Image quantization by nonlinear smoothing

Abstract

We present a quantization technique based on the partial differential equation (Equation presented) where (Equation presented) represents the derivative of the function u in the direction orthogonal to the gradient, Gσ is a linear convolution kernel, g is a decreasing function and f(s,t) is a lipschitz function. We assume that when t tends to +∞, f(s, t) tends uniformly to a function f∞(s) which has a finite number of zeros with negative derivative which act as atractors in the system and represent the quantization levels. The location of the zero-crossing of the function f∞(s) depends on the histogram of the initial image given by u0. We introduce a new energie based in the Lloyd model to compute the quantizer levels. We develop a numerical scheme to discretize the above equation and we present some experimental results.