Pipelined Execution of Windowed Image Computations

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<p>Many image processing operations manipulate an individual pixel using the values of other pixels in the 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.</p><p>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 at most N2/n2 (1 + δ) steps, where δ= (n/N + 6n3/wN2 + zw/N + zn2/N2). This produces a speed-up of z/1+δ over a single stage; δ, the overhead is quite small. We also show that the memory requirement per stage is O(wN +n2). With values of N, n and w that reflect the current state-of-the-art, over 20 pipeline stages can be sustained with less than 5% overhead for a 10M-pixel image. Each of these stages would require less than 128 Kbytes of storage.</p>

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