lam/models/rendering/flame_model/lbs.py

# -*- coding: utf-8 -*-

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# holder of all proprietary rights on this computer program.
# You can only use this computer program if you have closed
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#
# Copyright©2019 Max-Planck-Gesellschaft zur Förderung
# der Wissenschaften e.V. (MPG). acting on behalf of its Max Planck Institute
# for Intelligent Systems. All rights reserved.
#
# Contact: ps-license@tuebingen.mpg.de

from __future__ import absolute_import
from __future__ import print_function
from __future__ import division

import torch
import torch.nn.functional as F


def batch_rodrigues(rot_vecs, epsilon=1e-8, dtype=torch.float32):
    """Calculates the rotation matrices for a batch of rotation vectors
    Parameters
    ----------
    rot_vecs: torch.tensor Nx3
        array of N axis-angle vectors
    Returns
    -------
    R: torch.tensor Nx3x3
        The rotation matrices for the given axis-angle parameters
    """

    batch_size = rot_vecs.shape[0]
    device = rot_vecs.device

    angle = torch.norm(rot_vecs + 1e-8, dim=1, keepdim=True)
    rot_dir = rot_vecs / angle

    cos = torch.unsqueeze(torch.cos(angle), dim=1)
    sin = torch.unsqueeze(torch.sin(angle), dim=1)

    # Bx1 arrays
    rx, ry, rz = torch.split(rot_dir, 1, dim=1)
    K = torch.zeros((batch_size, 3, 3), dtype=dtype, device=device)

    zeros = torch.zeros((batch_size, 1), dtype=dtype, device=device)
    K = torch.cat([zeros, -rz, ry, rz, zeros, -rx, -ry, rx, zeros], dim=1).view(
        (batch_size, 3, 3)
    )

    ident = torch.eye(3, dtype=dtype, device=device).unsqueeze(dim=0)
    rot_mat = ident + sin * K + (1 - cos) * torch.bmm(K, K)
    return rot_mat


def vertices2landmarks(vertices, faces, lmk_faces_idx, lmk_bary_coords):
    """Calculates landmarks by barycentric interpolation

    Parameters
    ----------
    vertices: torch.tensor BxVx3, dtype = torch.float32
        The tensor of input vertices
    faces: torch.tensor Fx3, dtype = torch.long
        The faces of the mesh
    lmk_faces_idx: torch.tensor L, dtype = torch.long
        The tensor with the indices of the faces used to calculate the
        landmarks.
    lmk_bary_coords: torch.tensor Lx3, dtype = torch.float32
        The tensor of barycentric coordinates that are used to interpolate
        the landmarks

    Returns
    -------
    landmarks: torch.tensor BxLx3, dtype = torch.float32
        The coordinates of the landmarks for each mesh in the batch
    """
    # Extract the indices of the vertices for each face
    # BxLx3
    batch_size, num_verts = vertices.shape[:2]
    device = vertices.device

    lmk_faces = torch.index_select(faces, 0, lmk_faces_idx.view(-1)).view(
        batch_size, -1, 3
    )

    lmk_faces += (
        torch.arange(batch_size, dtype=torch.long, device=device).view(-1, 1, 1)
        * num_verts
    )

    lmk_vertices = vertices.view(-1, 3)[lmk_faces].view(batch_size, -1, 3, 3)

    landmarks = torch.einsum("blfi,blf->bli", [lmk_vertices, lmk_bary_coords])
    return landmarks


def lbs(
    pose,
    v_shaped,
    posedirs,
    J_regressor,
    parents,
    lbs_weights,
    pose2rot=True,
    dtype=torch.float32,
):
    """Performs Linear Blend Skinning with the given shape and pose parameters

    Parameters
    ----------
    betas : torch.tensor BxNB
        The tensor of shape parameters
    pose : torch.tensor Bx(J + 1) * 3
        The pose parameters in axis-angle format
    v_template: torch.tensor BxVx3
        The template mesh that will be deformed
    shapedirs : torch.tensor 1xNB
        The tensor of PCA shape displacements
    posedirs : torch.tensor Px(V * 3)
        The pose PCA coefficients
    J_regressor : torch.tensor JxV
        The regressor array that is used to calculate the joints from
        the position of the vertices
    parents: torch.tensor J
        The array that describes the kinematic tree for the model
    lbs_weights: torch.tensor N x V x (J + 1)
        The linear blend skinning weights that represent how much the
        rotation matrix of each part affects each vertex
    pose2rot: bool, optional
        Flag on whether to convert the input pose tensor to rotation
        matrices. The default value is True. If False, then the pose tensor
        should already contain rotation matrices and have a size of
        Bx(J + 1)x9
    dtype: torch.dtype, optional

