loss.py

import pytorch3d.loss
import torch
import torch.nn as nn
import torch.nn.functional as F
import numpy

from pytorch3d.ops import cot_laplacian
from pytorch3d.structures import Meshes

def mesh_laplacian_smoothing(meshes, method: str = "uniform"):
    r"""
    Computes the laplacian smoothing objective for a batch of meshes.
    This function supports three variants of Laplacian smoothing,
    namely with uniform weights("uniform"), with cotangent weights ("cot"),
    and cotangent curvature ("cotcurv").For more details read [1, 2].

    Args:
        meshes: Meshes object with a batch of meshes.
        method: str specifying the method for the laplacian.
    Returns:
        loss: Average laplacian smoothing loss across the batch.
        Returns 0 if meshes contains no meshes or all empty meshes.

    Consider a mesh M = (V, F), with verts of shape Nx3 and faces of shape Mx3.
    The Laplacian matrix L is a NxN tensor such that LV gives a tensor of vectors:
    for a uniform Laplacian, LuV[i] points to the centroid of its neighboring
    vertices, a cotangent Laplacian LcV[i] is known to be an approximation of
    the surface normal, while the curvature variant LckV[i] scales the normals
    by the discrete mean curvature. For vertex i, assume S[i] is the set of
    neighboring vertices to i, a_ij and b_ij are the "outside" angles in the
    two triangles connecting vertex v_i and its neighboring vertex v_j
    for j in S[i], as seen in the diagram below.

    .. code-block:: python

               a_ij
                /\
               /  \
              /    \
             /      \
        v_i /________\ v_j
            \        /
             \      /
              \    /
               \  /
                \/
               b_ij

        The definition of the Laplacian is LV[i] = sum_j w_ij (v_j - v_i)
        For the uniform variant,    w_ij = 1 / |S[i]|
        For the cotangent variant,
            w_ij = (cot a_ij + cot b_ij) / (sum_k cot a_ik + cot b_ik)
        For the cotangent curvature, w_ij = (cot a_ij + cot b_ij) / (4 A[i])
        where A[i] is the sum of the areas of all triangles containing vertex v_i.

    There is a nice trigonometry identity to compute cotangents. Consider a triangle
    with side lengths A, B, C and angles a, b, c.

    .. code-block:: python

               c
              /|\
             / | \
            /  |  \
         B /  H|   \ A
          /    |    \
         /     |     \
        /a_____|_____b\
               C

        Then cot a = (B^2 + C^2 - A^2) / 4 * area
        We know that area = CH/2, and by the law of cosines we have

        A^2 = B^2 + C^2 - 2BC cos a => B^2 + C^2 - A^2 = 2BC cos a

        Putting these together, we get:

        B^2 + C^2 - A^2     2BC cos a
        _______________  =  _________ = (B/H) cos a = cos a / sin a = cot a
           4 * area            2CH


    [1] Desbrun et al, "Implicit fairing of irregular meshes using diffusion
    and curvature flow", SIGGRAPH 1999.

    [2] Nealan et al, "Laplacian Mesh Optimization", Graphite 2006.
    """

    if meshes.isempty():
        return torch.tensor(
            [0.0], dtype=torch.float32, device=meshes.device, requires_grad=True
        )

    N = len(meshes)
    verts_packed = meshes.verts_packed()  # (sum(V_n), 3)
    faces_packed = meshes.faces_packed()  # (sum(F_n), 3)
    num_verts_per_mesh = meshes.num_verts_per_mesh()  # (N,)
    verts_packed_idx = meshes.verts_packed_to_mesh_idx()  # (sum(V_n),)
    weights = num_verts_per_mesh.gather(0, verts_packed_idx)  # (sum(V_n),)
    weights = 1.0 / weights.float()

    # We don't want to backprop through the computation of the Laplacian;
    # just treat it as a magic constant matrix that is used to transform
    # verts into normals
    with torch.no_grad():
        if method == "uniform":
            L = meshes.laplacian_packed()
        elif method in ["cot", "cotcurv"]:
            L, inv_areas = cot_laplacian(verts_packed, faces_packed)
            if method == "cot":
                norm_w = torch.sparse.sum(L, dim=1).to_dense().view(-1, 1)
                idx = norm_w > 0
                norm_w[idx] = 1.0 / norm_w[idx]
            else:
                L_sum = torch.sparse.sum(L, dim=1).to_dense().view(-1, 1)
                norm_w = 0.25 * inv_areas
        else:
            raise ValueError("Method should be one of {uniform, cot, cotcurv}")

    if method == "uniform":
        laplacian = L.mm(verts_packed)
    elif method == "cot":
        laplacian = L.mm(verts_packed) * norm_w - verts_packed
    elif method == "cotcurv":
        # pyre-fixme[61]: `norm_w` may not be initialized here.
        laplacian = (L.mm(verts_packed) - L_sum * verts_packed) * norm_w
    curvature = laplacian.norm(p=2, dim=1)

    return curvature

class LaplacianLoss(nn.Module):
    # faces: BxFx3
    def __init__(self, faces):
        super(LaplacianLoss, self).__init__()
        self.faces = faces
        self.criterion = nn.L1Loss(reduction='mean')

