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Local Geometric Descriptors for Multi-Scale Probabilistic Point Classification of Airborne LiDAR Point Clouds

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Modeling, Analysis, and Visualization of Anisotropy

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

Point classification is necessary for detection and extraction of geometric feature (folds, creases, junctions, surfaces), and subsequent 3D reconstruction of point-sampled geometry of topographic data captured using airborne LiDAR technology. Geometry-based point classification (line-, surface-, point-type features) is determined using shape of the local neighborhood, given by the local geometric descriptor (LGD) at every point in the point cloud. Covariance matrix of local neighborhoods is the conventionally used LGD in the LiDAR community. However, it is known that covariance analysis has drawbacks in detection of sharp features, which are a subset of the line-type features. Here, we compare the performance of new variants of existing LGDs, such as weighted covariance matrix, and that based on tensor voting concept, in geometric classification with that of covariance matrix. We propose a multi-scale probabilistic saliency map based on eigenvalues of the LGDs for computing the classification. Usually the state-of-the-art performance analyses of LGDs in the classification outcomes are done downstream after feature extraction. We propose that the comparisons may be done upstream at the classification stage itself, which can be achieved by expressing these LGDs as positive semidefinite second-order tensors. We perform qualitative comparisons of the tensor fields based on shape and orientation of the tensors, and the classification outcomes using visualizations. We visualize LGDs using superquadric tensor glyphs and point rendering, using our proposed saliency map as colormap. Our detailed comparative analysis shows that the new variant of LGDs based on tensor voting classify line-type features, especially sharp features, better than covariance-based LGDs. Our proposed LGD based on tensor voting performs better than the covariance matrix, for our goal of detecting sharp features, e.g. gabled roofs in buildings.

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Notes

  1. 1.

    Here, we use geometric classes and feature classes interchangeably.

  2. 2.

    Here, we disambiguate tensor voting as the algorithm, and voting tensor as the second-order tensor, which is the outcome of the algorithm.

  3. 3.

    In Figs. 1, 4, and 7–10, color coding correspond to a geometric class or the combination of classes a point belongs to, which is determined by using the saliency maps. We use the colorblind safe color palette options from ColorBrewer2.0 http://colorbrewer2.org/.

  4. 4.

    We have demonstrated results on fan-disk and smooth-feature datasets, apart from airborne LiDAR datasets, purely for more comprehensible comparative analysis of LGDs for classification.

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Acknowledgements

The authors wish to thank Akshay Jindal for running experiments; Srujana Merugu, Ingrid Hotz, T. K. Srikanth, and Vijay Natarajan, as well as several participants of Dagstuhl seminar 16142 for their helpful discussions; and anonymous reviewers for suggestions on improving the manuscript. This work has been partially funded by NRDMS programme of Dept. of Science and Technology, Government of India. The second co-author has been funded by sponsored projects with EMC2-RSA India Pvt.; and FRHS, Bangalore, during her graduate study.

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Authors and Affiliations

  1. Graphics-Visualization-Computing Lab, International Institute of Information Technology Bangalore, Bangalore, Karnataka, India

    Jaya Sreevalsan-Nair & Beena Kumari

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  1. Jaya Sreevalsan-Nair
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  2. Beena Kumari
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Correspondence to Jaya Sreevalsan-Nair .

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Editors and Affiliations

  1. Institute of Computer Science, University of Bonn, Bonn, Germany

    Thomas Schultz

  2. Department of Biomedical Engineering (IMT), Linköping University, Linköping, Sweden

    Evren Özarslan

  3. Department of Science & Technology, Linköping University, Norrköping, Sweden

    Ingrid Hotz

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Sreevalsan-Nair, J., Kumari, B. (2017). Local Geometric Descriptors for Multi-Scale Probabilistic Point Classification of Airborne LiDAR Point Clouds. In: Schultz, T., Özarslan, E., Hotz, I. (eds) Modeling, Analysis, and Visualization of Anisotropy. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-319-61358-1_8

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