A detailed description of a new approach to perceptual analysis and processing of medical images is given. Instead of traditional pattern recognition a new method of image analysis is presented, based on a syntactic description of the shapes selected on the image and graph-grammar parsing algorithms. This method of "Image Understanding" can be found as a model of mans' cognitive image understanding processes. The usefulness for the automatic understanding of the merit of medical images is demonstrated as well as the ability for giving useful diagnostic descriptions of the illnesses. As an application, the production of a content-based, automatically generated index for arranging and for searching medical images in multimedia medical databases is presented.