3D Cartographic Generalization of LiDAR Point Clouds Based on the Principle of Self-Similarity of a Deterministic Fractal Structure
DOI:
https://doi.org/10.11137/1982-3908_2023_46_52720Keywords:
Simplification methods, Geometric models, RoughnessAbstract
The rendering of virtual three-dimensional (3D) structures represented by Point Cloud (PC) allows the representation of internal and/or external environments to buildings. However, the compilation of 3D geometric models is influenced by the intrinsic characteristics of PCs, which can be mitigated by the application of an PC simplification operator. According to the mathematical norms of fractal geometry, it was assumed that a PC is characterized by self-similarity. Two experimental datasets acquired with an SLT in static mode indoors were used. Four tasks were accomplished: sampling and structuring of a PC to solve the problem of random distribution, from an octree structure; estimation of the curvature of the points and the roughness of a neighbourhood for the extraction of edge points by the analysis of self-similarity and application of the Statistical Outliers Remove (SOR) algorithm, for the elimination of outliers points; uniform voxelization, to simplify the intermediate points; application of the Iterative Closest Point (ICP) algorithm to register the sets generated in the same local coordinate system. The use of voxelization was satisfactory, but once the voxel size is manually defined, the PC can be oversimplified and lose essential characteristics. This can be minimized by the primary analysis of the edge points, generating a set that is uniform, less noisy, and self- similar to the original set. To achieve a minimum density of points to model an environment three-dimensionally, one must analyse the geometric self- similarity characteristics of the PC to produce a simplified set self-similar to the original, considering the premises of fractal geometry. It is recommended to create an automatic simplification process to minimize the subjectivity coming from the analyst.
References
An, Y., Wang, L., Ma, R. & Wang, J. 2021, ‘Geometric Properties Estimation from Line Point Clouds Using Gaussian-Weighted Discrete Derivatives’, IEEE Transactions on Industrial Electronics, vol. 68, no. 1, pp. 703–14.
Asgharian, L. & Ebrahimnezhad, H. 2020, ‘How many sample points are sufficient for 3D model surface representation and accurate mesh simplification?’, Multimedia Tools and Applications, vol. 79, no. 39–40, pp. 29595–620, DOI:10.1007/s11042-020-09395-3
Besl, P. & McKay, N. 1992, ‘A Method for Registration of 3-D Shapes, Trans’, PAMI, vol. 14, no. 2, pp. 239-56.
Benita, F., Perhac, J., Tunçer, B., Burkhard, R. & Schubiger, S. 2020, ‘3D-4D visualization of IoT data from Singapore’s National Science Experiment’, Journal of Spatial Science, vol. 67, no. 1, pp. 157–75, DOI:10.1080/14498596.2020.1726219
Döllner, J. 2020, ‘Geospatial Artificial Intelligence: Potentials of Machine Learning for 3D Point Clouds and Geospatial Digital Twins’, Journal of Photogrammetry, Remote Sensing and Geoinformation Science, vol. 88, no. 1, pp. 15–24, DOI:10.1007/s41064-020-00102-3
Dovrat, O., Lang, I. & Avidan, S. 2019, ‘Learning to Sample’, Proceedings of the Ieee/CVF Conference On Computer Vision And Pattern Recognition, pp. 2760–69.
Edgar, G. 2008, Measure, Topology, and Fractal Geometry, Springer, New York.
Garland, M. & Heckbert, P.S. 1997, ‘Surface simplification using quadric error metrics’, Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques, pp. 1–8.
Hinderink, S., Mandad, M. & Campen, M. 2022, ‘Angle-bounded 2D mesh simplification Image 1’, Computer-Aided Geometric Design, vol. 95, e102085, DOI:10.1016/j.cagd.2022.102085
Hoppe, H., DeRose, T., Duchamp, T., McDonald, J. & Stuetzle, W. 1993, ‘Mesh optimization’, Proceedings of the 20th Annual Conference on Computer Graphics and Interactive Techniques, pp. 19–26, DOI:10.1145/166117.166119
Hou, W., Zhang, X., Li, X., Lai, X. & Ding, M. 2013, ‘Poisson disk sampling in geodesic metric for DEM simplification’, International Journal of Applied Earth Observation and Geoinformation, vol. 23, pp. 264–72, DOI:10.1016/j.jag.2012.09.008
Ji, C., Li, Y., Fan, J. & Lan, S. 2019, ‘A Novel Simplification Method for 3D Geometric Point Cloud Based on the Importance of Point’, IEEE Access, vol. 7, pp. 129029-42.
