Vector quantization using genetic K-means algorithm for image compression

Abstract

In vector quantization (VQ), minimization of mean square error (MSE) between code book vectors and training vectors is a non-linear problem. Traditional Linde-Buzo-Gray (1980) type of algorithms converge to a local minimum, which depends on the initial code book. While most of the efforts in VQ have been directed towards designing effcient search algorithms for the code book, little has been done in evolving a procedure to obtain an optimum code book. This paper addresses the problem of designing a globally optimum code book using genetic algorithms (GAs). A hybrid GA called the genetic K-means algorithm (GKA) that combines the advantages of gradient descent algorithms and GAs have been proposed previously. In this algorithm, the gradient descent part helps to speed up the algorithm whereas the GA features help to obtain a global optimum. The standard K-means algorithm is used instead of crossover and a distance based mutation is defined specifically for this problem to effectively perturb the solutions. The GKA has been proved to converge to a global optimum with probability one. We applied GKA to VQ for image compression. Since most of the code book design algorithms are based on the LBG we compared the performance of the GKA with that of the LBG algorithm.