Local Versus Non-local Computation of Length of Digitized Curves

نویسندگان

  • Sanjeev R. Kulkarni
  • Sanjoy K. Mitter
  • T. J. Richardson
  • John N. Tsitsiklis
چکیده

In this paper, we consider the problem of computing the length of a curve from digitized versions of the curve using parallel computation. Our 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. We show that length cannot be computed locally from digitizations on rectangular tessellations. However, for a random tessellation and appropriate deterministic ones, we show that the length of straight line segments can be computed locally. Implications of our results for a method for image segmentation and a number of open problems are discussed.

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عنوان ژورنال:
  • IEEE Trans. Pattern Anal. Mach. Intell.

دوره 16  شماره 

صفحات  -

تاریخ انتشار 1993