MASH: Masked Anchored SpHerical Distances for 3D Shape Representation and Generation

2025-04-12

AI Summary

Modeling 3D shapes with complex geometry and arbitrary topology remains challenging. This paper proposes MASH, a multi-view parametric representation based on anchors and spherical distance functions. MASH models a 3D shape as a collection of observable local surface patches, uniquely integrating anchored spherical distance functions, spherical harmonic encoding, and differentiable parametric view-cone masks. This unifies implicit and explicit geometric representations while natively supporting arbitrary topology and high-fidelity geometry reconstruction. The representation is compact, fully differentiable, and optimization-friendly. Extensive experiments demonstrate state-of-the-art performance across surface reconstruction, generative modeling, completion, and fusion tasks. Moreover, MASH enables end-to-end, high-accuracy conversion from raw point clouds to high-quality parametric representations—achieving superior fidelity and robustness compared to prior methods.

Technology Category

• Machine Learning: Multi-instance/Multi-view Learning
• Computer Vision: 3D Computer Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

We introduce Masked Anchored SpHerical Distances (MASH), a novel multi-view and parametrized representation of 3D shapes. Inspired by multi-view geometry and motivated by the importance of perceptual shape understanding for learning 3D shapes, MASH represents a 3D shape as a collection of observable local surface patches, each defined by a spherical distance function emanating from an anchor point. We further leverage the compactness of spherical harmonics to encode the MASH functions, combined with a generalized view cone with a parameterized base that masks the spatial extent of the spherical function to attain locality. We develop a differentiable optimization algorithm capable of converting any point cloud into a MASH representation accurately approximating ground-truth surfaces with arbitrary geometry and topology. Extensive experiments demonstrate that MASH is versatile for multiple applications including surface reconstruction, shape generation, completion, and blending, achieving superior performance thanks to its unique representation encompassing both implicit and explicit features.

Problem

• Develop a novel 3D shape representation using spherical distances
• Convert point clouds into accurate MASH representations
• Enable versatile 3D applications like reconstruction and generation

Innovation

• Multi-view spherical distance representation for 3D shapes
• Spherical harmonics encode local surface patches
• Differentiable optimization converts point clouds accurately