1 October 1999 Fast parallel shrinking to residues
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The problem of shrinking the connected components of binary images to small residues is addressed. A new parallel algorithm is presented with the lowest known worst case time complexity as measured by iteration counts, i.e., ?(nc+nr)/2? iterations where the foreground of the image is contained within a rectangular region of size ncxnr pixels. The new algorithm also demonstrates superior average iteration counts in comparison with other shrinking algorithms on test images. The new algorithm uses a fully parallel application of an operator with an 8 pixel support. It reduces all connected components in any two-dimensional (2D) binary image to certain small 1, 2, or 3 pixel residues. It is potentially useful for component counting, as a fundamental step in connected component labeling algorithms implemented with fine grain realizations in 2D mesh computing architectures, and in other applications requiring preservation of foreground topology (connectivity).
Richard W. Hall, "Fast parallel shrinking to residues," Journal of Electronic Imaging 8(4), (1 October 1999). https://doi.org/10.1117/1.482713

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