Shape distributions

Abstract

Measuring the similarity between 3D shapes is a fundamental problem, with applications in computer graphics, computer vision, molecular biology, and a variety of other fields. A challenging aspect of this problem is to find a suitable shape signature that can be constructed and compared quickly, while still discriminating between similar and dissimilar shapes.In this paper, we propose and analyze a method for computing shape signatures for arbitrary (possibly degenerate) 3D polygonal models. The key idea is to represent the signature of an object as a shape distribution sampled from a shape function measuring global geometric properties of an object. 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.We find that the dissimilarities between sampled distributions of simple shape functions (e.g., the distance between two random points on a surface) provide a robust method for discriminating between classes of objects (e.g., cars versus airplanes) in a moderately sized database, despite the presence of arbitrary translations, rotations, scales, mirrors, tessellations, simplifications, and model degeneracies. They can be evaluated quickly, and thus the proposed method could be applied as a pre-classifier in a complete shape-based retrieval or analysis system concerned with finding similar whole objects. The paper describes our early experiences using shape distributions for object classification and for interactive web-based retrieval of 3D models.

Shape-similarity search of 3D models by using enhanced shape functions

“…As mentioned before, our shape features AD and AAD are extensions of Osada's D2 function [Osada02]. The most favorable qualities of the D2 is its topological and geometrical robustness, and the lack of need for pose normalization.…”

“…As mentioned before, our shape features AD and AAD are based on Osada's D2 [Osada02]. Of several different what they called shape functions, the D2 performed the best in terms of combined computational cost and retrieval performance.…”

“…The shape features are extension of the D2 shape functions proposed by Osada et al [Osada01,Osada02] …”

“…Osada et al [Osada01,Osada02] proposed what they called shape functions. Osada's shape functions have the advantage of being invariant to similarity transformation.…”

“…Our shape features are based on Osada's D2 shape function [Osada01,Osada02], having identical robustness characteristics. However, our shape features are more sensitive to shape variations by measuring not only the distance but mutual orientation of the surfaces on which a pair of points are located.…”