A compact shape descriptor for triangular surface meshes

Abstract

Three-dimensional shape-based descriptors have been widely used in object recognition and database retrieval. In the current work, we present a novel method called compact Shape-DNA (cShape-DNA) to describe the shape of a triangular surface mesh. While the original Shape-DNA technique provides an effective and isometric-invariant descriptor for surface shapes, the number of eigenvalues used is typically large. To further reduce the space and time consumptions, especially for large-scale database applications, it is of great interest to find a more compact way to describe an arbitrary surface shape. In the present approach, the standard Shape-DNA is first computed from the given mesh and then processed by surface area-based normalization and line subtraction. The proposed cShape-DNA descriptor is composed of some low frequencies of the discrete Fourier transform of the processed Shape-DNA. Several experiments are shown to illustrate the effectiveness and efficiency of the cShape-DNA method on 3D shape analysis, particularly on shape comparison and classification.

A graph-theoretic approach to 3D shape classification

“…The latter features, which are defined in terms of the Laplacian matrix eigenvalues, were shown to have good inter-class discrimination capabilities in 2D shape recognition [11], but they can easily be extended to 3D shape analysis using the eigenvalues of the LBO. On the other hand, for shape-DNA, GPS embedding, and F1-, F2-, and F3-features, the selected number of retained eigenvalues equals 10.…”

“…Baseline Methods For each of the 3D shape benchmarks used for experimentation, we will report the comparison results of GraphBDM against various state-of-the-art methods, including shape-DNA [1], compact shape-DNA [11], GPS embedding [9], and F1-, F2-, and F3-features [37]. The latter features, which are defined in terms of the Laplacian matrix eigenvalues, were shown to have good inter-class discrimination capabilities in 2D shape recognition [11], but they can easily be extended to 3D shape analysis using the eigenvalues of the LBO.…”

“…On the other hand, for shape-DNA, GPS embedding, and F1-, F2-, and F3-features, the selected number of retained eigenvalues equals 10. As suggested in [11], the dimension of the compact shape-DNA signature was set to 33. Performance Evaluation We randomly selected 30% shapes in the SHREC-2010 dataset to hold out for the test set, and the remaining shapes for training.…”

Algorithm BOSS (Bag-of-Salient local Spectrums) for non-rigid and partial 3D object retrieval

“…As an example of global methods, Zhanheng et al [14] have used the Laplace-Beltrami spectra model to generate 3D shape descriptors. Sun et al [10] suggested using heat kernel signature of a 3D object.…”

An Application of Manifold Learning in Global Shape Descriptors

“…The Laplace-Beltrami operator ∆ is a linear differential operator defined on the differentiable manifold M as the divergence of the gradient of a function f as the following form [17,27]: ∆f = div(grad(f )).…”