文章基本信息

标题：Rajan Transform and its uses in Pattern Recognition
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作者：E.N. Mandalapu ; E.G. Rajan
期刊名称：Informatica
印刷版ISSN：1514-8327
电子版ISSN：1854-3871
出版年度：2009
卷号：33
期号：2
出版社：The Slovene Society Informatika, Ljubljana
摘要：This transform was introduced in the year 1997 by Rajan [2], [4] on the lines of Hadamard Transform. This paper presents, in addition to its formulation, the algebraic properties of the transform and its uses in pattern recognition. Rajan Transform (RT) is a coding morphism by which a number sequence (integer, rational, real or complex) of length equal to any power of two is transformed into a highly correlated number sequence of the same length. It is a homomorphism that maps a set consisting of a number sequence, its graphical inverse and their cyclic and dyadic permutations, to a set consisting of a unique number sequence ensuring the invariance property under such permutations. This invariance property is also true for the permutation class of the dual sequence of the number sequence under consideration. A number sequence and its dual are like an object and its mirror image. For example, the four point sequences x(n) = 3, 1, 3, 3 and y(n) = 2, 4, 2, 2 are duals to each other. Observe that the sum of each sequence is 10 and one sequence could be obtained from the other by subtracting the elements of the other sequence from 5, which is half of its sum. Since RT of a number sequence is an organized number sequence with a high degree of correlation, it is suitable for effective data compression. This paper describes in detail the techniques of using RT for pattern recognition purposes. For example, pattern recognition operations like extracting lines, curves, isolated points and points of intersection of lines from a digital gray or colour image could be carried out using RT based fast algorithms.
关键词：transform; pattern classification; image processing; permutation invariant systems