Most image and signal processing algorithms are local algorithms, regardless of the specific physical nature of the images and signals. Because of the strong correlation of operations required to determine two neighboring elements, image processing can be substantially accelerated by using fast algorithms. Some considerations regarding the construction of such algorithms on the basis of recursive computation have been examined in this paper. The development of specific algorithms for fast local image processing requires further work, because we still do not have the explicit form of the algorithm for the determination of a general local function. We have discussed some particular examples of fast algorithms, including linear and median filtering. Linear filtering and algorithms with linear function evaluation are often used for digital image and signal processing in various fields. The general form of linear filtering can be determined using piecewise-linear approximation, which also ensures independence of the number of operations on window size, albeit at a cost of a certain loss of accuracy. By sacrificing some accuracy of linear filtering, we accelerate the processing, whereas higher accuracy is achieved by reducing the processing speed. © 1994 Plenum Publishing Corporation.
