Abstract
In indoor and outdoor navigation, finding the local position of a sphere in mapping space employing a laser scanning technique with low-cost sensors is a very challenging and daunting task. In this contribution, we illustrate how Gröbner basis techniques can be used to solve polynomial equations arising when algebraic and geometric measures for the error are used. The effectiveness of the suggested method is demonstrated, thanks to standard CAS software like Mathematica, using numerical examples of the real world.
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References
Franaszek, M., Cheok, G.S., Saidi, K.S., Witzgall, C.: Fitting spheres to range data from 3-D imaging systems. IEEE Trans. Instrum. Measur. 58(10), 3544–3553 (2009)
Józków, G., Thoth, C., Koppanyi, Z., Grejner - Brzezinska, D.: Combined matching of 2D and 3D kinect data to support indoor mapping and navigation. In: ASPRS 2014 Annual Conference, Luisville, Kentucky, USA, 23–28 March 2014
Ogundana, O., Coggrave, C., Burguete, R.L., Huntley, J.M.: Fast hough transform for automated detection of spheres in three-dimensional point clouds. Opt. Eng. 0001 46(5), 051002–051002-11 (2007)
Zhou, Z., Guan, Y., Zhan, X., Lu, T.: Robust algorithm for fitting Sphere to 3D point clouds in terrestrial laser scanning. In: The International Archives of Photogrammetry and Spatial Information Science, vol. XXXVII Part B5, Beijing, pp. 519–522 (2008)
Molnár, B., Toth, C.K., Detrekõi, A.: Accuracy test of microsoft kinect for human morphological measurements. In: International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, vol. XXXIX - B3, 2012 XXII ISPRS Congress, Melbourne, Australia, 25 August – 01 September 2012
Awange, J., Palancz, B., Lewis, R.H., Völgyesi, L.: Mathematical Geosciences. Springer, Heidelberg (2018)
DalleMole, V.L., do Rego, R.L.M.E., Araujo, A.F.R.: The self - organizing approach for surface reconstruction from unstructured point clouds. In: Matsopoulos, G.K. (ed.) Self-Organizing Maps, INTECH, pp. 167–188. Rijeka, Croatia (2010)
Sjoberg, J.: Neural Networks 1.2, Mathematica Adds On (2018). https://www.wolfram.com/products/applications/neuralnetworks/
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Lewis, R., Paláncz, B., Awange, J. (2018). Fitting a Sphere via Gröbner Basis. In: Davenport, J., Kauers, M., Labahn, G., Urban, J. (eds) Mathematical Software – ICMS 2018. ICMS 2018. Lecture Notes in Computer Science(), vol 10931. Springer, Cham. https://doi.org/10.1007/978-3-319-96418-8_38
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DOI: https://doi.org/10.1007/978-3-319-96418-8_38
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