×

zbMATH — the first resource for mathematics

Optimum scale selection for 3D point cloud classification through distance correlation. (English) Zbl 1444.62166
Aneiros, Germán (ed.) et al., Functional and high-dimensional statistics and related fields. Selected papers presented at the 5th international workshop on functional and operatorial statistics, IWFOS 2021, Brno, Czech Republic, June 23–25, 2021. Cham: Springer. Contrib. Stat., 213-220 (2020).
Summary: Multiple scale machine learning algorithms using handcrafted features are among the most efficient methods for 3D point cloud supervised classification and segmentation. Despite their proven good performance, there are still some aspects that are not fully solved, determining optimum scales being one of them. In this work, we analyze the usefulness of functional distance correlation to address this problem. Specifically, we propose to adjust functions to the distance correlation between each of the features, at different scales, and the labels of the points, and select as optimum scales those corresponding to the global maximum of said functions. The method, which to the best of our knowledge has been proposed in this context for the first time, was applied to a benchmark dataset and the results analyzed and compared with those obtained using other methods for scale selection.
For the entire collection see [Zbl 1446.62001].
MSC:
62R10 Functional data analysis
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62H20 Measures of association (correlation, canonical correlation, etc.)
68T05 Learning and adaptive systems in artificial intelligence
Software:
MASS (R); R
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Berrendero, J.R., Cuevas, A., Torrecilla, J.L.: Variable selection in functional data classification: a maxima-hunting proposal. Statistica Sinica, 619-638 (2016) · Zbl 1356.62079
[2] Brodu, N., Lague, D.: 3D terrestrial lidar data classification of complex natural scenes using a multi-scale dimensionality criterion: Applications in geomorphology. ISPRS Journal of Photogrammetry and Remote Sensing68, 121-134 (2012)
[3] Chaudhuri, P., Marron, J.: Scale space view of curve estimation. Ann. Stat, 408-428 (2000) · Zbl 1106.62318
[4] Demantké, J., Mallet, C., David, N., Vallet, B.: Dimensionality based scale selection in 3d lidar point clouds (2011)
[5] Dittrich, A., Weinmann, M., Hinz, S.: Analytical and numerical investigations on the accuracy and robustness of geometric features extracted from 3D point cloud data. ISPRS Journal of Photogrammetry and Remote Sensing126, 195- 208 (2017)
[6] Febrero-Bande, M., González-Manteiga, W., Oviedo de la Fuente, M.: Variable selection in functional additive regression models. Computational Statistics 34(2), 469-487 (2019) · Zbl 1417.62077
[7] Mallet, C., Bretar, F., Roux, M., Soergel, W., Heipke, Ch.: Relevance assessment of full-waveform lidar data for urban area classification. ISPRS Journal of Photogrammetry and Remote Sensing66(6), 571-584 (2011)
[8] Munoz, D., Bagnell, J., Vandapel, N., Hebert, M.: Contextual classification with functional max-margin Markov networks. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 975-982 (2009)
[9] Ordóñez, C., Oviedo de la Fuente, M., Roca-Pardiñas, J., Rodríguez-Pérez, J.L.: Determining optimum wavelengths for leaf water content estimation from reflectance: A distance correlation approach. Chemometrics and Intelligent Laboratory Systems173(15), 41-50 (2018)
[10] Pauly, M., Keiser, R., Gross, M.: Multi-scale feature extraction on pointsampled surfaces. Comput. Graph. Forum22(3), 281-289 (2003)
[11] Shannon, C.: A mathematical theory of communication. Bell Syst. Tech. J.27, 379-423 (1948) · Zbl 1154.94303
[12] Székely G.J., Rizzo, M.L., Bakirov, N.K.: Measuring and testing dependence by correlation of distances. Annals of Statistics35(6), 2769-2794 (2007) · Zbl 1129.62059
[13] Ullman, S.: The Interpretation of Structure from Motion: Proceedings of the Royal Society of London. Series B, Biological Sciences203(1153), 405-426 (1979)
[14] Venables, W.N., Ripley, B.D.: Modern Applied Statistics with S. Springer (2002) · Zbl 1006.62003
[15] Weinmann, M.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.