Retrieving Articulated 3-D Models Using Medial Surfaces and Their Graph Spectra

Abstract

We consider the use of medial surfaces to represent symmetries of 3-D objects. This allows for a qualitative abstraction based on a directed acyclic graph of components and also a degree of invariance to a variety of transformations including the articulation of parts. We demonstrate the use of this representation for 3-D object model retrieval. Our formulation uses the geometric information A preliminary version of this article was published in EMMCVPR 2005. In this extended version we have included results on the significantly larger McGill Shape Benchmark, making a stronger case for the advantages of our method for models with articulating parts. We have also included expanded introduction, medial surface computation, matching, indexing, experimental results, and discussion sections, along with several new figures. associated with each node along with an eigenvalue labeling of the adjacency matrix of the subgraph rooted at that node. We present comparative retrieval results against the techniques of shape distributions (Osada et al.) and harmonic spheres (Kazhdan et al.) on 425 models from the McGill Shape Benchmark, representing 19 object classes. For objects with articulating parts, the precision vs recall curves using our method are consistently above and to the right of those of the other two techniques, demonstrating superior retrieval performance. For objects that are rigid, our method gives results that compare favorably with these methods.

PANORAMA: A 3D Shape Descriptor Based on Panoramic Views for Unsupervised 3D Object Retrieval

“…Hilaga et al [21] introduced the multi-resolution Reeb graph, which represents a 3D objects topology and skeletal structure at various levels of detail. In [22] Zhang et al consider the use of medial surfaces to compute an equivalent directed acyclic graph of an object. In the work of Sundar et al [23], the 3D object passes through a thinning process producing a set of skeletal points, which finally form a directed acyclic graph by applying the minimum spanning tree algorithm.…”

3D shape matching by geodesic eccentricity

“…Only a limited number of objects in the database have articulated parts. As one of the main advantages of using eccentricity is its robustness with respect to articulation, we have turned to the McGill Shape Benchmark [33]. It contains several models from the Princeton repository and others added by the authors.…”

Matching shape graphs

“…We used the MPEG-7 dataset CE-Shape-1 part B and McGill 3D Shape Benchmark [5] for these two domains. While the MPEG-7 database consists of 70 classes and 20 shapes per class, the McGill database consists of 420 objects classified in 19 classes.…”