Reeb Graph Based Shape Retrieval for CAD

Abstract

Our recent work has described a framework for matching solid of mechanical artifacts models based on scale-space feature decomposition. In this work we adopt a method of comparing solid models based on Multiresolutional Reeb Graphs (MRG) similarity computations. This method was originally proposed by Hilaga et al. in [1]. Reeb Graph technique applies MRG structure to comparisons of approximate models found in the graphics community, such as polygonal meshes, faceted representation and Virtual Reality Modeling Language (VRML) models. First, we provide a brief review of shape matching using Multiresolutional Reeb Graphs and present an approach to matching solid models. Second, we show the performance of the Reeb Graph technique when handling primitive CAD models, such as cubes and spheres; then we perform experiments with more complex models, such as LEGO models and mechanical parts, and we discuss Reeb Graph technique’s performance on complex CAD models. Third, we emphasize several problems with the existing technique. Finally, we conclude with discussion of future work.

Machining feature-based similarity assessment algorithms for prismatic machined parts

“…Application-independent feature based approaches based on skeletons [Iyer04,Lou04,Sund03], shock graphs [Siddi99], Reeb graphs [Besp03,Hila01] and slope diagram [Ghos96,Tuzi00] have been also developed. However, these approaches tend to filter out important geometric details that play an important role in assessing similarity between machined parts.…”

A survey of content based 3D shape retrieval methods

“…Their method uses Reeb graphs based on a quotient function defined by an integral geodesic distance. Bespalov et al [12] investigate the application of Hilaga's method to solid models. They found that for solid models, minor changes in topology may result in significant differences in similarity.…”

A K-Means Clustering Based Shape Retrieval Technique for 3d Mesh Models

“…Hilaga et al (2001) used integral geodesic distance as a quotient function. Bespalov et al (2003) implemented Hilaga's procedure on solid models. They concluded that reeb graph matching method was sensitive to topology of 3D models and more work should be done to inhance the method.…”