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An Application of Manifold Learning in Global Shape Descriptors

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Department of Electrical Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA
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Marshfield Clinic Research Institute, Marshfield, WI 54449, USA
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Department of Computer Science, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA
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Department of Mechanical Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA
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Authors to whom correspondence should be addressed.
Algorithms 2019, 12(8), 171; https://doi.org/10.3390/a12080171
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)
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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