A New Criterion for Selecting the Conduction Function for Anisotropic Diffusion

H. Yi and P.H. Gregson (Canada)


anisotropic diffusion (AD), oversmoothing, conductionfunction (CF), flux, derivative of flux (DF), edge threshold.


The results obtained with current anisotropic diffusion (AD) techniques are image-dependent because the effects of the conduction function (CF) are not well understood. A significant problem is oversmoothing. This is problematic for applications that do not permit human intervention (robotics, surveillance, etc.). The goals of this paper are 1) to create a criterion for selecting the CF and 2) to understand AD so as to make it suitable for autonomous computer vision. We present an analysis of AD behaviour over the entire range of gradient magnitudes. We show that different ranges of gradient magnitude result in AD being a mathematically well-posed, a mathematically ill-posed or a "do nothing" process with a given CF. This leads to the requirement for two thresholds: one that defines edges and one that defines noise. Negative CFs that "move intensity uphill" are also explored. The need for, and effectiveness of, our analysis is illustrated by experiments.

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