Abstract
This paper addresses the issue of visualizing the right information among large data sets by proposing to represent raw data as a set of mathematically-based implicit curves. Implicit curves are proving to be a powerful yet underused tool. The methodology we propose not only allows a more relevant visualization of information, but also a faster and efficient access to it: (1) since curves are extracted and compressed during precomputation, real-time rendering is possible on the end-user’s computer, even for very large datasets; (2) this property can be extended by enabling real-time data access and transfer at the server level – i.e. simultaneously saving local storage costs and increasing raw data security. Our proposal also achieved a high compression ratio (3%) while maintaining the visual significance of the data and reducing discrete artifacts such as curve gaps and pixel aliasing. We based our tests using two-dimensional height maps, but extending it to more dimensions is not a problem since we can consider any two-dimensional slice in these data.
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Notes
- 1.
Where the compression rate is defined as explained in Sect. 2.3.
- 2.
The notation \([\![a,b]\!]\) denotes the closed integer interval from a to b.
- 3.
For simplification purpose we suppose that values of V are equidistant, which is true in our case since \(I = [\![0,255]\!]\).
References
Cai, C., Harrington, P.D.B., Davis, D.M.: Two-dimensional Fourier compression. Anal. Chem. 69(20), 4249–4255 (1997)
Catmull, E., Rom, R.: A class of local interpolating splines. In: Barnhill, R.E., Riesenfeld, R.F. (eds.) Computer Aided Geometric Design, pp. 317–326. Academic Press (1974). https://www.sciencedirect.com/science/article/pii/B9780120790500500205
Chalupa, D., Balaghan, P., Hawick, K.A., Gordon, N.A.: Computational methods for finding long simple cycles in complex networks. Know.-Based Syst. 125(C), 96–107 (2017)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. The MIT Press, Cambridge (2009)
Da Costa, J., Germain, C., Baylou, P.: Level curve tracking algorithm for textural feature extraction. In: Proceedings 15th International Conference on Pattern Recognition. ICPR-2000, vol. 3, pp. 909–912 (2000)
Dacorogna, B., Tanteri, C.: Advanced analysis for engineers. (Analyse avancée pour ingénieurs.). Enseignement des Mathématiques (PPUR), Presses Polytechniques et Universitaires Romandes, Lausanne (2002)
Debled-Rennesson, I., Jean-Luc, R., Rouyer-Degli, J.: Segmentation of discrete curves into fuzzy segments. Electron. Not. Discrete Mathem. 12, 372–383 (2003). 9th International Workshop on Combinatorial Image Analysis
Debled-Rennesson, I., Reveilles, J.P.: A linear algorithm for segmentation of digital curves. IJPRAI 9, 635–662 (1995)
Freeman, H.: On the encoding of arbitrary geometric configurations. IRE Trans. Electron. Comput. EC–10(2), 260–268 (1961)
Marty, M., et al.: Real-time renderings of multidimensional massive datacubes on jupyter notebook (2022)
Seidel, R.: A simple and fast incremental randomized algorithm for computing trapezoidal decompositions and for triangulating polygons. Comput. Geom. 1(1), 51–64 (1991)
Shannon, C.: Communication in the presence of noise. Proc. IRE 37(1), 10–21 (1949)
Yuksel, C., Schaefer, S., Keyser, J.: Parameterization and applications of catmull-rom curves. Comput. Aided Des. 43(7), 747–755 (2011). the 2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Acknowledgements
This work was supported by the Swiss Space Office/SEFRI, grant number ‘REF-1131-61001’ as a part of the Enhanced Data Cube Visualisation for Earth Observation project relative to the tasks planned with the European Space Agency (ESA). We would like to thank the seven members of the data scientist advisory group from the Gisat, ViTO, TU Wien, EURAC, Terrasigan, NASA, and ESA institutes for their support and advice. Special thanks are also due to Gutierrez Montserrat for the precious English review of the manuscript.
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Marty, M. et al. (2023). Implicit Curves: From Discrete Extraction to Applied Formalism. In: Cheng, LY. (eds) ICGG 2022 - Proceedings of the 20th International Conference on Geometry and Graphics. ICGG 2022. Lecture Notes on Data Engineering and Communications Technologies, vol 146. Springer, Cham. https://doi.org/10.1007/978-3-031-13588-0_62
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