Pattern matching in a digitized image

For motivation purpose, imagine the following continuous pattern-matching problem. Two continuous pictures, each consisting of unicolor regions, are given; one picture is called the scene and the other the pattern. The problem is to find all occurrences of the pattern in the scene. As a step toward efficient algorithmic handling of the continuous pattern-matching problem by computers, where discretized representations are involved, we consider pattern-matching problems where the pattern and the text are specified either in terms of the "continuous" properties, or through other exemplar digitized images-a variety of alternative specifications is considered. From the perspective of areas such as computer vision or image processing, our problem definitions identify an important gap in the fundamental theory of image formation and image processing-how to determine, even in the absence of noise, if a digitized image of a scene could contain an image of a given pattern. This is done using careful axiomatization. Such a "digitized-based" approach may lead toward building on the theory of string-matching algorithms (in one, or higher, dimensions) for the benefit of algorithmic pattern matching in image processing.