Abstract
In binary tomography, several algorithms are known for reconstructing binary images having some geometrical properties from their projections. In order to choose the appropriate reconstruction algorithm it is necessary to have a priori information of the image to be reconstructed. In this way we can improve the speed and reduce the ambiguity of the reconstruction. Our work is concerned with the problem of retrieving geometrical information from the projections themselves. We investigate whether it is possible to determine geometric features of binary images if only their projections are known. Most of the reconstruction algorithms based on geometrical information suppose hv-convexity or connectedness about the image to be reconstructed. We investigate those properties in detail, and also the task of separating 4- and 8-connected images. We suggest decision trees for the classification, and show some preliminary experimental results of applying them for the class of hv-convex and connected discrete sets.
This work was supported by OTKA grant T048476.
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References
Alpers, A., Brunetti, S.: Stability results for the reconstruction of binary pictures from two projections. Image and Vision Comp. 25, 1599–1608 (2007)
Balázs, P., Balogh, E., Kuba, A.: Reconstruction of 8-connected but not 4-connected hv-convex discrete sets. Disc. Appl. Math. 147, 149–168 (2005)
Balogh, E., Kuba, A., Dévényi, C., Del Lungo, A.: Comparison of algorithms for reconstructing hv-convex discrete sets. Lin. Alg. Appl. 339, 23–35 (2001)
Barcucci, E., Del Lungo, A., Nivat, M., Pinzani, R.: Reconstructing convex polyominoes from horizontal and vertical projections. Theor. Comput. Sci. 155, 321–347 (1996)
Barcucci, E., Del Lungo, A., Nivat, M., Pinzani, R.: Medians of polyominoes: A property for the reconstruction. Int. J. Imaging Systems and Techn. 9, 69–77 (1998)
Brunetti, S., Daurat, A.: An algorithm reconstructing convex lattice sets. Theor. Comput. Sci. 304, 35–57 (2003)
Brunetti, S., Del Lungo, A., Del Ristoro, F., Kuba, A., Nivat, M.: Reconstruction of 4- and 8-connected convex discrete sets from row and column projections. Lin. Alg. Appl. 339, 37–57 (2001)
Chrobak, M., Dürr, C.: Reconstructing hv-convex polyominoes from orthogonal projections. Inform. Process. Lett. 69(6), 283–289 (1999)
Herman, G.T., Kuba, A. (eds.): Discrete Tomography: Foundations, Algorithms and Applications. Birkhäuser, Boston (1999)
Herman, G.T., Kuba, A. (eds.): Advances in Discrete Tomography and its Applications. Birkhäuser, Boston (2007)
Kuba, A.: The reconstruction of two-directionally connected binary patterns from their two orthogonal projections. Comp. Vision, Graphics, and Image Proc. 27, 249–265 (1984)
Kuba, A.: Reconstruction in different classes of 2D discrete sets. In: Bertrand, G., Couprie, M., Perroton, L. (eds.) DGCI 1999. LNCS, vol. 1568, pp. 153–163. Springer, Heidelberg (1999)
Kuba, A., Balogh, E.: Reconstruction of convex 2D discrete sets in polynomial time. Theor. Comput. Sci. 283, 223–242 (2002)
Kuba, A., Nagy, A., Balogh, E.: Reconstruction of hv-convex binary matrices from their absorbed projections. Disc. Appl. Math. 139, 137–148 (2004)
Mitchell, T.M.: Machine Learning. McGraw-Hill, New York (1997)
Somol, P., Pudil, P., Nonovičová, J., Paclík, P.: Adaptive floating search methods in feature selection. Pattern Recog. Lett. 20, 1157–1163 (1999)
Quinlan, J.R.: C4.5: Programs for Machine Learning. Morgan Kaufmann, San Francisco (1993)
Weber, S., Schüle, T., Hornegger, J., Schnörr, C.: Binary tomography by iterating linear programs from noisy projections. In: Klette, R., Žunić, J. (eds.) IWCIA 2004. LNCS, vol. 3322, pp. 38–51. Springer, Heidelberg (2004)
Weber, S., Schüle, T., Kuba, A., Schnörr, C.: Binary tomography with deblurring. In: Reulke, R., Eckardt, U., Flach, B., Knauer, U., Polthier, K. (eds.) IWCIA 2006. LNCS, vol. 4040, pp. 375–388. Springer, Heidelberg (2006)
Woeginger, G.W.: The reconstruction of polyominoes from their orthogonal projections. Inform. Process. Lett. 77, 225–229 (2001)
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Balázs, P., Gara, M. (2008). Decision Trees in Binary Tomography for Supporting the Reconstruction of hv-Convex Connected Images. In: Blanc-Talon, J., Bourennane, S., Philips, W., Popescu, D., Scheunders, P. (eds) Advanced Concepts for Intelligent Vision Systems. ACIVS 2008. Lecture Notes in Computer Science, vol 5259. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88458-3_39
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DOI: https://doi.org/10.1007/978-3-540-88458-3_39
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