Kumar, K., Ledoux, H., Commandeur, T.J.F. & Stoter, J.E. 2017, ‘Modelling urban noise in CITYGML ADE: case of the Netherlands’, ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences, pp. 73–81, DOI:10.5194/isprs-annals-IV-4-W5-73-2017
Lang, I., Manor, A. & Avidan, S. 2020, ‘Samplenet: differentiable point cloud sampling’, Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 7578–88.
Lehner, H. & Dorffner, L. 2020, ‘Digital geoTwin Vienna: Towards a Digital Twin City as Geodata Hub’, PFG – Journal of Photogrammetry Remote Sensing and Geoinformation Science, vol. 88, pp. 63–75, DOI:10.1007/s41064-020-00101-4
Lv, C., Lin, W. & Zhao, B. 2021, ‘Approximate Intrinsic Voxel Structure for Point Cloud Simplification’, IEEE Transactions on Image Processing, vol. 30, pp. 7241–55.
Mandelbroi, B.B. 1975, The Fractal Geometry of Nature, WH Freeman and Company, New York.
Neuville, R., Pouliot, J., Poux, F., De Ridder, L. & Billen, R. 2018, ‘A Formalized 3D Geovisualization Illustrated to Selectivity Purpose of Virtual 3D City Model’, ISPRS International Journal of Geo-Information, vol. 7, no. 194, pp. 1–24, DOI:10.3390/ijgi7050194
Nikoohemat, S., Diakité, A.A., Zlatanova, S. & Vosselman, G. 2020, ‘Indoor 3D reconstruction from point clouds for optimal routing in complex buildings to support disaster management’, Automation in Construction, vol. 113, e103109, DOI:10.1016/j.autcon.2020.103109
Pauly, M., Gross, M. & Kobbelt, L.P. 2002, ‘Efficient simplification of point-sampled surfaces’, IEEE Visualization, pp. 1–8.
Rodríguez-Cuenca, B., García-Cortés, S., Ordóñez, C. & Alonso, M.C. 2015, ‘A study of the roughness and curvature in 3D point clouds to extract vertical and horizontal surfaces’, IEEE International Geoscience and Remote Sensing Symposium (IGARSS) 2015, Milan, pp. 4602–05, DOI:10.1109/IGARSS.2015.7326853
Rusu, R.B., Blodow, N. & Beetz, M. 2009, ‘Fast Point Feature Histograms (FPFH) for 3D registration’, IEEE International Conference on Robotics and Automation 2009, pp. 3212–17.
Rusu, R. & Cousins, S. 2011, ‘3D is here: Point Cloud Library (PCL)’, IEEE International Conference on Robotics and Automation 2011 (ICRA 2011), Shangai, China, pp. 1–4, DOI:10.1109/ICRA.2011.5980567
Sester, M. 2020, ‘Cartographic generalization’, Journal of Spatial Information Science, vol. 21, pp. 5–11, DOI:10.5311/JOSIS.2020.21.716
Xu, Y., Tong, X. & Stilla, U. 2021, ‘Voxel-based representation of 3D point clouds: methods, applications, and its potential use in the construction industry’, Automation in Construction, vol. 126, e103675, DOI:10.1016/j.autcon.2021.103675
Zhou, Q.-Y., Park, J. & Koltun, V. 2018, ‘Open3D: A Modern Library for 3D Data Processing’, ArXiv, viewed 26 January 2022, <https://arxiv.org/abs/1801.09847>.
Zou, B., Qiu, H. & Lu, Y. 2020, ‘Point Cloud Reduction and Denoising Based on Optimized Downsampling and Bilateral Filtering’, IEEE Access, vol. 8, pp. 136316–26.
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