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Proceedings Paper

Time-optimal solutions for digital geometry algorithms on enhanced meshes
Author(s): V. Bokka; H. Gurla; Stephan Olariu; Jim L. Schwing; Ivan Stojmenovic
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Paper Abstract

Consider a binary image pretiled, one pixel per processor, onto mesh of size (root)n X (root)n, enhanced with row and column buses. Our first contribution is to show an (Omega) (n1/6) time lower bound for the problem of deciding whether the image contains at least one black pixel. We then obtain time lower bounds for many other digital geometry problems by reducing this fundamental problem to all the other problems of interest. Specifically, the problems that we address are: detecting whether an image contains at least one black pixel, computing the convex hull of the image, computing the diameter of an image, deciding whether a set of digital points is a digital line, computing the minimum distance between two images, deciding whether two images are linearly separable, computing the perimeter, area and width of a given image. Our second contribution is to show that the time lower bounds obtained are tight by exhibiting simple O(n1/6) time algorithms for these problems. An interesting feature of these algorithms is that they use, directly or indirectly, an algorithm for the leftmost one problem recently developed by one of the authors.

Paper Details

Date Published: 4 January 1995
PDF: 12 pages
Proc. SPIE 2356, Vision Geometry III, (4 January 1995); doi: 10.1117/12.198620
Show Author Affiliations
V. Bokka, Old Dominion Univ. (United States)
H. Gurla, Old Dominion Univ. (United States)
Stephan Olariu, Old Dominion Univ. (United States)
Jim L. Schwing, Old Dominion Univ. (United States)
Ivan Stojmenovic, Univ. of Ottawa (Canada)

Published in SPIE Proceedings Vol. 2356:
Vision Geometry III
Robert A. Melter; Angela Y. Wu, Editor(s)

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