Time-optimal solutions for digital geometry algorithms on enhanced meshes

V. Bokka; H. Gurla; Stephan Olariu; Jim L. Schwing; Ivan Stojmenovic

doi:10.1117/12.198620

4 January 1995 Time-optimal solutions for digital geometry algorithms on enhanced meshes

V. Bokka, H. Gurla, Stephan Olariu, Jim L. Schwing, Ivan Stojmenovic

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) (n^1/6) 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(n^1/6) 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.

Citation Download Citation

V. Bokka, H. Gurla, Stephan Olariu, Jim L. Schwing, and Ivan Stojmenovic "Time-optimal solutions for digital geometry algorithms on enhanced meshes", Proc. SPIE 2356, Vision Geometry III, (4 January 1995); https://doi.org/10.1117/12.198620

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available