Computational geometry: an introduction
Computational geometry: an introduction
Theory of linear and integer programming
Theory of linear and integer programming
Polynomial time algorithms for finding integer relations among real numbers
SIAM Journal on Computing
Handbook of theoretical computer science (vol. A)
A subexponential randomized simplex algorithm (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
The real number model in numerical analysis
Journal of Complexity
A parametrization of digital planes by least-squares fits and generalizations
Graphical Models and Image Processing
Real data—integer solution problems with the Blum-Shub-Smale computational model
Journal of Complexity
Discrete analytical hyperplanes
Graphical Models and Image Processing
Linear Programming in Linear Time When the Dimension Is Fixed
Journal of the ACM (JACM)
Object discretizations in higher dimensions
Pattern Recognition Letters
Digital Planarity of Rectangular Surface Segments
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital Planar Segment Based Polyhedrization for Surface Area Estimation
IWVF-4 Proceedings of the 4th International Workshop on Visual Form
On the Complexity of Integer Programming in the Blum-Shub-Smale Computational Model
TCS '00 Proceedings of the International Conference IFIP on Theoretical Computer Science, Exploring New Frontiers of Theoretical Informatics
Recognition of Digital Naive Planes and Polyhedrization
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Recognizing arithmetic straight lines and planes
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
A linear incremental algorithm for naive and standard digital lines and planes recognition
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
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
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
Computational aspects of digital plane and hyperplane recognition
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
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We consider the following problem. Given a set of points M={p1,p2...pm}⊆ℝn, decide whether M is a portion of a digital hyperplane and, if so, determine its analytical representation. In our setting p1,p2...pm may be arbitrary points (possibly, with rational and/or irrational coefficients) and the dimension n may be any arbitrary fixed integer. We provide an algorithm that solves this digital hyperplane recognition problem by reducing it to an integer linear programming problem of fixed dimension within an algebraic model of computation. The algorithm performs O(mlogD) arithmetic operations, where D is a bound on the norm of the domain elements.