Local Smoothness in terms of Variance: the Adaptive Gaussian Filter

Several techniques, such as adaptive smoothing [9, 10] or anisotropic diffusion [4, 5] deal with the task of local smoothing. That is, preserving principal discontinuities and smoothing within regions. Unfortunately, these types of iterative techniques have as one of their main drawbacks, the determination of the threshold on the luminance gradient. There is no way to control it easily and researchers often fall into a trial-and-error procedure. In this paper an adaptive Gaussian filter that computes directly the local amount of Gaussian smoothing in terms of variance is presented. The local variance, σ∗(x, y), is selected, in a scale-space framework, through the minimal description length criterion (MDL). The MDL allows us to estimate the local smoothing in such a way that it respects the main discontinuities. The resulting smoothed image, in location x, y, is the intensity given by the convolution of the initial point I0(x, y) with its appropriate Gaussian kernel e − x 2+y2 2σ(x,y) . In fact, the proposed algorithm is not iterative, it is very stable, it is not based on derivatives nor requires any thresholds.