A linear incremental algorithm for naive and standard digital lines and planes recognition

Authors:
Lilian Buzer
Affiliations:
LLAIC, Université Clermont 1, IUT Département Informatique, B. P. 86, 63172 Aubiere Cedex, France
Venue:
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
Year:
2003

Citing 9
Cited 11

Computational geometry: an introduction

Computational geometry: an introduction
Linear programming in O(n × 3d2) time

Information Processing Letters
Algorithms in combinatorial geometry

Algorithms in combinatorial geometry
Small-dimensional linear programming and convex hulls made easy

Discrete & Computational Geometry
Computational geometry: algorithms and applications

Computational geometry: algorithms and applications
Efficient algorithms for geometric optimization

ACM Computing Surveys (CSUR)
Linear Programming in Linear Time When the Dimension Is Fixed

Journal of the ACM (JACM)
Recognizing arithmetic straight lines and planes

DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
A Las Vegas algorithm for linear programming when the dimension is small

SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science

A simple algorithm for digital line recognition in the general case

Pattern Recognition
Digital hyperplane recognition in arbitrary fixed dimension within an algebraic computation model

Image and Vision Computing
A generalized preimage for the digital analytical hyperplane recognition

Discrete Applied Mathematics
An efficient and quasi linear worst-case time algorithm for digital plane recognition

DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
On three constrained versions of the digital circular arc recognition problem

DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Invertible polygonalization of 3d planar digital curves and application to volume data reconstruction

ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part II
A composite and quasi linear time method for digital plane recognition

DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
A generalized preimage for the standard and supercover digital hyperplane recognition

DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Complexity analysis for digital hyperplane recognition in arbitrary fixed dimension

DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
An elementary algorithm for digital line recognition in the general case

DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Computational aspects of digital plane and hyperplane recognition

IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis

Quantified Score

Hi-index	0.00

Visualization

Abstract

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 Reveillès [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.