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

TL;DR

This paper introduces a novel continuous 3D shape representation using level-set parameters from neural fields, enabling robust shape analysis across transformations and improving tasks like classification, retrieval, and pose estimation.

Contribution

It extends shape analysis to level-set parameters, establishing a correlation framework and a hypernetwork for pose-conditioned shape generation, which is a novel approach in 3D shape analysis.

Findings

Effective shape classification across arbitrary poses

Improved retrieval accuracy using level-set parameters

Enhanced 6D object pose estimation performance

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.