SHARC: Reference point driven Spherical Harmonic Representation for Complex Shapes

2026-04-02

AI Summary

This work addresses the challenge of efficiently representing complex 3D shapes with arbitrary topologies in a high-fidelity manner by proposing a spherical harmonic distance field method based on optimized interior reference points. The approach jointly optimizes the sparsity, centrality, and visibility of these reference points and integrates ray-casting sampling, fast spherical harmonic transforms, configurable low-pass filtering, and local consistency constraints to construct a compact yet geometrically accurate implicit field representation. The resulting method achieves superior reconstruction accuracy and computational efficiency compared to existing techniques while maintaining model simplicity, thereby significantly enhancing the representational capacity for intricate geometries.

Abstract

We propose SHARC, a novel framework that synthesizes arbitrary, genus-agnostic shapes by means of a collection of Spherical Harmonic (SH) representations of distance fields. These distance fields are anchored at optimally placed reference points in the interior volume of the surface in a way that maximizes learning of the finer details of the surface. To achieve this, we employ a cost function that jointly maximizes sparsity and centrality in terms of positioning, as well as visibility of the surface from their location. For each selected reference point, we sample the visible distance field to the surface geometry via ray-casting and compute the SH coefficients using the Fast Spherical Harmonic Transform (FSHT). To enhance geometric fidelity, we apply a configurable low-pass filter to the coefficients and refine the output using a local consistency constraint based on proximity. Evaluation of SHARC against state-of-the-art methods demonstrates that the proposed method outperforms existing approaches in both reconstruction accuracy and time efficiency without sacrificing model parsimony. The source code is available at https://github.com/POSE-Lab/SHARC.

Problem

• shape representation
• complex shapes
• distance fields
• spherical harmonics
• 3D reconstruction

Innovation

• Spherical Harmonic Representation
• Reference Point Optimization
• Distance Field
• Fast Spherical Harmonic Transform
• Shape Reconstruction