Scale Invariance in Projection Selection Using Binary Tomography

• Autorzy: Lékó Gábor , Balázs Péter

Identyfikatory

DOI

10.3233/FI-2020-1897

• Języki publikacji: EN

Abstrakty

EN

In this paper, we propose two strategies of reducing the amount of data needed for binary tomographic reconstructions. We study how the direction dependency changes by reducing the resolution of an image and we point out how to specify the most informative angles for the original image using its downscaled version. We also show how to predict the final acceptable resolution. Applications of the proposed strategies are also mentioned.

Słowa kluczowe

EN

binary tomography; direction dependency; informative angles; projection selection; reconstruction; resolution invariance; scale-invariance

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2020
• Tom: Vol. 172, nr 2
• Strony: 129--142
• Opis fizyczny: Bibliogr. 26 poz., rys., tab., wykr.

Twórcy

autor

Lékó Gábor

• Department of Image Processing and Computer Graphics, University of Szeged, Arpád tér 2. H-6720, Szeged, Hungary

autor

Balázs Péter

• Department of Image Processing and Computer Graphics, University of Szeged, Arpád tér 2. H-6720, Szeged, Hungary

Bibliografia

• [1] Herman GT. Fundamentals of Computerized Tomography: Image Reconstruction from Projections. Springer, 2nd edition, 2009. doi:10.1007/978-1-84628-723-7.
• [2] Kak AC, Slaney M. Principles of Computerized Tomographic Imaging. IEEE Press, New York, 1988.
• [3] Herman GT, Kuba A. Discrete Tomography: Foundations, Algorithms, and Applications. Birkhäuser Basel, 1999. doi:10.1007/978-1-4612-1568-4.
• [4] Herman GT, Kuba A. Advances in Discrete Tomography and Its Applications. Birkhäuser Basel, 2007.
• [5] Nagy A, Kuba A. Reconstruction of binary matrices from fan-beam projections. Acta Cybernetica, 2005. 17(2):359-385. URL http://cyber.bibl.u-szeged.hu/index.php/actcybern/article/view/3672.
• [6] Varga L, Balázs P, Nagy A. Direction-dependency of binary tomographic reconstruction algorithms. Computational Modeling in Imaging Sciences. Graphical Models, 2011. 73(6):365-375. URL https://doi.org/10.1016/j.gmod.2011.06.006.
• [7] Gardner RJ. Geometric Tomography. Encyclopedia of Mathematics and its Applications. Cambridge University Press, 2 edition, 2006. doi:10.1017/CBO9781107341029.
• [8] Gardner RJ, Gritzmann P. Discrete Tomography: Determination of Finite Sets by X-Rays. Transactions of the American Mathematical Society, 1997. 379:2271-2295. URL https://www.jstor.org/stable/2155510.
• [9] Gardner RJ, Gritzmann P. Uniqueness and Complexity in Discrete Tomography. Chapter 4 of [3]. 1999 pp 85-113. doi:10.1007/978-1-4612-1568-4_4.
• [10] Haque MA, Ahmad MO, Swamy MNS, Hasan MK, Lee SY. Adaptive Projection Selection for Computed Tomography. IEEE Transactions on Image Processing, 2013. 22(12):5085-5095.
• [11] Dabravolski A, Batenburg K, Sijbers J. Dynamic angle selection in X-ray computed tomography. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 2014. 324:17-24. URL https://doi.org/10.1016/j.nimb.2013.08.077.
• [12] Bang TQ, Jeon I. CT Reconstruction from a Limited Number of X-Ray Projections. World Academy of Science, Engineering and Technology, International Journal of Mechanical and Mechatronics Engineering, 2011. 5(10):2038-2040. ISNI-0000000091950263.
• [13] Batenburg KJ, Palenstijn WJ, Balázs P, Sijbers J. Dynamic angle selection in binary tomography. Computer Vision and Image Understanding, 2013. 117(4):306-318. URL https://doi.org/10.1016/j.cviu.2012.07.005.
• [14] Varga L, Balázs P, Nagy A. Projection Selection Algorithms for Discrete Tomography. In: Lecture Notes in Computer Science, volume 6474. Springer, 2010 pp. 390-401. doi:10.1007/978-3-642-17688-3_37.
• [15] Lékó G, Balázs P. Sequential Projection Selection Methods for Binary Tomography. In: Lecture Notes in Computer Science, volume 10986. Springer, 2018 pp. 1-12. (Under publishing).
• [16] Presenti A, Sijbers J, den Dekker AJ, Beenhouwer JD. CAD-based defect inspection with optimal view angle selection based on polychromatic X-ray projection images. In: 9th Conference on Industrial Computed Tomography, Padova, Italy. 2019 pp. 1-5. URL https://hdl.handle.net/10067/1578340151162165141.
• [17] Alpers A, Gritzmann P. On double-resolution imaging and discrete tomography. SIAM Journal of Discrete Mathematics, 2018. 32(2):1369-1399. doi:10.1137/17M1115629.
• [18] Gardner RJ, Gritzmann P, Prangenberg D. On the computational complexity of reconstructing lattice sets from their X-rays. Discrete Mathematics, 1999. 202(1-3):45-71. URL https://doi.org/10.1016/S0012-365X(98)00347-1.
• [19] Burt PJ, Adelson EH. The Laplacian Pyramid as a Compact Image Code. IEEE Transactions on Communications, 1983. COM-31(4):532-540. doi:10.1109/TCOM.1983.1095851.
• [20] Wall BF, Kendall GM, Edwards AA, Bouffler S, Muirhead CR, Meara JR. What are the risks from medical X-rays and other low dose radiation? The British Journal of Radiology, 2006. 79(940):285-294. doi:10.1259/bjr/55733882.
• [21] Kalra MK, Maher MM, Toth TL, Hamberg LM, Blake MA, Shepard J, Saini S. Strategies for CT Radiation Dose Optimization. Radiology, 2004. 230(3):619-628. doi:10.1148/radiol.2303021726.
• [22] Gray SB. Local Properties of Binary Images in Two Dimensions. IEEE Transactions on Computers, 1971. C-20(5):551-561. doi:10.1109/T-C.1971.223289.
• [23] Prokop RJ, Reeves AP. A survey of moment-based techniques for unoccluded object representation and recognition. CVGIP: Graphical Models and Image Processing, 1992. 54(5):438-460. URL https://doi.org/10.1016/1049-9652(92)90027-U.
• [24] Wang Z, Bovik AC. A universal image quality index. IEEE Signal Processing Letters, 2002. 9(3):81-84. doi:10.1109/97.995823.
• [25] Balázs P, Brunetti S. A measure of Q-convexity. In: Lecture Notes in Computer Science, volume 9647. Springer, 2016 pp. 219-230. doi:10.1007/978-3-319-32360-2_17.
• [26] Watson A. Perimetric Complexity of Binary Digital Images. The Mathematica Journal, 2012. 14. doi:10.3888/tmj.14-5.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).