Moving average algorithms for diamond, hexagon, and general polygonal shaped window operations

This paper presents fast moving window algorithms for calculating local statistics in a diamond, hexagon, and general polygonal shaped windows of an image which is important for real-time applications. The algorithms for a diamond shaped window requires only seven or eight additions and subtractions per pixel. A fast sparse algorithm only needs four additions and subtractions for a sparse diamond shaped window. A number of other shapes of diamond windows such as skewed or parallelogram shaped diamond, long diamond, and lozenged diamond shaped, are also investigated. Similar algorithms are also developed for hexagon shaped windows. The computation for a hexagon window only needs eight additions and subtractions for each pixel. Fast algorithms for general polygonal shaped windows are also developed. The computation cost of all these algorithms is independent of the window size. A variety of synthetic and real images have been tested.