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An Optimized Framework for Plane-Probing Algorithms

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Abstract

A plane-probing algorithm computes the normal vector of a digital plane from a starting point and a predicate “Is a point \({x}\) 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. However, several existing plane-probing algorithms return the correct normal vector only for some specific starting points and an approximation otherwise, e.g., the H- and R-algorithm proposed in Lachaud et al. (J Math Imaging Vis 59(1):23–39, 2017). In this paper, we present a general framework for these plane-probing algorithms that provides a way of retrieving the correct normal vector from any starting point, while keeping their main features. There are \(O(\omega \log \omega )\) calls to the predicate in the worst-case scenario, where \(\omega \) is the thickness of the underlying digital plane, but far fewer calls are experimentally observed on average. In the context of digital surface analysis, the resulting algorithm is expected to be of great interest for normal estimation and shape reconstruction.

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Authors and Affiliations

  1. Univ. Savoie Mont Blanc, CNRS, LAMA, Univ. Grenoble Alpes, 73000, Chambéry, France

    Jacques-Olivier Lachaud

  2. LAMA, UMR 5127 CNRS, Université Savoie Mont Blanc, 73000, Chambéry, France

    Jocelyn Meyron

  3. INSA Lyon, LIRIS, UMR CNRS 5205, University of Lyon, 69622, Lyon, France

    Tristan Roussillon

Authors
  1. Jacques-Olivier Lachaud
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  2. Jocelyn Meyron
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  3. Tristan Roussillon
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Correspondence to Tristan Roussillon.

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This work has been partly funded by CoMeDiC ANR-15-CE40-0006 and PARADIS ANR-18-CE23-0007-01 research grants.

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Lachaud, JO., Meyron, J. & Roussillon, T. An Optimized Framework for Plane-Probing Algorithms. J Math Imaging Vis 62, 718–736 (2020). https://doi.org/10.1007/s10851-020-00965-6

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