            all_depths, all_colors, all_densities = self.unify_samples(depths_coarse, colors_coarse, densities_coarse,
                                                                       depths_fine, colors_fine, densities_fine)

            # Aggregate
            rgb_final, depth_final, weights = self.ray_marcher(all_colors, all_densities, all_depths, rendering_options)
        else:
            rgb_final, depth_final, weights = self.ray_marcher(colors_coarse, densities_coarse, depths_coarse, rendering_options)

        return rgb_final, depth_final, weights.sum(2)

    def run_model(self, planes, decoder, sample_coordinates, sample_directions, options):
        sampled_features = sample_from_planes(self.plane_axes, planes, sample_coordinates, padding_mode='zeros', box_warp=options['box_warp'])

        out = decoder(sampled_features, sample_directions)
        if options.get('density_noise', 0) > 0:
            out['sigma'] += torch.randn_like(out['sigma']) * options['density_noise']
        return out

    def sort_samples(self, all_depths, all_colors, all_densities):
        _, indices = torch.sort(all_depths, dim=-2)
        all_depths = torch.gather(all_depths, -2, indices)
        all_colors = torch.gather(all_colors, -2, indices.expand(-1, -1, -1, all_colors.shape[-1]))
        all_densities = torch.gather(all_densities, -2, indices.expand(-1, -1, -1, 1))
        return all_depths, all_colors, all_densities

    def unify_samples(self, depths1, colors1, densities1, depths2, colors2, densities2, normals1=None, normals2=None):
        all_depths = torch.cat([depths1, depths2], dim=-2)
        all_colors = torch.cat([colors1, colors2], dim=-2)
        all_densities = torch.cat([densities1, densities2], dim=-2)

        if normals1 is not None and normals2 is not None:
            all_normals = torch.cat([normals1, normals2], dim=-2)
        else:
            all_normals = None

        _, indices = torch.sort(all_depths, dim=-2)
        all_depths = torch.gather(all_depths, -2, indices)
        all_colors = torch.gather(all_colors, -2, indices.expand(-1, -1, -1, all_colors.shape[-1]))
        all_densities = torch.gather(all_densities, -2, indices.expand(-1, -1, -1, 1))
        if all_normals is not None:
            all_normals = torch.gather(all_normals, -2, indices.expand(-1, -1, -1, all_normals.shape[-1]))
            return all_depths, all_colors, all_normals, all_densities

        return all_depths, all_colors, all_densities

    def sample_stratified(self, ray_origins, ray_start, ray_end, depth_resolution, disparity_space_sampling=False):
        """
        Return depths of approximately uniformly spaced samples along rays.
        """
        N, M, _ = ray_origins.shape
        if disparity_space_sampling:
            depths_coarse = torch.linspace(0,
                                           1,
                                           depth_resolution,
                                           device=ray_origins.device).reshape(1, 1, depth_resolution, 1).repeat(N, M, 1, 1)
            depth_delta = 1 / (depth_resolution - 1)
            depths_coarse += torch.rand_like(depths_coarse) * depth_delta
            depths_coarse = 1. / (1. / ray_start * (1. - depths_coarse) + 1. / ray_end * depths_coarse)
        else:
            if type(ray_start) == torch.Tensor:
                depths_coarse = math_utils.linspace(ray_start, ray_end, depth_resolution).permute(1, 2, 0, 3)
                depth_delta = (ray_end - ray_start) / (depth_resolution - 1)
                depths_coarse += torch.rand_like(depths_coarse) * depth_delta[..., None]
            else:
                depths_coarse = torch.linspace(ray_start, ray_end, depth_resolution, device=ray_origins.device).reshape(1, 1, depth_resolution,
                                                                                                                        1).repeat(N, M, 1, 1)
                depth_delta = (ray_end - ray_start) / (depth_resolution - 1)
                depths_coarse += torch.rand_like(depths_coarse) * depth_delta

        return depths_coarse

    def sample_importance(self, z_vals, weights, N_importance):
        """
        Return depths of importance sampled points along rays. See NeRF importance sampling for more.
        """
        with torch.no_grad():
            batch_size, num_rays, samples_per_ray, _ = z_vals.shape

            z_vals = z_vals.reshape(batch_size * num_rays, samples_per_ray)
            weights = weights.reshape(batch_size * num_rays, -1)  # -1 to account for loss of 1 sample in MipRayMarcher

