From Gestalt Theory to Image Analysis
The theory in these notes was taught between 2002 and 2005 at the graduate schools of Ecole Normale Superieure ´ de Cachan, Ecole Polytechnique de Palaiseau, U- versitat Pompeu Fabra, Barcelona, Universitat de les Illes of Balears, Palma, and ` University of California at Los Angeles. It is also being taught by Andres 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 ?nd the text easy at the computer vision side and accessible on the mathematical level. The prerequisites are elementary calculus and probability from the ?rst two undergraduate years of any science course. All slightly more advanced notions in probability (inequalities, s- chastic 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 ba- ground is. The mathematics students do not ?nd the mathematics dif?cult 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: mat- matics, vision, and algorithms. We will in particular explain what a digital image is and how the elementary structures can be computed. We wish to emphasize why we are publishing these notes in a mathematics c- lection.
Over 130 illustrations throughout the textDetailed exercises at the end of each chapterLarge number of examples, of specific images on which the theory is tested are included