A graphical overview of the proposed FACE algorithm. Given an input image I sized m x n, we first precompute an optimized layout or rectangles L, which partitions an area around a central pixel (red circle) into several rectangles of appropriate shapes and sizes. The layout L is constructed for a given maximal tolerated error emax and image resolution. For each possible intensity value k (and for each channel), we pre-compute image f(I-k) (equation 3) over the entire image channel and integrate it into a corresponding Summed Area Table Sk. At this point (main loop), the Layout L is slid over the image, by positioning its central pixel over each pixel in position p of I; for each pixel in p having intensity I[p], the combined contribution from all pixels inside a rectangle of L is quickly computed, in constant time, by accessing Sk with k= I[p]. Summing this over all the rectangles of L, we get an approximation of V[p] (Equation 1) for that pixel. The layout L is also used to compute, for every pixel, the maximal value of that pixel, that is, value Vmax (Equation 5). The per-pixel division of these two images gives us the final image, which is then linearly mapped in the final output image, as normal.
