Vector Quantization using Genetic &Means Algorithm for Image Compression

In Vector Quantization (VQ), minimization of Mean Square Error (MSE) between code book vectors and training vectors is a non-linear problem. Traditional LBG 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 efficient search algorithms for 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). GAS have been applied to many function optimization problems and have been shown to be good in finding optimal and near optimal solutions. GAS work on a coding of the parameter set over which the search has to be performed, rather than the parameters themselves. These encoded parameters are called solutions or chromosomes and the objective function value at a solution is the objective function value at the corresponding parameters. GAS solve optimization problems using a population of a fixed number solutions. A solution is a string of symbols. GAS evolve over generations. During each generation, they produce a new population from the current population by applying genetic operators viz., natural selection, crossover, and mutation. A solution consists of a string of symbols, typically binary symbols. Each solution in the population is associated with a figure of merit (fitness value) depending on the value of the function to be optimized. The selection operator selects a solution from the current population for the next population with probability proportional to its fitness value. Crossover operates on two solution string,s and results in another two stings. Typical crossover operator exchange the segments of selected stings across a crossover point with a probability. The mutation operator toggles each position in a string with a probability, called Mutation probability. For a detail study on GA, readers are referred to [2].