Computational geometry: an introduction
Computational geometry: an introduction
Linear Programming in Linear Time When the Dimension Is Fixed
Journal of the ACM (JACM)
Digital Planarity of Rectangular Surface Segments
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Discrete Applied Mathematics
An elementary digital plane recognition algorithm
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
Digital planar surface segmentation using local geometric patterns
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
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
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This paper introduces a new method for the naive digital plane recognition problem As efficient as existing alternatives, it is the only method known to the author that also guarantees a quasi linear time complexity in the worst case The approach presented can be used to determine if a set of n points is a naive digital hyperplane in ℤd in O(n log2D) worst case time where D represents the size of a bounding box that encloses the points In addition, the approach succeeds in reducing the naive digital plane recognition problem to a two-dimensional convex optimization program Thus, the solution space is planar and only simple two-dimensional geometrical methods need to be applied during the recognition process The algorithm is a composite of simple techniques based on one-dimensional optimization: Megiddo Oracle for linear programming and two-dimensional discrete geometry.