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Discrete plane segmentation and estimation from a point cloud using local geometric patterns

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Abstract

This paper presents a method for segmenting a 3D point cloud into planar surfaces using recently obtained discrete-geometry results. In discrete geometry, a discrete plane is defined as a set of grid points lying between two parallel planes with a small distance, called thickness. In contrast to the continuous case, there exist a finite number of local geometric patterns (LGPs) appearing on discrete planes. Moreover, such an LGP does not possess the unique normal vector but a set of normal vectors. By using those LGP properties, we first reject non-linear points from a point cloud, and then classify non-rejected points whose LGPs have common normal vectors into a planar-surface-point set. From each segmented point set, we also estimate the values of parameters of a discrete plane by minimizing its thickness.

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Authors and Affiliations

  1. Laboratoire d’Informatique de l’Institut Gaspard-Monge, UMR CNRS 8049 A2SI-ESIEE, Cité Descartes, Université Paris-Est, BP 99, 93162, Noisy-le-Grand Cedex, France

    Yukiko Kenmochi, Lilian Buzer & Akihiro Sugimoto

  2. National Institute of Informatics, Chiyoda, Tokyo, 101-8430, Japan

    Akihiro Sugimoto

  3. Department of Computer, Information and Communication Sciences, Tokyo University of Agriculture and Technology, 2-24-16 Naka-cho, Koganedai, Tokyo, 184-8588, Japan

    Ikuko Shimizu

Authors
  1. Yukiko Kenmochi
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  2. Lilian Buzer
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  3. Akihiro Sugimoto
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  4. Ikuko Shimizu
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Corresponding author

Correspondence to Yukiko Kenmochi.

Additional information

Yukiko Kenmochi received her B. Eng., M. Eng., and D. Eng. degrees in information and computer sciences from Chiba University, Japan, in 1993, 1995, and 1998, respectively. She joined Japan Advanced Institute of Science and Technology as a research associate in 1998, and Okayama University, Japan, as a lecturer in 2003. Since 2004, she has been a CNRS researcher at Gaspard-Monge Institute, Université Paris-Est, France, and a member of the A2SI laboratory, ESIEE. She received a Best Paper Award of Information and System Society from IEICE in 2005. Her research interest includes discrete geometry for computer imagery.

Lilian Buzer received his Ingénieur’s degree in informatics from ISIMA, France, in 1999, and his Ph.D. degree in informatics from the Blaise Pascal University, Clermont-Ferrand, France, in 2002. Since 2003, he has been an assistant professor at ESIEE, France. He is a member of the A2SI laboratory, ESIEE, and of Gaspard-Monge Institute, Université Paris-Est.

His research interests include discrete geometry and computational geometry.

Akihiro Sugimoto received his B. Sc., M. Sc., and D.Eng. degrees in mathematical engineering from the University of Tokyo in 1987, 1989, and 1996, respectively. After working at Hitachi Advanced Research Laboratory, ATR, and Kyoto University, he joined the National Institute of Informatics, Japan, where he is currently a professor. From 2006 to 2007, he was a visiting professor at ESIEE, France. He received a Paper Award from the Information Processing Society in 2001. He is a member of IEEE.

He is interested in mathematical methods in engineering. In particular, his current main research interests include discrete mathematics, approximation algorithm, vision geometry, and modeling of human vision.

Ikuko Shimizu received her B. Sc., M. Sc., and Ph.D. degrees in mathematical engineering and information physics from the University of Tokyo, Japan, in 1994, 1996, and 1999, respectively. In 1999, she was a research associate at Saitama University, Japan. Currently, she is a lecturer in the Department of Computer, Information and Communication Sciences at Tokyo University of Agriculture and Technology, Japan. She is a member of IPSJ, IEICE, SICE, and IEEE. Her research interests include computer vision and 3D modeling.

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Kenmochi, Y., Buzer, L., Sugimoto, A. et al. Discrete plane segmentation and estimation from a point cloud using local geometric patterns. Int. J. Autom. Comput. 5, 246–256 (2008). https://doi.org/10.1007/s11633-008-0246-1

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  • DOI: https://doi.org/10.1007/s11633-008-0246-1

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