Abstract
In this paper I am interested in transformation of digitized images by affine applications; the discrete nature of a computer screen makes this operation rather difficult. I propose to discretize real affine applications in order to obtain quasi-affine transformations which are similar to the calculus of real applications in fixed point arithmetic. Until now, the computer graphists avoided this digitization, replacing it by other methods (inverse mapping, over-sampling) which require heavy calculation. I present an algorithm for the determination of reciprocal images of a point by a quasi-affine transformation; this algorithm will permit the transformation of digitized images by discrete affine applications. In general, a one-to-one mapping is not obtained, but it is possible to determine where the points are without antecedent or those with more than one antecedent. In addition if the affine application is sufficiently dilating, the associated discrete transformation is inversible. The algorithm I propose uses integer arithmetic with only tests and additions (no multiplication nor division) so that it can be quickly performed.
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