Local versus nonlocal computation of length of digitized curves

Author

Kulkarni, S.R. ; Mitter, S.K. ; Richardson, T.J. ; Tsitsiklis, J.N.

Author_Institution

Dept. of Electr. Eng., Princeton Univ., NJ, USA

Volume

16

Issue

7

fYear

1994

fDate

7/1/1994 12:00:00 AM

Firstpage

711

Lastpage

718

Abstract

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

Keywords

computational complexity; computational geometry; image segmentation; parallel algorithms; deterministic tessellation; digitization level; image segmentation; inherent parallel computational complexity; length of digitized curves; local computation; nonlocal computation; parallel computation; random tessellation; Algorithm design and analysis; Computational complexity; Computational geometry; Computational modeling; Concurrent computing; Image segmentation; Laboratories; Military computing; Parallel architectures; Stochastic processes;

fLanguage

English

Journal_Title

Pattern Analysis and Machine Intelligence, IEEE Transactions on

Publisher

ieee

ISSN

0162-8828

Type

jour

DOI

10.1109/34.297951

Filename

297951