            # smooth weights
            weights = torch.nn.functional.max_pool1d(weights.unsqueeze(1).float(), 2, 1, padding=1)
            weights = torch.nn.functional.avg_pool1d(weights, 2, 1).squeeze()
            weights = weights + 0.01

            z_vals_mid = 0.5 * (z_vals[:, :-1] + z_vals[:, 1:])
            importance_z_vals = self.sample_pdf(z_vals_mid, weights[:, 1:-1],
                                                N_importance).detach().reshape(batch_size, num_rays, N_importance, 1)
        return importance_z_vals

    def sample_pdf(self, bins, weights, N_importance, det=False, eps=1e-5):
        """
        Sample @N_importance samples from @bins with distribution defined by @weights.
        Inputs:
            bins: (N_rays, N_samples_+1) where N_samples_ is "the number of coarse samples per ray - 2"
            weights: (N_rays, N_samples_)
            N_importance: the number of samples to draw from the distribution
            det: deterministic or not
            eps: a small number to prevent division by zero
        Outputs:
            samples: the sampled samples
        """
        N_rays, N_samples_ = weights.shape
        weights = weights + eps  # prevent division by zero (don't do inplace op!)
        pdf = weights / torch.sum(weights, -1, keepdim=True)  # (N_rays, N_samples_)
        cdf = torch.cumsum(pdf, -1)  # (N_rays, N_samples), cumulative distribution function
        cdf = torch.cat([torch.zeros_like(cdf[:, :1]), cdf], -1)  # (N_rays, N_samples_+1)
        # padded to 0~1 inclusive

        if det:
            u = torch.linspace(0, 1, N_importance, device=bins.device)
            u = u.expand(N_rays, N_importance)
        else:
            u = torch.rand(N_rays, N_importance, device=bins.device)
        u = u.contiguous()

        inds = torch.searchsorted(cdf, u, right=True)
        below = torch.clamp_min(inds - 1, 0)
        above = torch.clamp_max(inds, N_samples_)

        inds_sampled = torch.stack([below, above], -1).view(N_rays, 2 * N_importance)
        cdf_g = torch.gather(cdf, 1, inds_sampled).view(N_rays, N_importance, 2)
        bins_g = torch.gather(bins, 1, inds_sampled).view(N_rays, N_importance, 2)

        denom = cdf_g[..., 1] - cdf_g[..., 0]
        denom[denom < eps] = 1  # denom equals 0 means a bin has weight 0, in which case it will not be sampled
        # anyway, therefore any value for it is fine (set to 1 here)

        samples = bins_g[..., 0] + (u - cdf_g[..., 0]) / denom * (bins_g[..., 1] - bins_g[..., 0])
        return samples

    def normal_forward(self, planes, decoder, ray_origins, ray_directions, rendering_options):
        max_batch = 100000
        self.plane_axes = self.plane_axes.to(ray_origins.device)

        if rendering_options['ray_start'] == rendering_options['ray_end'] == 'auto':
            ray_start, ray_end = math_utils.get_ray_limits_box(ray_origins, ray_directions, box_side_length=rendering_options['box_warp'])
            is_ray_valid = ray_end > ray_start
            if torch.any(is_ray_valid).item():
                ray_start[~is_ray_valid] = ray_start[is_ray_valid].min()
                ray_end[~is_ray_valid] = ray_start[is_ray_valid].max()
            depths_coarse = self.sample_stratified(ray_origins, ray_start, ray_end, rendering_options['depth_resolution'],
                                                   rendering_options['disparity_space_sampling'])
        else:
            # Create stratified depth samples
            depths_coarse = self.sample_stratified(ray_origins, rendering_options['ray_start'], rendering_options['ray_end'],
                                                   rendering_options['depth_resolution'], rendering_options['disparity_space_sampling'])

        batch_size, num_rays, samples_per_ray, _ = depths_coarse.shape

        # Coarse Pass
        sample_coordinates = (ray_origins.unsqueeze(-2) + depths_coarse * ray_directions.unsqueeze(-2)).reshape(batch_size, -1, 3)
        sample_directions = ray_directions.unsqueeze(-2).expand(-1, -1, samples_per_ray, -1).reshape(batch_size, -1, 3)

        sample_coordinates.requires_grad_()
        # input.requires_grad_()
        with torch.set_grad_enabled(True):
            colors = torch.zeros((sample_coordinates.shape[0], sample_coordinates.shape[1], 32), device=sample_coordinates.device)
            sigmas = torch.zeros((sample_coordinates.shape[0], sample_coordinates.shape[1], 1), device=sample_coordinates.device)

