I found the preprint somewhat confusing with its talk of approximate residuals and "pushing" pixels. Let me propose another way to think of this and someone can

I found the preprint somewhat confusing with its talk of approximate residuals and "pushing" pixels. Let me propose another way to think of this and someone can tell me if I'm off base. Disclaimer, I haven't read the source code. Consider a grayscale morphological operator such as erosion. For each pixel, you would replace the value with the minimum value found inside a structuring element surrounding the pixel. This is kind of like a weird morphological operator with a 3x3 box structuring element, where instead of choosing values based on a simple criterion such as 'min' or 'max' you use information from an approximation of the image gradient. If the gradient magnitude is above some threshold, you select the neighbor pixel in the 3x3 structuring element in the opposite direction of the gradient. This generally has the effect of making the edges more pronounced. Intuitively, you're distorting the image by "pinching" along the edges. To prevent weird color artifacts, they're using edges computed on grayscale data so that the identical morphological filter is applied to each color channel. It seems similar but not identical to the method described in this paper: T. A. Mahmoud and S. Marshall, Edge-Detected Guided Morphological Filter for Image Sharpening 2008 http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.384.8621&rep=rep1&type=pdf http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.384... In any case, great looking results! Proof that neural networks have not yet made thinking obsolete.