On Running Windowed Image Computations on a Pipeline

Many image processing operations manipulate an individual pixel using the values of other pixels in the given pixel's neighborhood. Such operations are called windowed operations. The size of the windowed operation is a measure of the size of the given pixel's neighborhood. A windowed computation applies a windowed operation on all pixels of the image. An image processing application is typically a sequence of windowed computations. While windowed computations admit high parallelism, the cost of inputting and outputting the image often restricts the computation to a few computational units. In this paper we analytically study the running of a sequence of z windowed computations, each of size w, on a z-stage pipelined computational model. For an N × N image and n × n input/output bandwidth per stage, we show that the sequence of windowed computations can be run in N2/n2 (1 + δ) steps, where δ = (n/N + 3n2/wN + zw/N). This produces a speed-up of z/1+δ over a single stage. Generally, N ≫ n >; z, w; so the overhead, δ, is dominated by the term which is typically small. This also indicates the time to be relatively independent of the number of stages z.