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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. 711718, July, 1994.  
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@article{ 10.1109/34.297951, author = {S.R. Kulkarni and S.K. Mitter and R.J. Richardson and J.N. Tsitsiklis}, title = {Local Versus Nonlocal Computation of Length of Digitized Curves}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {16}, number = {7}, issn = {01628828}, year = {1994}, pages = {711718}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.297951}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  Local Versus Nonlocal Computation of Length of Digitized Curves IS  7 SN  01628828 SP711 EP718 EPD  711718 A1  S.R. Kulkarni, A1  S.K. Mitter, A1  R.J. Richardson, A1  J.N. Tsitsiklis, PY  1994 KW  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 VL  16 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
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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