# Topology matching for fully automatic similarity estimation of 3D shapes

@article{Hilaga2001TopologyMF, title={Topology matching for fully automatic similarity estimation of 3D shapes}, author={Masaki Hilaga and Yoshihisa Shinagawa and Taku Komura and Tosiyasu L. Kunii}, journal={Proceedings of the 28th annual conference on Computer graphics and interactive techniques}, year={2001} }

There is a growing need to be able to accurately and efficiently search visual data sets, and in particular, 3D shape data sets. This paper proposes a novel technique, called Topology Matching, in which similarity between polyhedral models is quickly, accurately, and automatically calculated by comparing Multiresolutional Reeb Graphs (MRGs). The MRG thus operates well as a search key for 3D shape data sets. In particular, the MRG represents the skeletal and topological structure of a 3D shape… Expand

#### Figures, Tables, and Topics from this paper

#### 2,256 Citations

Topology-Varying Shape Matching and Modeling

- 2015

The automatic creation of man-made 3D objects is an active area in computer graphics. Computer-assisted mixing and blending of components or subcomponents from existing example shapes can help users… Expand

Generation and Matching of 3 D Shape Subparts Marcin Novotni

- 2005

The task of setting up correspondences between 3D shapes is a prerequisite for numerous computer graphics applications, which has been performed manually up to now. We present an automatic method for… Expand

Skeleton based shape matching and retrieval

- Mathematics, Computer Science
- 2003 Shape Modeling International.
- 2003

The method encodes the geometric and topological information in the form of a skeletal graph and uses graph matching techniques to match the skeletons and to compare them and also describes a visualization tool to aid in the selection and specification of the matched objects. Expand

Non-Rigid 3 D Model Retrieval Based on Topological Structure and Shape Diameter Function

- 2016

With the increasing popularity of 3D technology like 3D printing, 3D modeling, etc., there is a growing need for searching similar models on the Internet. Subsequently, matching non-rigid shapes has… Expand

Scale-space representation of 3D models and topological matching

- Mathematics, Computer Science
- SM '03
- 2003

A framework for shape matching through scale-space decomposition of 3D models through spectral decomposition is presented, based on recent developments in efficient hierarchical decomposing of metric data using its spectral properties. Expand

Deformable Model Retrieval Based on Topological and Geometric Signatures

- Computer Science, Medicine
- IEEE Trans. Vis. Comput. Graph.
- 2007

A novel method for efficient matching and retrieval of 3D deformable models using Topological Point Ring (TPR) analysis to locate reliable topological points and rings and captures both local and global geometric information to characterize each of these topological features. Expand

The Augmented Multiresolution Reeb Graph Approach for Content-based Retrieval of 3d Shapes

- Computer Science, Mathematics
- Int. J. Shape Model.
- 2005

This article presents a 3D shape matching method for 3D mesh models applied to content-based search in database of 3D objects based on the multiresolution Reeb graph, which reveals very performant for the retrieval and the classification of similar 3D shapes. Expand

Research on Similarity Measurements of 3D Models Based on Skeleton Trees

- Mathematics, Computer Science
- Comput.
- 2017

A method of similarity measurement of 3D models, in which the similarity between3D models is easily, accurately and automatically calculated by means of skeleton trees constructed by a simple rule, is proposed. Expand

Spherical Mapping Based Descriptors for 3D Object Matching

- Mathematics
- EUROCON 2007 - The International Conference on "Computer as a Tool"
- 2007

Matching 3D objects by their similarity is a fundamental problem in computer vision, multimedia databases, molecular biology, computer graphics and a variety of other fields. A challenging aspect of… Expand

Spherical Mapping : A Powerful Tool for 3 D Object Matching

- 2006

Abstract: Matching 3D objects by their similarity is a fundamental problem in computer vision, multimedia databases, molecular biology, computer graphics and a variety of other fields. A challenging… Expand

#### References

SHOWING 1-10 OF 54 REFERENCES

Matching 3D models with shape distributions

- Mathematics, Computer Science
- Proceedings International Conference on Shape Modeling and Applications
- 2001

The primary motivation for this approach is to reduce the shape matching problem to the comparison of probability distributions, which is simpler than traditional shape matching methods that require pose registration, feature correspondence or model fitting. Expand

Flexible Syntactic Matching of Curves and Its Application to Automatic Hierarchical Classification of Silhouettes

- Mathematics, Computer Science
- IEEE Trans. Pattern Anal. Mach. Intell.
- 1999

This paper presents extensive experiments where the flexible algorithm to match curves under substantial deformations and arbitrary large scaling and rigid transformations, and defines a dissimilarity measure which is used in order to organize the image database into shape categories. Expand

A Method for Registration of 3-D Shapes

- Computer Science, Mathematics
- IEEE Trans. Pattern Anal. Mach. Intell.
- 1992

A general-purpose, representation-independent method for the accurate and computationally efficient registration of 3-D shapes including free-form curves and surfaces based on the iterative closest point (ICP) algorithm. Expand

A Spherical Representation for Recognition of Free-Form Surfaces

- Mathematics, Computer Science
- IEEE Trans. Pattern Anal. Mach. Intell.
- 1995

This approach to modelling and recognizing 3D objects has three main advantages: it is applicable to complex curved surfaces that cannot be handled by conventional techniques; it reduces the recognition problem to the computation of similarity between spherical distributions; in particular, the recognition algorithm does not require any combinatorial search. Expand

A feature-based approach for smooth surfaces

- Computer Science
- SMA '97
- 1997

A new feature-based approach for smooth surfaces where the smooth surfaces are assumed to be 2-dimensional @differentiable manifolds within a theoretical framework and critical points such as peaks, pits, and passes are used as the shape features. Expand

Shape Representation and Recognition from Multiscale Curvature

- Mathematics, Computer Science
- Comput. Vis. Image Underst.
- 1997

We present a technique for shape representation and the recognition of objects based on multiscale curvature information. It provides a single framework for both the decomposition and recognition of… Expand

Level set diagrams of polyhedral objects

- Mathematics, Computer Science
- SMA '99
- 1999

This work proposes a new paradigm for constructing one dimensional axial structures associated with a polyhedral object, called the level set diagrams, which are associated with scalar functions defined over the set of vertices of a polyhedron. Expand

Skeletonization of Three-Dimensional Object Using Generalized Potential Field

- Mathematics, Computer Science
- IEEE Trans. Pattern Anal. Mach. Intell.
- 2000

In this paper, the potential-based skeletonization approach for 2D medial axis transform (MAT), which identifies object skeleton as potential valleys using a Newtonian potential model in place of the… Expand

An Algorithm for the Medial Axis Transform of 3D Polyhedral Solids

- Computer Science
- IEEE Trans. Vis. Comput. Graph.
- 1996

An algorithm for determining the medial axis transform (MAT) for general 3D polyhedral solids of arbitrary genus without cavities, with nonconvex vertices and edges, is developed. Expand

Contour trees and small seed sets for isosurface traversal

- Computer Science, Mathematics
- SCG '97
- 1997

This paper gives the first methods to obtain seed sets that are provably small in size based on a variant of the contour tree (or topographic change tree), and develops a simple approximation algorithm giving a seed set of size at most twice the size of the minimum once the contours tree is known. Expand