            head = 0
            while head < sample_coordinates.shape[1]:
                out = self.run_model(planes, decoder, sample_coordinates[:, head:head + max_batch], sample_directions[:, head:head + max_batch],
                                     rendering_options)
                colors[:, head:head + max_batch] = out['rgb']
                sigmas[:, head:head + max_batch] = out['sigma']
                head += max_batch
            colors_coarse = colors
            densities_coarse = sigmas

            input_grad = torch.autograd.grad(torch.sum(densities_coarse), sample_coordinates, create_graph=False)[0]
            normal = -input_grad

        normals_coarse = normal.reshape(batch_size, num_rays, samples_per_ray, normal.shape[-1])

        colors_coarse = colors_coarse.reshape(batch_size, num_rays, samples_per_ray, colors_coarse.shape[-1])
        densities_coarse = densities_coarse.reshape(batch_size, num_rays, samples_per_ray, 1)

        # Fine Pass
        N_importance = rendering_options['depth_resolution_importance']
        if N_importance > 0:
            _, _, weights = self.ray_marcher(colors_coarse, densities_coarse, depths_coarse, rendering_options)

            depths_fine = self.sample_importance(depths_coarse, weights, N_importance)

            sample_directions = ray_directions.unsqueeze(-2).expand(-1, -1, N_importance, -1).reshape(batch_size, -1, 3)
            sample_coordinates = (ray_origins.unsqueeze(-2) + depths_fine * ray_directions.unsqueeze(-2)).reshape(batch_size, -1, 3)

            sample_coordinates.requires_grad_()
            with torch.set_grad_enabled(True):
                colors = torch.zeros((sample_coordinates.shape[0], sample_coordinates.shape[1], 32), device=sample_coordinates.device)
                sigmas = torch.zeros((sample_coordinates.shape[0], sample_coordinates.shape[1], 1), device=sample_coordinates.device)

                head = 0
                while head < sample_coordinates.shape[1]:
                    out = self.run_model(planes, decoder, sample_coordinates[:, head:head + max_batch], sample_directions[:, head:head + max_batch],
                                         rendering_options)
                    colors[:, head:head + max_batch] = out['rgb']
                    sigmas[:, head:head + max_batch] = out['sigma']
                    head += max_batch
                colors_fine = colors
                densities_fine = sigmas

                input_grad = torch.autograd.grad(torch.sum(densities_fine), sample_coordinates, create_graph=False)[0]
                normal = -input_grad
            normals_fine = normal.reshape(batch_size, num_rays, N_importance, normal.shape[-1])

            colors_fine = colors_fine.reshape(batch_size, num_rays, N_importance, colors_fine.shape[-1])
            densities_fine = densities_fine.reshape(batch_size, num_rays, N_importance, 1)

            all_depths, all_colors, all_normals, all_densities = self.unify_samples(depths_coarse, colors_coarse, densities_coarse,
                                                                                    depths_fine, colors_fine, densities_fine, normals_coarse,
                                                                                    normals_fine)

            # Aggregate
            rgb_final, depth_final, normal_final, weights = self.ray_marcher(all_colors, all_densities, all_depths, rendering_options, all_normals)
        else:
            rgb_final, depth_final, normal_final, weights = self.ray_marcher(colors_coarse, densities_coarse, depths_coarse, rendering_options,
                                                                             normals_coarse)

        return rgb_final, depth_final, normal_final, weights.sum(2)


from torch_utils import misc


@misc.profiled_function
def dict2obj(d):
    # if isinstance(d, list):
    #     d = [dict2obj(x) for x in d]
    if not isinstance(d, dict):
        return d

    class C(object):
        pass

    o = C()
    for k in d:
        o.__dict__[k] = dict2obj(d[k])
    return o


from torch_utils import persistence


@persistence.persistent_class
class Pytorch3dRasterizer(nn.Module):
    ## TODO: add support for rendering non-squared images, since pytorc3d supports this now
    """  Borrowed from https://github.com/facebookresearch/pytorch3d
    Notice:
        x,y,z are in image space, normalized
        can only render squared image now
    """

    def __init__(self, image_size=224):
        """
        use fixed raster_settings for rendering faces
        """
        super().__init__()
        raster_settings = {
            'image_size': image_size,
            'blur_radius': 0.0,
            'faces_per_pixel': 1,
            'bin_size': None,
            'max_faces_per_bin': None,
            'perspective_correct': False,
            'cull_backfaces': True
        }
        # raster_settings = dict2obj(raster_settings)
        self.raster_settings = raster_settings

