1. A method of processing a digital, input image, comprising: providing said digital input image, I, in physical memory, said input image having color information in a native color space for each image pixel; providing a processing device coupled to said physical memory to access said input image I and create an output image, h, by implementing the following steps: applying an image filtering sequence to said input image I, wherein said image filtering sequence applies a filtering algorithm to each pixel of said input image I relative to its surrounding pixels within a window w having a fixed, predefined radius of r pixels extending from a center pixel, pixels of said input image I being processed, in turn, as said center pixel relative to their corresponding window w; the applying of said image filtering sequence including: (a) for a first of said window w of a first pixel in said input image I to be processed according to said filtering algorithm, defining an extended window bigger than said first window w with said first window at its center; (b) determining statistics needed for said filtering algorithm for all pixels within said extended window; (c) applying said filtering algorithm to all center pixels whose corresponding window w fit fully within said extended window; (d) shifting said extended window within said input image by one unit-shift at a time, wherein at each unit-shift: (i) new statistics are determined for only the new pixels encompassed by the shifted extended window, said new pixels defining a new row or column within the shifted extended window; and (ii) applying said filtering algorithm to all center pixels whose corresponding window w extends to said new row or column.