A digital naive plane is a subset of points (x, y, z) β Z 3 verifying a double inequality h β€ ax + by + cz < h + max{|a|, |b|, |c|} where (a, b, c) β R/ {(0,0,0)} and h β R. Given a finite subset of Z 3 , a problem is to determine whether or not there exists a digital naive plane containing it. This
A linear incremental algorithm for naive and standard digital lines and planes recognition
β Scribed by Lilian Buzer
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 435 KB
- Volume
- 65
- Category
- Article
- ISSN
- 1524-0703
No coin nor oath required. For personal study only.
β¦ Synopsis
We present a new linear incremental method for digital hyperplanes recognition. The first linear incremental algorithm was given for 8-connected planar lines by Debled-Rennesson and Reveill e es [IJPRAI 9(6) (1995) 635]. Our method determines if any given set of points is a piece of a line in the plane (or a plane in space). We describe the transformation of the recognition problem into a linear programming (LP) problem relative to the naive and standard hyperplanes definitions. Then we present the LP Megiddo algorithm in linear time and explain its improvement toward a linear incremental method.
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