Efficient many-to-many feature matching under the l1 norm |
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Authors: | M. Fatih Demirci Yusuf Osmanlioglu Ali Shokoufandeh Sven Dickinson |
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Affiliation: | 1. TOBB University of Economics and Technology, Sög?ütözü, Ankara 06560, Turkey;2. Drexel University, Philadelphia, PA 19104, USA;3. University of Toronto, Toronto, Ontario, Canada M5S 3G4;1. University of York, UK;2. Universitá Ca’ Foscari Venezia, Italy;3. University of Alicante, Spain;4. GREYC, CNRS UMR 6072, ENSICAEN, France;1. Eurocopter, ETZR, Aéroport International Marseille Provence, 13725 Marignane Cedex, France;2. LGI2P, Site EERIE de l’EMA, Parc Scientifique George Besse, 30035 Nîmes Cedex 1, France;3. Mines ParisTech, CRI, 35 rue Saint Honoré, 77305 Fontainebleau Cedex, France;1. Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences, 9 Dengzhuang S Rd., Beijing, 100094, China;2. University of Chinese Academy of Sciences, Beijing, 100049, China;1. Department of Economics and Finance, University of Texas Rio Grande Valley, United States;2. Department of Economics, University of Connecticut, United States;1. Department of Computer Science, Pondicherry Engineering College, Puducherry, India;2. Department of Computer Science, Pondicherry University, Puducherry, India |
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Abstract: | Matching configurations of image features, represented as attributed graphs, to configurations of model features is an important component in many object recognition algorithms. Noisy segmentation of images and imprecise feature detection may lead to graphs that represent visually similar configurations that do not admit an injective matching. In previous work, we presented a framework which computed an explicit many-to-many vertex correspondence between attributed graphs of features configurations. The framework utilized a low distortion embedding function to map the nodes of the graphs into point sets in a vector space. The Earth Movers Distance (EMD) algorithm was then used to match the resulting points, with the computed flows specifying the many-to-many vertex correspondences between the input graphs. In this paper, we will present a distortion-free embedding, which represents input graphs as metric trees and then embeds them isometrically in the geometric space under the l1 norm. This not only improves the representational power of graphs in the geometric space, it also reduces the complexity of the previous work using recent developments in computing EMD under l1. Empirical evaluation of the algorithm on a set of recognition trials, including a comparison with previous approaches, demonstrates the effectiveness and robustness of the proposed framework. |
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