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, 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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