Implementation of variational level set methods and Chan-Vese model in electrical impedance tomography

• Autorzy: Rymarczyk T. , Filipowicz S. F. , Sikora J.
• Konferencja: Computer Applications in Electrical Engineering 2010 [Poznań, April 19-21, 2010]
• Języki publikacji: EN

Abstrakty

EN

The problem of the image reconstruction in Electrical Impedance Tomography (EIT) is a highly ill-posed inverse problem. The Chan-Vese method is an established model for numerical problems. In contrast to the traditional level set method, interfaces between the subdomains are represented as discontinuities in the level set function. Moreover, no more than one function is needed to represent any numbers of phases. The iterative algorithms are based a combination of the finite element method, level set methods, variational level set methods and Chan-Vese model.

Słowa kluczowe

EN

electrical impedance tomography; EIT; Chan-Vese model; iterative algorithm

PL

tomografia impedancyjna; algorytm iteracyjny; model Chana-Vese

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Poznan University of Technology Academic Journals. Electrical Engineering
• Rocznik: 2010
• Tom: No. 63
• Strony: 51--61
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Rymarczyk T.

autor

Filipowicz S. F.

autor

Sikora J.

• Electrical Engineering Institute

Bibliografia

• [1] Chan T. and Vese L., “Active contours without edges”, IEEE Trans. Imag. Proc., vol. 10, pp. 266-277, 2001.
• [2] Filipowicz S.F., Rymarczyk T.: Tomografia impedancyjna, pomiary, konstrukcje i metody tworzenia obrazu. BelStudio, Warsaw 2003.
• [3] Li C., Xu C., Gui C., and M. D. Fox., “Level set evolution without re-initialization: A new variational formulation”, In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), volume 1, pages 430-436, 2005.
• [4] Mumford D., Shah J.: Optimal approximation by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math., (42):577-685, 1989.
• [5] Osher S., Fedkiw R.: Level Set Methods and Dynamic Implicit Surfaces. Springer, New York 2003.
• [6] Osher S., Sethian J.A.: Fronts Propagating with Curvature Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations. J. Comput. Phys. 79, 12-49, 1988.
• [7] Osher, S., Fedkiw, R.: Level Set Methods: An Overview and Some Recent Results. J. Comput. Phys. 169, 463-502, 2001.
• [8] Osher S., Santosa F.: Level set methods for optimization problems involving geometry and constraints. Frequencies of a two-density inhomogeneous drum. Journal of Computational Physics, 171, pp. 272-288, 2001.
• [9] Rymarczyk T., Filipowicz S.F., Sikora J.: Level set methods for an inverse problem in electrical impedance tomography. 5th International Symposium on Process Tomography In Poland, Zakopane, 2008.
• [10] Sethian J.A.: Level Set Methods and Fast Marching Methods. Cambridge Univeristy Press 1999.
• [11] Sikora J.: Algorytmy numeryczne w tomografii impedancyjnej i wiroprądowej. WPW, Warszawa, 2000.
• [12] Sikora J.: Podstawy metody elementów skończonych. Instytut Elektrotechniki, Warszawa, 2008.
• [13] Tai C., Chung E., Chan T.: Electrical impedance tomography using level set representation and total variational regularization. Journal of Computational Physics, vol. 205, no. 1, pp. 357-372, 2005.
• [14] Vese L., Chan T.: A new multiphase level set framework for image segmentation via the Mumford and Shah model. CAM Report 01-25, UCLA Math. Dept., 2001.