For motivation purpose, imagine the following continuous pattern-match
ing problem. Two continuous pictures, each consisting of unicolor regi
ons, are given; one picture is called the scene and the other the patt
ern. The problem is to find all occurrences of the pattern in the scen
e. As a step toward efficient algorithmic handling of the continuous p
attern-matching problem by computers, where discretized representation
s are involved, we consider pattern-matching problems where the patter
n and the text are specified either in terms of the ''continuous'' pro
perties, or through other exemplar digitized images-a variety of alter
native specifications is considered. From the perspective of areas suc
h as computer vision or image processing, our problem definitions iden
tify 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 al
gorithms (in one, or higher, dimensions) for the benefit of algorithmi
c pattern matching in image processing.