Digital Plane Recognition with Fewer Probes

  • Tristan RoussillonEmail author
  • Jacques-Olivier Lachaud
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11414)


We present a new plane-probing algorithm, i.e., an algorithm that computes the normal vector of a digital plane from a starting point and a predicate “Is a point \(\varvec{x}\) in the digital plane?”. This predicate is used to probe the digital plane as locally as possible and decide on-the-fly the next points to consider. We show that this algorithm returns the same vector as another plane-probing algorithm proposed in Lachaud et al. (J. Math. Imaging Vis., 59, 1, 23–39, 2017), but requires fewer probes. The theoretical upper bound is indeed lowered from \(O(\omega \log \omega )\) to \(O(\omega )\) calls to the predicate, where \(\omega \) is the arithmetical thickness of the digital plane, and far fewer calls are experimentally observed on average. This reduction is made possible by a study that shows how to avoid computations that do not contribute to the final solution. In the context of digital surface analysis, this new algorithm is expected to be of great interest for normal estimation and shape reconstruction.


Digital plane recognition Normal estimation Plane-probing algorithm 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Université de Lyon, INSA Lyon, LIRIS, UMR CNRS 5205VilleurbanneFrance
  2. 2.Université Savoie Mont Blanc, LAMA, UMR CNRS 5127Le Bourget-du-LacFrance

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