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An Application of Manifold Learning in Global Shape Descriptors

1
Department of Electrical Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA
2
Marshfield Clinic Research Institute, Marshfield, WI 54449, USA
3
Department of Computer Science, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA
4
Department of Mechanical Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA
*
Authors to whom correspondence should be addressed.
Algorithms 2019, 12(8), 171; https://doi.org/10.3390/a12080171 (registering DOI)
Received: 28 May 2019 / Revised: 16 July 2019 / Accepted: 14 August 2019 / Published: 16 August 2019
(This article belongs to the Special Issue Algorithms for Manifold Learning and Its Applications)
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Abstract

With the rapid expansion of applied 3D computational vision, shape descriptors have become increasingly important for a wide variety of applications and objects from molecules to planets. Appropriate shape descriptors are critical for accurate (and efficient) shape retrieval and 3D model classification. Several spectral-based shape descriptors have been introduced by solving various physical equations over a 3D surface model. In this paper, for the first time, we incorporate a specific manifold learning technique, introduced in statistics and machine learning, to develop a global, spectral-based shape descriptor in the computer graphics domain. The proposed descriptor utilizes the Laplacian Eigenmap technique in which the Laplacian eigenvalue problem is discretized using an exponential weighting scheme. As a result, our descriptor eliminates the limitations tied to the existing spectral descriptors, namely dependency on triangular mesh representation and high intra-class quality of 3D models. We also present a straightforward normalization method to obtain a scale-invariant and noise-resistant descriptor. The extensive experiments performed in this study using two standard 3D shape benchmarks—high-resolution TOSCA and McGill datasets—demonstrate that the present contribution provides a highly discriminative and robust shape descriptor under the presence of a high level of noise, random scale variations, and low sampling rate, in addition to the known isometric-invariance property of the Laplace–Beltrami operator. The proposed method significantly outperforms state-of-the-art spectral descriptors in shape retrieval and classification. The proposed descriptor is limited to closed manifolds due to its inherited inability to accurately handle manifolds with boundaries. View Full-Text
Keywords: manifold learning; Laplacian Eigenmap; scale-invariant shape descriptor; shape retrieval manifold learning; Laplacian Eigenmap; scale-invariant shape descriptor; shape retrieval
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Bashiri, F.S.; Rostami, R.; Peissig, P.; D’Souza, R.M.; Yu, Z. An Application of Manifold Learning in Global Shape Descriptors. Algorithms 2019, 12, 171.

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