A Composite and Quasi Linear Time Method for Digital Plane Recognition

  • Lilian Buzer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4245)


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 ℤ d in O(n log2 D) 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.


Normal Vector Side Length Search Domain Linear Programming Technique Binary Optimization 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Lilian Buzer
    • 1
  1. 1.Laboratory CNRS-UMLV-ESIEEUMR 8049, ESIEENoisy le GrandFrance

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