Reeb Graph Based Shape Retrieval for CAD

TLDR

Reeb Graph techniques, originally proposed by Hilaga et al., are used to compare approximate 3D models such as polygonal meshes and VRML representations, and have been applied to solid mechanical artifact matching via scale‑space feature decomposition. This study evaluates and seeks to improve solid model matching using Multiresolutional Reeb Graph similarity, reviewing the method, highlighting its limitations, and outlining future research directions. The authors compute Multiresolutional Reeb Graph similarity between solid models, testing the approach on primitive CAD shapes and on more complex LEGO and mechanical part models. The technique performs well on primitive CAD models and remains effective on complex LEGO and mechanical part models.

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.