Image and geometry processing with Oriented and Scalable Map |
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| Institution: | 1. Science Department, “Roma Tre” University, via della Vasca Navale 84, Rome, Italy;2. E.V.O. srl, Rome 00134, Italy;1. Department of Mathematics, London School of Economics and Political Science, UK;2. MSIS and RUTCOR, Rutgers University, NJ, USA;3. QuantOM, HEC Management School, University of Liege, Belgium;4. Institute of Mathematics and Statistics, University of São Paulo, Brazil;1. College of Intelligence and Computing, Tianjin Key Lab of Cognitive Computing and Application, Tianjin University, Tianjin, China;2. State Grid Tianjin Electric Power Company, China;3. School of Computer Science and Engineering, Central South University, Changsha 410083, China;4. School of Information Science, Japan Advanced Institute of Science and Technology, Japan;1. Department of Instrument Science and Technology, College of Biomedical Engineering and Instrument Science, Zhejiang University, Hangzhou, Zhejiang 310027, China;2. Department of Psychiatry, Department of Neuroscience and Physiology, School of Medicine, New York University, New York, NY 10016, USA;3. Neuro-Electronics Research Flanders (NERF), IMEC, Leuven, Belgium;4. Brain & Cognition Research Unit, KU Leuven, Leuven, Belgium;5. VIB, Leuven, Belgium;6. Department of Neuroscience, Columbia University Medical Center, New York, NY 10019, USA;7. Department of Molecular and Cellular Biology, Department of Neuroscience, Baylor College of Medicine, Houston, TX 77030, USA;8. The Picower Institute for Learning and Memory, Massachusetts Institute of Technology, Cambridge, MA 02134, USA;9. The Neuroscience Institute, New York University School of Medicine, New York, NY 10016, USA;1. Department of Mathematics, Bharathiar University, Coimbatore - 641 046, Tamil Nadu, India;2. Department of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210096, China |
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| Abstract: | We turn the Self-organizing Map (SOM) into an Oriented and Scalable Map (OS-Map) by generalizing the neighborhood function and the winner selection. The homogeneous Gaussian neighborhood function is replaced with the matrix exponential. Thus we can specify the orientation either in the map space or in the data space. Moreover, we associate the map’s global scale with the locality of winner selection. Our model is suited for a number of graphical applications such as texture/image synthesis, surface parameterization, and solid texture synthesis. OS-Map is more generic and versatile than the task-specific algorithms for these applications. Our work reveals the overlooked strength of SOMs in processing images and geometries. |
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| Keywords: | Self-organizing map Orientation Scale Computer graphics |
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