4 January 1995 Time-optimal solutions for digital geometry algorithms on enhanced meshes
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Proceedings Volume 2356, Vision Geometry III; (1995) https://doi.org/10.1117/12.198620
Event: Photonics for Industrial Applications, 1994, Boston, MA, United States
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.
© (1995) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
V. Bokka, V. Bokka, H. Gurla, H. Gurla, Stephan Olariu, Stephan Olariu, Jim L. Schwing, Jim L. Schwing, Ivan Stojmenovic, Ivan Stojmenovic, } "Time-optimal solutions for digital geometry algorithms on enhanced meshes", Proc. SPIE 2356, Vision Geometry III, (4 January 1995); doi: 10.1117/12.198620; https://doi.org/10.1117/12.198620
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