    # x,y: BxVx3
    def forward(self, x, y):
        batch_size = x.shape[0]
        mesh_x = Meshes(
            verts=x,
            faces=self.faces.unsqueeze(0).expand(batch_size, -1, -1)
        )

        mesh_y = Meshes(
            verts=y,
            faces=self.faces.unsqueeze(0).expand(batch_size, -1, -1)
        )

        curvature_x = mesh_laplacian_smoothing(mesh_x, method='cotcurv')
        # curvature_y = mesh_laplacian_smoothing(mesh_y, method='cotcurv')

        # loss = self.criterion(curvature_x, curvature_y)
        loss = curvature_x.mean()

        return loss

class NormalConsistencyLoss(nn.Module):
    # faces: BxFx3
    def __init__(self, faces):
        super(NormalConsistencyLoss, self).__init__()
        self.faces = faces

    # x,y: BxVx3
    def forward(self, x):
        batch_size = x.shape[0]
        mesh_x = Meshes(
            verts=x,
            faces=self.faces.unsqueeze(0).expand(batch_size, -1, -1)
        )

        return pytorch3d.loss.mesh_normal_consistency(mesh_x)

# https://github.com/hongsukchoi/Pose2Mesh_RELEASE/blob/master/lib/core/loss.py
class NormalVectorLoss(nn.Module):
    # face: Fx3
    def __init__(self, face):
        super(NormalVectorLoss, self).__init__()
        self.face = face

    def forward(self, coord_out, coord_gt):
        face = torch.LongTensor(self.face).cuda()

        v1_out = coord_out[:, face[:, 1], :] - coord_out[:, face[:, 0], :]
        v1_out = F.normalize(v1_out, p=2, dim=2)  # L2 normalize to make unit vector
        v2_out = coord_out[:, face[:, 2], :] - coord_out[:, face[:, 0], :]
        v2_out = F.normalize(v2_out, p=2, dim=2)  # L2 normalize to make unit vector
        v3_out = coord_out[:, face[:, 2], :] - coord_out[:, face[:, 1], :]
        v3_out = F.normalize(v3_out, p=2, dim=2)  # L2 nroamlize to make unit vector

        v1_gt = coord_gt[:, face[:, 1], :] - coord_gt[:, face[:, 0], :]
        v1_gt = F.normalize(v1_gt, p=2, dim=2)  # L2 normalize to make unit vector
        v2_gt = coord_gt[:, face[:, 2], :] - coord_gt[:, face[:, 0], :]
        v2_gt = F.normalize(v2_gt, p=2, dim=2)  # L2 normalize to make unit vector
        normal_gt = torch.cross(v1_gt, v2_gt, dim=2)
        normal_gt = F.normalize(normal_gt, p=2, dim=2)  # L2 normalize to make unit vector

        cos1 = torch.abs(torch.sum(v1_out * normal_gt, 2, keepdim=True))
        cos2 = torch.abs(torch.sum(v2_out * normal_gt, 2, keepdim=True))
        cos3 = torch.abs(torch.sum(v3_out * normal_gt, 2, keepdim=True))
        loss = torch.cat((cos1, cos2, cos3), 1)
        return loss.mean()

epsilon = 1e-16
class EdgeLengthLoss(nn.Module):
    def __init__(self, face, relative_length=False):
        super(EdgeLengthLoss, self).__init__()
        self.face = face
        self.relative_length = relative_length

    def forward(self, coord_out, coord_gt):
        face = torch.LongTensor(self.face).cuda()

        d1_out = torch.sqrt(epsilon +
            torch.sum((coord_out[:, face[:, 0], :] - coord_out[:, face[:, 1], :]) ** 2, 2, keepdim=True))
        d2_out = torch.sqrt(epsilon +
            torch.sum((coord_out[:, face[:, 0], :] - coord_out[:, face[:, 2], :]) ** 2, 2, keepdim=True))
        d3_out = torch.sqrt(epsilon +
            torch.sum((coord_out[:, face[:, 1], :] - coord_out[:, face[:, 2], :]) ** 2, 2, keepdim=True))

        d1_gt = torch.sqrt(epsilon + torch.sum((coord_gt[:, face[:, 0], :] - coord_gt[:, face[:, 1], :]) ** 2, 2, keepdim=True))
        d2_gt = torch.sqrt(epsilon + torch.sum((coord_gt[:, face[:, 0], :] - coord_gt[:, face[:, 2], :]) ** 2, 2, keepdim=True))
        d3_gt = torch.sqrt(epsilon + torch.sum((coord_gt[:, face[:, 1], :] - coord_gt[:, face[:, 2], :]) ** 2, 2, keepdim=True))

        diff1 = torch.abs(d1_out - d1_gt)
        diff2 = torch.abs(d2_out - d2_gt)
        diff3 = torch.abs(d3_out - d3_gt)
        if self.relative_length:
            diff1 = diff1 / d1_gt
            diff2 = diff2 / d2_gt
            diff3 = diff3 / d3_gt
        loss = torch.cat((diff1, diff2, diff3), 1)
        return loss.mean()