The work of this thesis can be seen as a first step towards the characterization and quality evaluation of the class of local geometric distortions. In the last years the problem of evaluating the perceptual impact of geometric distortions in images has received an increasing attention from the watermarking community, due to the central role that such distortions play in watermarking theory. As a matter of fact, the application of a geometric distortion to a watermarked image causes a de-synchronization between the watermark embedder a detector that in most cases prevents the correct extraction of the watermark. A first step to solve the problems with geometric attacks is the characterization of the class of perceptually admissible distortions, defined as the class of geometric distortions whose effect cannot be perceived, or is judged acceptable, by a human observer. This requires the development of models to treat the distortions from a mathematical point of view. In this context, the first part of the thesis focuses on modeling local geometric transformations from a mathematical point of view. Watermarking is not the only field where an analysis of geometric distortion in images would be useful. In all the applications dealing with geometric distortions the availability of an objective quality metric capable of dealing with this kind of distortions would be of invaluable help. Thus, in the second part of the thesis, two objective quality metrics for the perceptual evaluation of geometrically distorted images have been introduced.