Implicit-ARAP: Efficient Handle-Guided Deformation of High-Resolution Meshes and Neural Fields via Local Patch Meshing

2024-05-21

arXiv.org

AI Summary

Existing neural field deformation methods struggle to simultaneously achieve high surface quality, robustness, and efficiency under spatial constraints. This paper proposes an efficient handle-constrained neural field deformation framework. First, it constructs a discrete signed distance function (SDF) representation based on local patch-based meshes, achieving higher geometric fidelity than Marching Cubes. Second, it introduces two As-Rigid-As-Possible (ARAP) deformation pipelines—the first to unify ARAP optimization across both high-resolution explicit meshes and neural implicit fields. The method integrates SDF-gradient-driven patch projection, implicit field modeling, and constraint-aware geometric solving, ensuring scalability and numerical stability. Experiments demonstrate significant improvements over state-of-the-art baselines in deformation fidelity, computational efficiency, and robustness—enabling real-time interactive editing of million-patch meshes and complex neural fields.

Technology Category

• Machine Learning: Learning with Manifolds
• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: 3D Computer Vision

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

In this work, we present the local patch mesh representation for neural signed distance fields. This technique allows to discretize local regions of the level sets of an input SDF by projecting and deforming flat patch meshes onto the level set surface, using exclusively the SDF information and its gradient. Our analysis reveals this method to be more accurate than the standard marching cubes algorithm for approximating the implicit surface. Then, we apply this representation in the setting of handle-guided deformation: we introduce two distinct pipelines, which make use of 3D neural fields to compute As-Rigid-As-Possible deformations of both high-resolution meshes and neural fields under a given set of constraints. We run a comprehensive evaluation of our method and various baselines for neural field and mesh deformation which show both pipelines achieve impressive efficiency and notable improvements in terms of quality of results and robustness. With our novel pipeline, we introduce a scalable approach to solve a well-established geometry processing problem on high-resolution meshes, and pave the way for extending other geometric tasks to the domain of implicit surfaces via local patch meshing.

Problem

• Handle-guided deformation of neural 3D fields
• Balancing surface quality with computational efficiency
• Optimizing As-Rigid-As-Possible energy via local patches

Innovation

• Handle-guided neural field deformation via local patches
• Discretizes level sets using flat mesh projection
• Optimizes As-Rigid-As-Possible energy for surface quality