PARameter-free Analysis of DIgital Surfaces (PARADIS)

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ANR JCJC AAPG 2018
ANR-18-CE23-0007-01
December 2018 - March 2024

Short description

This project focuses on the geometry of digital surfaces, which are boundaries of voxel sets. These data mainly come from the segmentation of 3D digital images. Keeping the digital nature of the data is often an advantage. However, a drawback is its poor geometry at any resolution. The challenge is to enhance its geometry by estimating extra data for each surface element, such as a relevant normal vector. The idea is to gather the geometrical information around each surface element within a patch of adaptive size: a piece of digital plane that locally fits to the digital surface. The covering of a digital surface by maximal pieces of digital plane is however hard because of their combinatorial explosion. An opportunity to make a breakthrough in this issue is the recent development of plane-probing algorithms. Based on these algorithms, we propose a new way of analyzing digital surfaces without any parameter. We expect a positive impact in graphics and 3D image analysis.

Members

Permanent members

Students

Publications

Project works

  1. image
    Decomposition of~Rational Discrete Planes,
    Sébastien Labbé and Tristan Roussillon,
    Third International Joint Conference on Discrete Geometry and Mathematical Morphology, p. 54–66, 2024.
    [doi]  [hal]  [file]  [teaser]  [poster] 
  2. image
    Delaunay property and proximity results of the L-algorithm for digital plane probing,
    Jui-Ting Lu, Tristan Roussillon, Jacques-Olivier Lachaud and David Coeurjolly,
    Theoretical Computer Science, Vol. 1011, 2024.
    [doi]  [hal]  [file] 
  3. image
    Combinatorial Generation of Planar Sets,
    Tristan Roussillon,
    Journal of Mathematical Imaging and Vision, Vol. 65, No. 5, p. 702–717, 2023.
    [doi]  [hal]  [file] 
  4. image
    Approximation of Digital Surfaces by a Hierarchical Set of Planar Patches,
    Jocelyn Meyron and Tristan Roussillon,
    IAPR Second International Conference on Discrete Geometry and Mathematical Morphology, 2022.
    [hal]  [file] 
  5. image
    A New Lattice-based Plane-probing Algorithm,
    Jui-Ting Lu, Tristan Roussillon and David Coeurjolly,
    IAPR Second International Conference on Discrete Geometry and Mathematical Morphology 2022.
    [hal]  [file] 
  6. image
    An Optimized Framework for Plane-Probing Algorithms,
    Jacques-Olivier Lachaud, Jocelyn Meyron and Tristan Roussillon,
    Journal of Mathematical Imaging and Vision, Vol. 62, No. 5, p.718–736, 2020.
    [doi] [hal] [file] 
  7. image
    Three characterizations of a self-similar aperiodic 2-dimensional subshift,
    Sébastien Labbé,
    Chapter written for a book in preparation edited by Nathalie Aubrun and Michael Rao. 2020.
    [arXiv:2012.03892]
  8. image
    Digital Plane Recognition with Fewer Probes,
    Tristan Roussillon and Jacques-Olivier Lachaud,
    21st IAPR International Conference on Discrete Geometry for Computer Imagery, Vol. 11414, p.380–393, Mar 2019.
    [doi] [hal] [pres] [file] 

Preliminary works

  1. image
    Two Plane-Probing Algorithms for the Computation of the Normal Vector to a Digital Plane,
    Jacques-Olivier Lachaud, Xavier Provençal and Tristan Roussillon,
    Journal of Mathematical Imaging and Vision, Vol. 59, No. 1, p.23 – 39, Sep 2017.
    [doi] [hal] [file] 
  2. image
    An output-sensitive algorithm to compute the normal vector of a digital plane,
    Jacques-Olivier Lachaud, Xavier Provençal and Tristan Roussillon,
    Journal of Theoretical Computer Science, Vol. 624, p.73–88, Apr 2016.
    [doi] [hal] [file] 
  3. image
    Computation of the normal vector to a digital plane by sampling signicant points,
    Jacques-Olivier Lachaud, Xavier Provençal and Tristan Roussillon,
    19th IAPR International Conference on Discrete Geometry for Computer Imagery, Apr 2016.
    [hal] [pres] [file] 

Meetings and oral presentations

  1. First meeting, Lyon, January 8, 2019
  2. Oral presentation at DGCI, Paris, March 28 2019
  3. Working meeting, Chambéry, May 15, 2019
  4. Working meeting, Bordeaux, May 28-29, 2019
  5. Second general meeting, July 3, 2019
  6. Working meeting, Chambéry, October 21, 2019
  7. Oral presentation (in french) for the working group about discrete geometry, Marseille, November 12 2019
  8. General meeting, Lyon, February 4-5, 2020
  9. Two-hour virtual meeting, February 17, 2021
  10. Two-hour virtual meeting, February 24, 2021
  11. Oral presentation (in french) for the working group about discrete geometry, March 16 2021
  12. Oral presentation at DGDVC, March 20 2021
  13. General meeting, Chambéry, February 2-3, 2022
  14. Oral presentation at DGMM, Strasbourg, October 25-27 2022
  15. Jui-Ting Lu's Phd-thesis Defense, Lyon, December 21 2023