Hurwitz-Radon operator in monochromatic medical image reconstruction

• Autorzy: Jakóbczak D. , Kosiński W.
• Języki publikacji: EN

Abstrakty

EN

In this paper the method, dedicated for medical images reconstruction, will be presented. One of them called the method of the Hurwitz-monochromatic (e.g. black and white) images. The method is based on a family of Hurwitz-Radon matrices. The matrices possess columns composed of orthonormal vectors. The operator of Hurwitz-Radon (OHR), built from that matrices, is described. It is shown how to create the orthogonal and discrete OHR and how to use it in a process of curve interpolation. The method needs suitable choice of nodes, i.e. points of the curve to be compressed: they should be equidistance in one of coordinates. Application of MHR gives a high level of compression (up to 99 %) and a very good interpolation accuracy in the process of reconstruction of contours. Its use in the computer tomography is also effective. Orthogonal OHR can be regarded as a linear and discrete model in the supervised (machine) learning [5]. It is shown how to use it in approximation of data. Created from the family of N-1 HR matrices and completed with the identical matrix, system of matrices is orthogonal only for vector spaces of dimensions N=2,4,8. Orthogonality of columns and rows is very important and significant for stability and high precision of calculations.

Słowa kluczowe

EN

compression; Hurwitz-Radon matrix; contour; curve reconstruction; tomography

PL

kompresja; macierze Hurwitza-Radona; kontur; rekonstrukcja krzywej; tomografia

• Wydawca: University of Silesia, Institute of Informatics, Computer Systems Department
• Czasopismo: Journal of Medical Informatics & Technologies
• Rocznik: 2007
• Tom: Vol. 11
• Strony: 69--78
• Opis fizyczny: Bibliogr. 11 poz., rys., tab.

Twórcy

autor

Jakóbczak D.

• Chair of Computer Science and Management, Koszalin Technological University, Koszalin, Poland

autor

Kosiński W.

Bibliografia

• [1] R. CIERNIAK, Tomografia komputerowa. Budowa urządzeń CT. Algorytmy rekonstrukcyjne. Wydawnictwo EXIT, Warszawa 2005.
• [2] B. ECKMANN, “Topology, algebra, analysis- relations and missing links”, Notices of AMS, vol. 46(5), pp. 520-527, 1999.
• [3] P. KICIAK, Podstawy modelowania krzywych i powierzchni. Zastosowania w grafice komputerowej. WNT, Warszawa 2005.
• [4] J. MARKER, I. BRAUDE, K. MUSETH and D. BREEN, “Contour-Based Surface Reconstruction using Implicit Curve Fitting, and Distance Field Filtering and Interpolation”, Volume Graphics 2006, pp. 1-9, 2006.
• [5] T. POGGIO, S. SMALE, “The Mathematics of Learning: Dealing with Data”, Notices of the American Mathematical Society, vol. 50(5), pp. 537-544, 2003.
• [6] A. PRZELASKOWSKI, Kompresja danych. Podstawy. Metody bezstratne. Kodery obrazów. Wydawnictwo BTC, 2005.
• [7] W. SIEŃKO, W. CITKO, D. JAKÓBCZAK, “Learning and system modeling via Hamiltonian neural networks” in: Artificial Intelligence and Soft Computing - ICAISC 2004, 7th Int. Conference, Zakopane, Poland, June 2004,
• [8] RUTKOWSKI L., SIEKMANN J., TADEUSIEWICZ R., ZADEH A., (Eds.), Lecture Notes on Artificial Intelligence, vol. 3070, , Springer-Verlag, Berlin, Heidelberg, pp. 266-271, 2004.
• [9] R. STAROPOLSKI, „Przegląd metod bezstratnej kompresji obrazów medycznych”, Studia Informatica, vol. 2(58), pp. 49-66, 2004.
• [10] G. TATOŃ, E. ROKITA, M. SIERŻĘGA, S. KŁĘK, J. KULIG, A. URBANIK, „Oprogramowanie do rekonstrukcji i analizy 3D obrazów diagnostycznych”, Polish Journal of Radiology, vol. 70(3), pp. 64-72, 2005.
• [11] D. JAKÓBCZAK, Zastosowanie dyskretnego, ortogonalnego operatora Hurwitza-Radona w kompresji i rekonstrukcji konturów obrazów monochromatycznych, Praca doktorska, PJWSTK, Warszawa, listopad 2006.