Skeletal-Anchored Dual Harmonics for Structured 3D Modeling

2026-06-05

AI Summary

This work addresses the challenge of simultaneously preserving fine geometric details and structural consistency in 3D modeling from unstructured point clouds. To this end, we propose a novel shape representation that optimizes interior anchor points and constructs surface patches parameterized by dual-channel spherical harmonics anchored at these points. By jointly optimizing geometry, anchor positions, orientations, and connectivity, our method recovers both high-fidelity surfaces and compact meso-scale skeletons in a unified framework. Our approach is the first to integrate dual-channel spherical harmonics with interior anchors, enabling compact encoding of anisotropic local geometry and adaptive spatial support. Experiments demonstrate that the proposed method achieves accurate reconstruction and structured representation across a variety of complex shapes.

Abstract

We present Skeletal-Anchored Dual Harmonics (SADH), a novel 3D shape representation that tightly couples local surface geometry with internal meso-skeletal organization. SADH represents a shape as a collection of compact surface patches rooted on internal anchors optimized directly inside the object volume. Each patch is parameterized using a dual-channel spherical harmonic (SH) formulation, where one channel models local radial geometry while the other defines adaptive patch support through a generalized viewing cone. Unlike isotropic primitives such as medial spheres or Gaussian kernels, SH patches directly encode anisotropic local surface geometry together with adaptive spatial support, enabling compact representation of detailed and directionally varying surface regions. Starting from unorganized point clouds, SADH jointly optimizes surface geometry, anchor locations, patch orientations, and structural connectivity through a staged optimization process that progressively forms a coherent meso-skeletal structure. A geodesic anchor graph further preserves structural relationships between neighboring patches. Experiments on complex 3D shapes demonstrate that SADH achieves accurate surface reconstruction together with compact and coherent skeletal organization across a wide range of geometries.

Problem

• 3D shape representation
• skeletal structure
• surface reconstruction
• point clouds
• anisotropic geometry

Innovation

• Skeletal-Anchored Dual Harmonics
• spherical harmonics
• anisotropic surface representation
• meso-skeletal structure
• structured 3D modeling