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Local Versus Nonlocal Computation of Length of Digitized Curves
July 1994 (vol. 16 no. 7)
pp. 711-718

Considers the problem of computing the length of a curve from digitized versions of the curve using parallel computation. The authors' aim is to study the inherent parallel computational complexity of this problem as a function of the digitization level. Precise formulations for the digitization, the parallel computation, and notions of local and nonlocal computations are given. It is shown that length cannot be computed locally from digitizations on rectangular tessellations. However, for a random tessellation and appropriate deterministic ones, the authors show that the length of straight line segments can be computed locally. Implications of the authors' results for a method for image segmentation and a number of open problems are discussed.

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Index Terms:
parallel algorithms; computational complexity; image segmentation; computational geometry; local computation; nonlocal computation; length of digitized curves; parallel computation; inherent parallel computational complexity; digitization level; random tessellation; deterministic tessellation; image segmentation
S.R. Kulkarni, S.K. Mitter, R.J. Richardson, J.N. Tsitsiklis, "Local Versus Nonlocal Computation of Length of Digitized Curves," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, no. 7, pp. 711-718, July 1994, doi:10.1109/34.297951
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