Differentiable Voxelization and Mesh Morphing

TL;DR

This work addresses differentiable voxelization of 3D meshes by computing occupancy from a generalized winding number $W(q, \Sigma)$ and face solid angles $\Omega_i(q)$, enabling gradients with respect to the input mesh and GPU acceleration. It introduces an ATAN2-based solid-angle formulation and a flipped-duplication technique to handle open surfaces, delivering robust, near-binary occupancy and efficient computation. The framework is demonstrated on mesh morphing, where a neural network deforms the voxelized mesh under voxelization-ground-truth supervision, and is evaluated against baselines across multiple resolutions, achieving state-of-the-art accuracy and efficiency on ShapeNet-like data. Overall, the differentiable voxelization enables gradient-based mesh optimization and 3D reconstruction tasks, including CT-based pipelines, by integrating geometry-aware voxel representations directly into learning workflows.

Abstract

In this paper, we propose the differentiable voxelization of 3D meshes via the winding number and solid angles. The proposed approach achieves fast, flexible, and accurate voxelization of 3D meshes, admitting the computation of gradients with respect to the input mesh and GPU acceleration. We further demonstrate the application of the proposed voxelization in mesh morphing, where the voxelized mesh is deformed by a neural network. The proposed method is evaluated on the ShapeNet dataset and achieves state-of-the-art performance in terms of both accuracy and efficiency.

Figures (4)

• Figure 1: Differentiable voxelization algorithm converts a 3D mesh into a 3D grid of occupancy voxels by the winding number and solid angles on GPU. The first row shows hard cases of the voxelization of 3D meshes using traditional methods, where the mesh is not watertight, contains irregular triangles, or is formed by combinations of shapes or with complex geometry. The second row shows the voxelization results of the proposed differentiable voxelization algorithm, followed by the re-cubifying.
• Figure 2: The naive computation of the solid angles like Eq. \ref{['eq:occu']} (TOP) leads tufted covers near the original surfaces. The proposed differentiable voxelization algorithm replaces $arctan$ by ${\rm ATAN2}$ to address this issue, which obtains almost binary occupancy and reconstruction in high accuracy (BLOW).
• Figure 3: The flipped duplication converts the open meshes into almost closed meshes, which can be voxelized by the proposed differentiable voxelization algorithm.
• Figure 4: Mesh morphing is a process of deforming a 3D mesh to another 3D mesh by a neural network. The proposed differentiable voxelization facilitates the optimization of mesh morphing, which admits the computation of gradients with respect to the input mesh under the supervision or conditions of voxelization ground truth.