Coordinate descent optimization for one-to-one correspondence and supervised classification of 3D shapes

Recent developments in shape analysis and retrieval play an important role in a wide variety of applications that potentially require matching of objects with different geometries. In shape classification, there is no natural way to represent an object but the similarity measure, distance between re...

Full description

Saved in:
Bibliographic Details
Published in:Applied mathematics and computation 2021-01, Vol.388, p.125539, Article 125539
Main Authors: Samir, Chafik, Huang, Wen
Format: Article
Language:English
Subjects:
Artificial Intelligence
Computer Science
Computer Vision and Pattern Recognition
Coordinate descent
Manifold learning
Mathematics
Optimization and Control
Optimization on manifolds
Parameterized surfaces registration
Shape classification
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Recent developments in shape analysis and retrieval play an important role in a wide variety of applications that potentially require matching of objects with different geometries. In shape classification, there is no natural way to represent an object but the similarity measure, distance between representations or descriptors, depends heavily on the strategy of computing optimal correspondences. In this paper we introduce a new numerical method for registering surfaces. Thus, finding an optimal one-to-one correspondence between their shapes. Unfortunately, solving this type of optimization problem is generally hard because the solutions space is nonlinear with no natural manifold structure on it. To overcome such limitations we make use of recent methods to represent objects then we find optimal correspondences using a discretized approximation of the search space. The proposed method has the advantage of extending the Riemannian analysis of 3D curves in a natural way for surfaces. We demonstrate the proposed algorithms using different public datasets for 2D and 3D objects matching and classification.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2020.125539