Continuous Generalized Procrustes analysis |
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| Affiliation: | 1. Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain;2. Computer Vision Center, Universitat Autònoma de Barcelona, Building O, Barcelona, Spain;3. Fundació Privada Sant Antoni Abat, Rambla de l''Exposició, 59-69, Vilanova i la Geltrú, Spain;4. Universitat Politècnica de Catalunya, Av. Víctor Balguer 1, Vilanova i la Geltrú, Spain;5. Carnegie Mellon University, Robotics Institute, 5000 Forbes Avenue, Pittsburgh, PA, USA;1. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada T6G 2V4;2. Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia;3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland;2. XLIM-SIC UMR CNRS 6172, Signals, Images and Communications Laboratory, University of Poitiers, France;1. RECOD Lab, Institute of Computing (IC), University of Campinas (Unicamp) – Av. Albert Einstein, 1251, Campinas 13083-852, SP, Brazil;2. Department of Computer Engineering and Industrial Automation (DCA), School of Electrical and Computer Engineering (FEEC), University of Campinas (Unicamp) – Av. Albert Einstein, 400, Campinas 13083-852, SP, Brazil;3. Paris-Est University, IGN/SR, MATIS Lab, 73 avenue de Paris, 94160 Saint-Mandé, France;4. CNAM, CEDRIC Lab, 292 rue Saint-Martin, 75141 Paris Cedex 03, France;1. School of Science & Technology, Tianjin University of Finance & Economics, China;2. School of Computer Science & Technology, Tianjin University, China;3. Department of Computing, University of Surrey, United Kingdom |
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| Abstract: | Two-dimensional shape models have been successfully applied to solve many problems in computer vision, such as object tracking, recognition, and segmentation. Typically, 2D shape models are learned from a discrete set of image landmarks (corresponding to projection of 3D points of an object), after applying Generalized Procustes Analysis (GPA) to remove 2D rigid transformations. However, the standard GPA process suffers from three main limitations. Firstly, the 2D training samples do not necessarily cover a uniform sampling of all the 3D transformations of an object. This can bias the estimate of the shape model. Secondly, it can be computationally expensive to learn the shape model by sampling 3D transformations. Thirdly, standard GPA methods use only one reference shape, which can might be insufficient to capture large structural variability of some objects.To address these drawbacks, this paper proposes continuous generalized Procrustes analysis (CGPA). CGPA uses a continuous formulation that avoids the need to generate 2D projections from all the rigid 3D transformations. It builds an efficient (in space and time) non-biased 2D shape model from a set of 3D model of objects. A major challenge in CGPA is the need to integrate over the space of 3D rotations, especially when the rotations are parameterized with Euler angles. To address this problem, we introduce the use of the Haar measure. Finally, we extended CGPA to incorporate several reference shapes. Experimental results on synthetic and real experiments show the benefits of CGPA over GPA. |
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| Keywords: | Procrustes analysis 2D shape model Continuous approach |
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