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Efficient 3D reflection symmetry detection A view-based approach.pdf

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Efficient 3D reflection symmetry detection A view-based approach.pdf

Graphical Models 83 (2016) 2–14 Contents lists available at ScienceDirect Graphical Models journal homepage: /locate/gmod E?cient 3D re?ection symmetry detection: A view-based approach Bo Li a,?, Henry Johan b, Yuxiang Ye a, Yijuan Lu a a Department of Computer Science, Texas State University, San Marcos, USA b Visual Computing, Fraunhofer IDM@NTU, Singapore article info Article history: Received 2 March 2015 Revised 14 September 2015 Accepted 16 September 2015 Available online 26 September 2015 Keywords: Symmetry detection Re?ection symmetry View-based approach Viewpoint entropy Matching abstract Symmetries exist in many 3D models while e?ciently ?nding their symmetry planes is important and useful for many related applications. This paper presents a simple and e?cient view-based re?ection symmetry detection method based on the viewpoint entropy features of a set of sample views of a 3D model. Before symmetry detection, we align the 3D model based on the Continuous Principal Component Analysis (CPCA) method. To avoid the high computational load resulting from a directly combinatorial matching among the sample views, we develop a fast symmetry plane detection method by ?rst generating a candidate symmetry plane based on a matching pair of sample views and then verifying whether the number of remaining matching pairs is within a minimum number. Experimental results and two related applications demonstrate better accuracy, e?ciency, robustness and versatility of our algorithm than state-of-the-art approaches. ? 2015 Elsevier Inc. All rights reserved. 1. Introduction Symmetry is an important clue for geometry perception: it is not only in many man-made models, but also widely exists in the nature [1]. Symmetry has been used in many applications such as: 3D alignment [2], shape matching [3], remeshing [4], 3D model segmentation [5] and retrieval [6]. However, existing symmetry detection algorithms still have much room for improvement in terms of both simplicity and e?ci