1 September 1995 Image quantization by nonlinear smoothing
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Abstract
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 fs(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.
© (1995) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Luis Alvarez, Luis Alvarez, Julio Esclarin, Julio Esclarin, } "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
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