Alphabet independent and dictionary scaled matching

The rapidly growing need for analysis of digitized images in multimedia systems has lead to a variety of interesting problems in multidimensional pattern matching. One of the problems is that of scaled matching, finding all appearances of a pattern in a text in all sizes. Another important problem is dictionary matching, quick search through a dictionary of preprocessed patterns in order to find all dictionary patterns that appear in the input text. In this paper we provide a very simple algorithm for two dimensional scaled matching. Our algorithm is the first linear-time alphabet-independent scaled matching algorithm, Its running time is O(|T|), where|T| is the text size, and is independent of |Σ|, the size of the alphabet. The main idea behind our algorithm is identifying and exploiting a scaling invariant property of patterns. Our technique generalizes to produce the first known algorithm for scaled dictionary matching. We can find all appearances of all dictionary patterns that appear in the input text in any discrete scale. The time bounds of our algorithm are equal to the best known exact (no scaling) two dimensional dictionary matching algorithms.