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From Gestalt Theory to Image Analysis: A Probabilistic Approach (Interdisciplinary Applied Mathematics)

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The theory in these notes was taught between 2002 and 2005 at the graduate schools of Ecole Normale Sup´erieure de Cachan, Ecole Polytechnique de Palaiseau, Universitat Pompeu Fabra, Barcelona, Universitat de les Illes of Balears, Palma, and University of California at Los Angeles. It is also being taught by Andr`es Almansa at the Facultad de Ingeneria, Montevideo.

This text will be of interest to several kinds of audience. Our teaching experience proves that specialists in image analysis and computer vision find the text easy at the computer vision side and accessible on the mathematical level. The prerequisites are elementary calculus and probability from the first two undergraduate years of any science course. All slightly more advanced notions in probability (inequalities, stochastic geometry, large deviations, etc.) will be either proved in the text or detailed in several exercises at the end of each chapter. We have always asked the students to do all exercises and they usually succeed regardless of what their science background is. The mathematics students do not find the mathematics difficult and easily learn through the text itself what is needed in vision psychology and the practice of computer vision. The text aims at being self-contained in all three aspects: mathematics, vision, and algorithms. We will in particular explain what a digital image is and how the elementary structures can be computed.
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