We present a quantization technique based on the partial differential equation (∂u/∂t) = g(||∇(Gσ * u)||) |∇u|div(∇u/|∇u|) + f(u, t) where |∇u|div(∇u/|∇u|) represents the derivative of the function u in the direction orthogonal to the gradient, Gs 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 attractors in the system and represent the quantization levels. The location of the zero-crossing of the function f∞s(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.
"Image quantization by nonlinear smoothing", Proc. SPIE 2567, Investigative and Trial Image Processing, (1 September 1995); doi: 10.1117/12.218473; https://doi.org/10.1117/12.218473