Real two dimensional scaled matching

Scaled Matching refers to the problem of finding all locations in the text where the pattern, proportionally enlarged according to an arbitrary real-sized scale, appears. Scaled matching is an important problem that was originally inspired by Computer Vision. Finding a combinatorial definition that captures the concept of real scaling in discrete images has been a challenge in the pattern matching field. No definition existed that captured the concept of real scaling in discrete images, without assuming an underlying continuous signal, as done in the image processing field. We present a combinatorial definition for real scaled matching that scales images in a pleasing natural manner. We also present efficient algorithms for real scaled matching. The running time of our algorithm is as follows. If T is a two-dimensional n × n text array and P is a m × m pattern array, we find in T all occurrences of P scaled to any real value in time O(nm³ + n²m log m).