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.