Image quantization by nonlinear smoothing

Luis Alvarez; Julio Esclarin

doi:10.1117/12.218473

1 September 1995 Image quantization by nonlinear smoothing

Luis Alvarez, Julio Esclarin

Proceedings Volume 2567, Investigative and Trial Image Processing; (1995) https://doi.org/10.1117/12.218473
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

Abstract

We present a quantization technique based on the partial differential equation (∂u/∂t) = g(||∇(G_σ * 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, G_s 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.

Citation Download Citation

Luis Alvarez and Julio Esclarin "Image quantization by nonlinear smoothing", Proc. SPIE 2567, Investigative and Trial Image Processing, (1 September 1995); https://doi.org/10.1117/12.218473

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