    def forward(self, vertices, faces, attributes=None, h=None, w=None):
        fixed_vertices = vertices.clone()
        fixed_vertices[..., :2] = -fixed_vertices[..., :2]
        raster_settings = self.raster_settings
        if h is None and w is None:
            image_size = raster_settings['image_size']
        else:
            image_size = [h, w]
            if h > w:
                fixed_vertices[..., 1] = fixed_vertices[..., 1] * h / w
            else:
                fixed_vertices[..., 0] = fixed_vertices[..., 0] * w / h

        meshes_screen = Meshes(verts=fixed_vertices.float(), faces=faces.long())
        pix_to_face, zbuf, bary_coords, dists = rasterize_meshes(
            meshes_screen,
            image_size=image_size,
            blur_radius=raster_settings['blur_radius'],
            faces_per_pixel=raster_settings['faces_per_pixel'],
            bin_size=raster_settings['bin_size'],
            max_faces_per_bin=raster_settings['max_faces_per_bin'],
            perspective_correct=raster_settings['perspective_correct'],
            cull_backfaces=raster_settings['cull_backfaces']
        )
        vismask = (pix_to_face > -1).float()
        D = attributes.shape[-1]
        attributes = attributes.clone();
        attributes = attributes.view(attributes.shape[0] * attributes.shape[1], 3, attributes.shape[-1])
        N, H, W, K, _ = bary_coords.shape
        mask = pix_to_face == -1
        pix_to_face = pix_to_face.clone()
        pix_to_face[mask] = 0
        idx = pix_to_face.view(N * H * W * K, 1, 1).expand(N * H * W * K, 3, D)
        pixel_face_vals = attributes.gather(0, idx).view(N, H, W, K, 3, D)
        pixel_vals = (bary_coords[..., None] * pixel_face_vals).sum(dim=-2)
        pixel_vals[mask] = 0  # Replace masked values in output.
        pixel_vals = pixel_vals[:, :, :, 0].permute(0, 3, 1, 2)
        pixel_vals = torch.cat([pixel_vals, vismask[:, :, :, 0][:, None, :, :]], dim=1)
        # print(image_size)
        # import ipdb; ipdb.set_trace()
        return pixel_vals


# borrowed from https://github.com/daniilidis-group/neural_renderer/blob/master/neural_renderer/vertices_to_faces.py
def face_vertices(vertices, faces):
    """
    :param vertices: [batch size, number of vertices, 3]
    :param faces: [batch size, number of faces, 3]
    :return: [batch size, number of faces, 3, 3]
    """
    assert (vertices.ndimension() == 3)
    assert (faces.ndimension() == 3)
    assert (vertices.shape[0] == faces.shape[0])
    assert (vertices.shape[2] == 3)
    assert (faces.shape[2] == 3)

    bs, nv = vertices.shape[:2]
    bs, nf = faces.shape[:2]
    device = vertices.device
    faces = faces + (torch.arange(bs, dtype=torch.int32).to(device) * nv)[:, None, None]
    vertices = vertices.reshape((bs * nv, 3))
    # pytorch only supports long and byte tensors for indexing
    return vertices[faces.long()]


# ---------------------------- process/generate vertices, normals, faces
def generate_triangles(h, w, margin_x=2, margin_y=5, mask=None):
    # quad layout:
    # 0 1 ... w-1
    # w w+1
    # .
    # w*h
    triangles = []
    for x in range(margin_x, w - 1 - margin_x):
        for y in range(margin_y, h - 1 - margin_y):
            triangle0 = [y * w + x, y * w + x + 1, (y + 1) * w + x]
            triangle1 = [y * w + x + 1, (y + 1) * w + x + 1, (y + 1) * w + x]
            triangles.append(triangle0)
            triangles.append(triangle1)
    triangles = np.array(triangles)
    triangles = triangles[:, [0, 2, 1]]
    return triangles


def transform_points(points, tform, points_scale=None, out_scale=None):
    points_2d = points[:, :, :2]