    Returns
    -------
    verts: torch.tensor BxVx3
        The vertices of the mesh after applying the shape and pose
        displacements.
    joints: torch.tensor BxJx3
        The joints of the model
    """

    batch_size = pose.shape[0]
    device = pose.device

    # Get the joints
    # NxJx3 array
    J = vertices2joints(J_regressor, v_shaped)

    # 3. Add pose blend shapes
    # N x J x 3 x 3
    ident = torch.eye(3, dtype=dtype, device=device)
    if pose2rot:
        rot_mats = batch_rodrigues(pose.view(-1, 3), dtype=dtype).view(
            [batch_size, -1, 3, 3]
        )

        pose_feature = (rot_mats[:, 1:, :, :] - ident).view([batch_size, -1])
        # (N x P) x (P, V * 3) -> N x V x 3
        pose_offsets = torch.matmul(pose_feature, posedirs).view(batch_size, -1, 3)
    else:
        pose_feature = pose[:, 1:].view(batch_size, -1, 3, 3) - ident
        rot_mats = pose.view(batch_size, -1, 3, 3)

        pose_offsets = torch.matmul(pose_feature.view(batch_size, -1), posedirs).view(
            batch_size, -1, 3
        )

    v_posed = pose_offsets + v_shaped

    # 4. Get the global joint location
    J_transformed, A = batch_rigid_transform(rot_mats, J, parents, dtype=dtype)

    # 5. Do skinning:
    # W is N x V x (J + 1)
    W = lbs_weights.unsqueeze(dim=0).expand([batch_size, -1, -1])
    # (N x V x (J + 1)) x (N x (J + 1) x 16)
    num_joints = J_regressor.shape[0]
    T = torch.matmul(W, A.view(batch_size, num_joints, 16)).view(batch_size, -1, 4, 4)

    homogen_coord = torch.ones(
        [batch_size, v_posed.shape[1], 1], dtype=dtype, device=device
    )
    v_posed_homo = torch.cat([v_posed, homogen_coord], dim=2)
    v_homo = torch.matmul(T, torch.unsqueeze(v_posed_homo, dim=-1))

    verts = v_homo[:, :, :3, 0]

    return verts, J_transformed, A[:, 1]


def vertices2joints(J_regressor, vertices):
    """Calculates the 3D joint locations from the vertices

    Parameters
    ----------
    J_regressor : torch.tensor JxV
        The regressor array that is used to calculate the joints from the
        position of the vertices
    vertices : torch.tensor BxVx3
        The tensor of mesh vertices

    Returns
    -------
    torch.tensor BxJx3
        The location of the joints
    """

    return torch.einsum("bik,ji->bjk", [vertices, J_regressor])


def blend_shapes(betas, shape_disps):
    """Calculates the per vertex displacement due to the blend shapes


    Parameters
    ----------
    betas : torch.tensor Bx(num_betas)
        Blend shape coefficients
    shape_disps: torch.tensor Vx3x(num_betas)
        Blend shapes

    Returns
    -------
    torch.tensor BxVx3
        The per-vertex displacement due to shape deformation
    """

    # Displacement[b, m, k] = sum_{l} betas[b, l] * shape_disps[m, k, l]
    # i.e. Multiply each shape displacement by its corresponding beta and
    # then sum them.
    blend_shape = torch.einsum("bl,mkl->bmk", [betas, shape_disps])
    return blend_shape


def transform_mat(R, t):
    """Creates a batch of transformation matrices
    Args:
        - R: Bx3x3 array of a batch of rotation matrices
        - t: Bx3x1 array of a batch of translation vectors
    Returns:
        - T: Bx4x4 Transformation matrix
    """
    # No padding left or right, only add an extra row
    return torch.cat([F.pad(R, [0, 0, 0, 1]), F.pad(t, [0, 0, 0, 1], value=1)], dim=2)


def batch_rigid_transform(rot_mats, joints, parents, dtype=torch.float32):
    """
    Applies a batch of rigid transformations to the joints

    Parameters
    ----------
    rot_mats : torch.tensor BxNx3x3
        Tensor of rotation matrices
    joints : torch.tensor BxNx3
        Locations of joints
    parents : torch.tensor BxN
        The kinematic tree of each object
    dtype : torch.dtype, optional:
        The data type of the created tensors, the default is torch.float32

    Returns
    -------
    posed_joints : torch.tensor BxNx3
        The locations of the joints after applying the pose rotations
    rel_transforms : torch.tensor BxNx4x4
        The relative (with respect to the root joint) rigid transformations
        for all the joints
    """

    joints = torch.unsqueeze(joints, dim=-1)

    rel_joints = joints.clone().contiguous()
    rel_joints[:, 1:] = rel_joints[:, 1:] - joints[:, parents[1:]]

    transforms_mat = transform_mat(rot_mats.view(-1, 3, 3), rel_joints.view(-1, 3, 1))
    transforms_mat = transforms_mat.view(-1, joints.shape[1], 4, 4)

    transform_chain = [transforms_mat[:, 0]]
    for i in range(1, parents.shape[0]):
        # Subtract the joint location at the rest pose
        # No need for rotation, since it's identity when at rest
        curr_res = torch.matmul(transform_chain[parents[i]], transforms_mat[:, i])
        transform_chain.append(curr_res)

    transforms = torch.stack(transform_chain, dim=1)

    # The last column of the transformations contains the posed joints
    posed_joints = transforms[:, :, :3, 3]

    joints_homogen = F.pad(joints, [0, 0, 0, 1])

    rel_transforms = transforms - F.pad(
        torch.matmul(transforms, joints_homogen), [3, 0, 0, 0, 0, 0, 0, 0]
    )

    return posed_joints, rel_transforms