A simple multi-layer test to verify the implementation. Function: G(z) = [z_0 * z_1, z_0**2 * z_1] Ground Truth Hessian Penalty: [4, 16 *

Convert rotations given as axis/angle to quaternions. Args: axis_angle: Rotations given as a vector in axis angle form,

Convert rotations given as axis/angle to quaternions. Args: axis_angle: Rotations given as a vector in axis angle form,

Convert rotations given as axis/angle to quaternions. Args: axis_angle: Rotations given as a vector in axis angle form,

Computes a similarity transform (sR, t) that takes a set of 3D points S1 (3 x N) closest to a set of 3D points S2, where R is an 3x3 rota

Mean joint acceleration error often referred to as "Protocol #1" in many papers.

:param Pin: Nx(numjoints*3) :param rep_type: 'matrot'/'aa' for matrix rotations or axis-angle :return:

This function is borrowed from https://github.com/nkolot/SPIN/utils/geometry.py Find camera translation that brings 3D joints S closest to 2

Params: -- matrix1: N1 x D -- matrix2: N2 x D Returns: -- dist: N1 x N2 dist[i, j] == distance(matrix

This matches the implementation in Denoising Diffusion Probabilistic Models: Create sinusoidal timestep embeddings. :param timesteps: a 1-D

Solves for the depth offset of the model to approx. orth with persp camera.

Initialize the camera translation via triangle similarity, by using the torso joints . :param model_joints: SMPL model with pre joints

Create graph operation for negative log-likelihood calculation