Retrieving articulated 3-D models using medial surfaces

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.

A new convexity measurement for 3D meshes

“…Experiments are carried out on the widely-used McGill Articulated 3D Shape Benchmark [25], which consists of 10 categories containing 255 watertight meshes, and retrieval performance is evaluated by the Precision-recall plot as well as four quantitative measures (NN, 1-Tier, 2-Tier, DCG) [24]. Table 1 shows results for methods that utilize our approaches (i.e., CD and C(M )) and other two convexity measures (i.e., C 1 (M ) and C 2 (M )) to represent a 3D object and employ the L 1 norm to calculate the dissimilarity between two signatures.…”

3D shape matching by geodesic eccentricity

“…[24]), one can identify the aspects discussed above (see Figure 8 and Tables 1 and 2). For classes with simple topology (e.g.…”

“…This paper shows the results on the 10 enumerated classes. See [24] for results of other methods for the same benchmark.…”

“…However, they are also used in dynamic environments such as web page retrieval [7]. Given a query object Q and retrieval result R contain- [24], with kind permission of Springer Science and Business Media): results of three other methods on the same database: medial surfaces (MS) [24], harmonic spheres (HS) [14], and shape distributions (SD) [17]. Precision: horizontal axis, recall: vertical axis.…”

Efficient 3D Model Retrieval using Cubic Spline Interpolation-Shape Distribution

“…Ankerst et al [12] proposed a Shape Histogram algorithm, which is easier to understand and implement, but it has a relatively poor retrieval effect. The local feature can be listed as the 3D shape context [13], Conformal factor [6], and Poisson histogram descriptor [3]. The commonly used retrieval methods before 2008 can be referred in [16].…”