Mathematical methods for geometry reconstruction and shape analysis
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- Matematisk institutt [3782]
Abstract
The last decades have witnessed an exponential growth in the amounts of data that are collected, stored, and shared worldwide daily. In many scientific disciplines, information consists of a set of sample points describing some phenomena. A natural question deals with geometry reconstruction, i.e., the recovery of shape through some representations. Approximation theory has traditionally focused on the case of data points sampled from smooth curves and surfaces; however, in most real-world scenarios, data is affected by noise and potentially other imperfections. To analyse and compare data automatically, shape descriptions are often preferred to representations: despite the latter being more complete than the former, they do not necessarily disclose any high-level information useful to discriminate between shapes. This thesis addresses a range of problems in geometry reconstruction and shape analysis, motivated in the light of real-world applications, including the need to identify geometric relationships in mechanical engineering, the approximation of noisy point clouds in life and earth sciences and the recognition of proteins from an ensemble of geometries in structural biology.List of papers
Paper I. Andrea Raffo, Oliver J. D. Barrowclough and Georg Muntingh. “Reverse engineering of CAD models via clustering and approximate implicitization”. In: Computer Aided Geometric Design. Vol. 80, (2020), DOI: 10.1016/j.cagd.2020.101876. The article is included in the thesis. Also available at: https://doi.org/10.1016/j.cagd.2020.101876 |
Paper II. Andrea Raffo and Silvia Biasotti. “Weighted quasi-interpolant spline approximations: Properties and applications”. In: Numerical Algorithms. Vol. 87, (2021), pp. 819–847. DOI: 10.1007/s11075-020-00989-4. The article is included in the thesis. Also available at: https://doi.org/10.1007/s11075-020-00989-4 |
Paper III. Andrea Raffo and Silvia Biasotti. “Data-driven quasi-interpolant spline surfaces for point cloud approximation”. In: Computers & Graphics. Vol. 89, (2020), pp. 144-155. DOI: 10.1016/j.cag.2020.05.004. The article is included in the thesis. Also available at: https://doi.org/10.1016/j.cag.2020.05.004 |
Paper IV. Chiara Romanengo, Andrea Raffo, Silvia Biasotti and Bianca Falcidieno. “Extraction of geometric primitives from 3D point clouds for CAD applications”. In: Computer-Aided Design, (2023), 103479. The paper is included in the thesis. The published version is available at: https://doi.org/10.1016/j.cad.2023.103479 |
Paper V. Chiara Romanengo, Andrea Raffo, Yifan Qie, Nabil Answer and Bianca Falcidieno. “Fit4CAD: A point cloud benchmark for fitting simple geometric primitives in CAD objects”. In: Computers & Graphics. Vol. 102, (2022), pp. 133–143. DOI: 10.1016/j.cag.2021.09.013. The article is included in the thesis. Also available at: https://doi.org/10.1016/j.cag.2021.09.013 |
Paper VI. Andrea Raffo, Ulderico Fugacci, Silvia Biasotti, Walter Rocchia, Yonghuai Liu, Ekpo Otu, Reyer Zwiggelaar, David Hunter, Evangelia I. Zacharaki, Eleftheria Psatha, Dimitrios Laskos, Gerasimos Arvanitis, Konstantinos Moustakas, Tunde Aderinwale, Charles Christoffer, Woong-Hee Shin, Daisuke Kihara, Andrea Giachetti, Huu-Nghia Nguyen, Tuan-Duy Nguyen, Vinh-Thuyen Nguyen-Truong, Danh Le-Thanh, Hai-Dang Nguyen and Minh-Triet Tran “SHREC 2021: Retrieval and classification of protein surfaces equipped with physical and chemical properties”. In: Computers & Graphics. Vol. 99, (2021), pp. 1–21. DOI: 110.1016/j.cag.2021.06.010. The article is included in the thesis. Also available at: https://doi.org/10.1016/j.cag.2021.06.010 |