ABSTRACT
Per-patch variance evaluation The first step of the guided image filter is to determine whether an edge exists in each patch within a given image. The size of a patch is given by the parameter ω defining the total number of pixels (often evaluated from a given width for convenience) on the patch in a local neighborhood around each pixel in the image. The filter identifies edges by measuring the statistical variance of the pixel intensity values I inside the patch. So for a patch of size ω centered on pixel k, this statistical variance kσ is given by the following formula:
σ I μω ,
where kω is the set of pixels in the patch, jI is the intensity of pixel j, and kμ is the mean intensity inside the patch. It is fairly obvious that for a patch containing an edge, the statistical variance of pixel intensity values will be high due to the polarized intensities of pixels that define the edge. In the case where there is no visual edge, the statistical variance of pixel intensity values should be low because intensity values should span a narrow range. Computation of this per-patch variance and mean can both be accelerated by using summed area tables for both the intensity and squared intensity values in the image. Once the patch’s variance is computed, the value of A, or more precisely, what we call the per-patch kA , is given by the formula
σA σ ε .
