Diamond, Hexagon, and General Polygonal Shaped Window Smoothing

This paper presents fast recursive or moving windows algorithms for calculating local means in a diamond, hexagon and general polygonal shaped windows of an image. The algorithms for diamond shaped window require only seven or eight additions and subtractions per pixel. 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 hexagon window only needs eight additions and subtractions for each pixel. Fast algorithms for general polygonal shaped windows are also developed. The computation costs of all these algorithms are independent of the window size. A variety of synthetic and real images have been tested.