A Physicist’s View on Partial 3D Shape Matching

A new algorithm is presented to compute nonrigid, possibly partial comparisons of shapes defined by unstructured triangulations of their surfaces. The algorithm takes as input a pair of surfaces with each surface given by a distinct and unrelated triangulation. Its goal is to define a possibly parti...

Full description

Saved in:
Bibliographic Details
Published in:Algorithms 2023-07, Vol.16 (7), p.346
Main Authors: Koehl, Patrice, Orland, Henri
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Apexes
Computing costs
Datasets
Deep learning
Geometry
Machine learning
Mapping
optimal transport
Physicists
shape matching
Signatures
Statistical physics
Transportation planning
Triangulation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A new algorithm is presented to compute nonrigid, possibly partial comparisons of shapes defined by unstructured triangulations of their surfaces. The algorithm takes as input a pair of surfaces with each surface given by a distinct and unrelated triangulation. Its goal is to define a possibly partial correspondence between the vertices of the two triangulations, with a cost associated with this correspondence that can serve as a measure of the similarity of the two shapes. To find this correspondence, the vertices in each triangulation are characterized by a signature vector of features. We tested both the LD-SIFT signatures, based on the concept of spin images, and the wave kernel signatures obtained by solving the Shrödinger equation on the triangulation. A cost matrix C is constructed such that C(k,l) is the norm of the difference of the signature vectors of vertices k and l. The correspondence between the triangulations is then computed as the transport plan that solves the optimal transport or optimal partial transport problem between their sets of vertices. We use a statistical physics approach to solve these problems. The presentation of the proposed algorithm is complemented with examples that illustrate its effectiveness and manageable computing cost.
ISSN:1999-4893
1999-4893
DOI:10.3390/a16070346