Faster Two Dimensional Scaled Matching

• Published in: Algorithmica Vol. 56; no. 2; pp. 214 - 234
• Main Authors: Amir, Amihood, Chencinski, Eran
• Format: Journal Article
• Language: English
• Published: New York Springer-Verlag 01.02.2010; Springer
• Subjects: Algorithm Analysis and Problem Complexity; Algorithmics. Computability. Computer arithmetics; Algorithms; Applied sciences; Artificial intelligence; Computer Science; Computer science; control theory; systems; Computer Systems Organization and Communication Networks; Data Structures and Information Theory; Exact sciences and technology; Mathematics of Computing; Pattern recognition. Digital image processing. Computational geometry; Theoretical computing; Theory of Computation; Scaled pattern matching; Theory of discrete image processing; Multidimensional pattern matching; Multimedia; Image analysis; Dictionaries; Image theory; Image processing; Occupation time; Text; Pattern matching
• ISSN: 0178-4617; 1432-0541
• DOI: 10.1007/s00453-008-9173-3

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, proportionally enlarged according to an arbitrary real-sized scale, in a given text. The currently fastest known algorithm for this problem uses techniques from dictionary matching to solve the problem in O ( nm 3 + n 2 m log  m ) time using O ( nm 3 + n 2 ) space, where T is a two-dimensional n × n text array and P is a two-dimensional m × m pattern array. We present a new approach for solving the scaled matching problem improving both the running time and the space requirements. Our algorithm runs in O ( n 2 m ) time and uses O ( n 2 ) space.