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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. |