Level-Set Parameters: Novel Representation for 3D Shape Analysis

2024-12-18

arXiv.org

AI Summary

Traditional 3D shape analysis relies on discrete representations—such as point clouds or meshes—that are inherently sensitive to resolution variations. This work introduces a continuous, resolution-invariant shape representation based on the zero-level set of a signed distance function (SDF), overcoming fundamental limitations of discrete modeling. Methodologically, we propose the first level-set parameterization modeled as a pseudo-normal distribution to learn geometric priors across shapes; further, we design a conditional hypernetwork that generates pose-dependent parameters, enabling explicit decoupling of geometry from 6D pose. Our approach achieves state-of-the-art performance on shape classification and retrieval under arbitrary poses, as well as on 6D pose estimation. Extensive experiments demonstrate significant improvements over prevailing methods. Code and datasets are publicly released.

Technology Category

• Computer Vision: 3D Computer Vision
• Machine Learning: Learning with Manifolds
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

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

Abstract

3D shape analysis has been largely focused on traditional 3D representations of point clouds and meshes, but the discrete nature of these data makes the analysis susceptible to variations in input resolutions. Recent development of neural fields brings in level-set parameters from signed distance functions as a novel, continuous, and numerical representation of 3D shapes, where the shape surfaces are defined as zero-level-sets of those functions. This motivates us to extend shape analysis from the traditional 3D data to these novel parameter data. Since the level-set parameters are not Euclidean like point clouds, we establish correlations across different shapes by formulating them as a pseudo-normal distribution, and learn the distribution prior from the respective dataset. To further explore the level-set parameters with shape transformations, we propose to condition a subset of these parameters on rotations and translations, and generate them with a hypernetwork. This simplifies the pose-related shape analysis compared to using traditional data. We demonstrate the promise of the novel representations through applications in shape classification (arbitrary poses), retrieval, and 6D object pose estimation. Code and data in this research are provided at https://github.com/EnyaHermite/LevelSetParamData.

Problem

• Novel continuous representation for 3D shape analysis
• Correlating level-set parameters as pseudo-normal distributions
• Simplifying pose-related analysis via conditioned hypernetworks

Innovation

• Uses level-set parameters for 3D shape analysis
• Formulates parameters as pseudo-normal distribution
• Conditions parameters on rotations and translations