    # 'input points must use original range'
    if points_scale:
        assert points_scale[0] == points_scale[1]
        points_2d = (points_2d * 0.5 + 0.5) * points_scale[0]
    # import ipdb; ipdb.set_trace()

    batch_size, n_points, _ = points.shape
    trans_points_2d = torch.bmm(
        torch.cat([points_2d, torch.ones([batch_size, n_points, 1], device=points.device, dtype=points.dtype)], dim=-1),
        tform
    )
    if out_scale:  # h,w of output image size
        trans_points_2d[:, :, 0] = trans_points_2d[:, :, 0] / out_scale[1] * 2 - 1
        trans_points_2d[:, :, 1] = trans_points_2d[:, :, 1] / out_scale[0] * 2 - 1
    trans_points = torch.cat([trans_points_2d[:, :, :2], points[:, :, 2:]], dim=-1)
    return trans_points


def batch_orth_proj(X, camera):
    ''' orthgraphic projection
        X:  3d vertices, [bz, n_point, 3]
        camera: scale and translation, [bz, 3], [scale, tx, ty]
    '''
    camera = camera.clone().view(-1, 1, 3)
    X_trans = X[:, :, :2] + camera[:, :, 1:]
    X_trans = torch.cat([X_trans, X[:, :, 2:]], 2)
    shape = X_trans.shape
    Xn = (camera[:, :, 0:1] * X_trans)
    return Xn


def angle2matrix(angles):
    ''' get rotation matrix from three rotation angles(degree). right-handed.
    Args:
        angles: [batch_size, 3] tensor containing X, Y, and Z angles.
        x: pitch. positive for looking down.
        y: yaw. positive for looking left.
        z: roll. positive for tilting head right.
    Returns:
        R: [batch_size, 3, 3]. rotation matrices.
    '''
    angles = angles * (np.pi) / 180.
    s = torch.sin(angles)
    c = torch.cos(angles)

    cx, cy, cz = (c[:, 0], c[:, 1], c[:, 2])
    sx, sy, sz = (s[:, 0], s[:, 1], s[:, 2])

    zeros = torch.zeros_like(s[:, 0]).to(angles.device)
    ones = torch.ones_like(s[:, 0]).to(angles.device)

    # Rz.dot(Ry.dot(Rx))
    R_flattened = torch.stack(
        [
            cz * cy, cz * sy * sx - sz * cx, cz * sy * cx + sz * sx,
            sz * cy, sz * sy * sx + cz * cx, sz * sy * cx - cz * sx,
            -sy, cy * sx, cy * cx,
        ],
        dim=0)  # [batch_size, 9]
    R = torch.reshape(R_flattened, (-1, 3, 3))  # [batch_size, 3, 3]
    return R


import cv2


# end_list = np.array([17, 22, 27, 42, 48, 31, 36, 68], dtype = np.int32) - 1
def plot_kpts(image, kpts, color='r', end_list=[19]):
    ''' Draw 68 key points
    Args:
        image: the input image
        kpt: (68, 3).
    '''
    if color == 'r':
        c = (255, 0, 0)
    elif color == 'g':
        c = (0, 255, 0)
    elif color == 'b':
        c = (255, 0, 0)
    image = image.copy()
    kpts = kpts.copy()
    radius = max(int(min(image.shape[0], image.shape[1]) / 200), 1)
    for i in range(kpts.shape[0]):
        st = kpts[i, :2]
        if kpts.shape[1] == 4:
            if kpts[i, 3] > 0.5:
                c = (0, 255, 0)
            else:
                c = (0, 0, 255)
        if i in end_list:
            continue
        ed = kpts[i + 1, :2]
        image = cv2.line(image, (int(st[0]), int(st[1])), (int(ed[0]), int(ed[1])), (255, 255, 255), radius)
        image = cv2.circle(image, (int(st[0]), int(st[1])), radius, c, radius * 2)

    return image


import cv2


def fill_mouth(images):
    # Input: images: [batch, 1, h, w]
    device = images.device
    mouth_masks = []
    for image in images:
        image = image[0].cpu().numpy()
        image = image * 255.
        copyImg = image.copy()
        h, w = image.shape[:2]
        mask = np.zeros([h + 2, w + 2], np.uint8)
        cv2.floodFill(copyImg, mask, (0, 0), (255, 255, 255), (0, 0, 0), (254, 254, 254), cv2.FLOODFILL_FIXED_RANGE)
        # cv2.imwrite("debug.png", copyImg)
        copyImg = torch.tensor(copyImg).to(device).to(torch.float32) / 127.5 - 1
        mouth_masks.append(copyImg.unsqueeze(0))
    mouth_masks = torch.stack(mouth_masks, 0)
    mouth_masks = ((mouth_masks * 2. - 1.) * -1. + 1.) / 2.
    # images = (images.bool() | mouth_masks.bool()).float()
    res = (images + mouth_masks).clip(0, 1)

    return res