Fawaz Hjouj
ABSTRACT
We consider the two-dimensional parallel beam Tomography problem in which both the object being imaged and the projection directions are unknown. Specifically: Given unsorted set of Radon projections that correspond to angles φj=0°, 1°, ..., 179°. Our main goal is to determine (align) the projections with their angles.
We introduce a type of Local Radon Transform from which we propose a distance formula between any two Radon projections. We solve the problem by combining the second order Geometric Moments of these projections together with this measure of distance. We validate our framework on synthetic images and real images.
- Deans S.R (1983). The Radon Transform and Some of Its Applications, John Wiley& Sons, Inc. New York, USA, 1983.Google Scholar
- E. Malhotra et al. Tomographic reconstruction from projections with unknown view angles exploiting moment-based relationships. (ICIP).IEEE, 2016, 1759--1763. https: //doi.org/10.1109/ICIP.2016.7532660Google Scholar
- S. Basu and Y. Bresler. Uniqueness of tomography with unknown view angles. IEEE Trans. Image Process. 2000, vol. 9, no.6, 094--1106Google Scholar
- S.Basuand Y.Bresler,"Feasibility of tomography with unknown view angles, IEEE Trans. Image Process 2000, vol.9, no. 6, 1107--1122,Google Scholar
- M.-S. Phan, E. Baudrier, L. Mazo, and M. Tajine, "Angular difference measure between tomographic projections taken at unknown directions in 2d," IEEE International Conference on Image Processing (ICIP), 2014, pp. 1738--1742Google ScholarCross Ref
- R. Coifman, Y. Shkolnisky, F. Sigworth, and A. Singer. Graph laplacian tomography from unknown random projections. IEEE Transactions on Image Processing 2008, 17, 10 (2008), 1891--1899,Google Scholar
- A. Singer and H.Wu. Two-dimensional tomography from noisy projections taken at unknown random directions. SIAM J Imaging 2013, Sc, 6(1):136--175Google Scholar
- D. B. Salzman, "A method of general moments for orienting 2D projections of unknown 3D objects," Computer Vision Graph 1990, vol. 50, no. 2, pp. 129--156Google Scholar
- M. Krause, J.-M. Hausherr, and W. Krenkel, "(micro)-crack detection using local radon transform," Materials Science and Engineering 2010, vol. 527, no. 26, pp. 7126--7131Google Scholar
- R. Pourreza, T. Banaee, H. Pourreza, and R. D. Kakhki, "A radon transform based approach for extraction of blood vessels in conjunctival images. in Mexican International Conference on Artificial Intelligence. Springer, 2008, 948--956Google ScholarDigital Library
- Hjouj F, Kammler DW. Identification of reflected, scaled, translated, and rotated objects from their Radon projections. IEEE Trans Image Process 2008, 17(3):301--10.Google Scholar
- Hjouj F. Linear Transformation Recognition Using Radon Transform. Journal of Mathematical Sciences & Computer Applications 2011, 1 (2): 40--47. doi: 10.5147/0038.Google Scholar
Index Terms
- Towards Tomography with Random Orientation
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