Sparse Geometric Representation Through Local Shape Probing

TL;DR

This paper introduces a novel shape analysis method using Local Probing Fields to create a sparse, geometrically meaningful shape representation that effectively handles complex shapes and features.

Contribution

The paper presents a new shape representation based on Local Probing Fields, enabling sparse decomposition and handling of mixed intrinsic dimensionality shapes.

Findings

Effective shape resampling demonstrated on synthetic and real data

Point set denoising improved using the new shape representation

Handles shapes with both surfaces and curves successfully

Abstract

We propose a new shape analysis approach based on the non-local analysis of local shape variations. Our method relies on a novel description of shape variations, called Local Probing Field (LPF), which describes how a local probing operator transforms a pattern onto the shape. By carefully optimizing the position and orientation of each descriptor, we are able to capture shape similarities and gather them into a geometrically relevant dictionary over which the shape decomposes sparsely. This new representation permits to handle shapes with mixed intrinsic dimensionality (e.g. shapes containing both surfaces and curves) and to encode various shape features such as boundaries. Our shape representation has several potential applications; here we demonstrate its efficiency for shape resampling and point set denoising for both synthetic and real data.