A New Approach for the Reconstruction of Object-Based Images in Discrete Tomography

• Autorzy: Brocchi S.

Identyfikatory

DOI

10.3233/FI-2014-1111

• Języki publikacji: EN

Abstrakty

EN

In this paper we tackle the problem of the reconstruction of object based images, specifically formed by a set of circles inside a ring. By analyzing the projections of the image, we are able to determine some coordinates corresponding to interest points that give significant information about features of the image of aid in the reconstruction. Our approach yields promising results in comparison to other methods in literature. Finally, we discuss how a similar approach could be extended to more complex problems deriving from tomographic applications, in order to develop an efficient method exploiting the prior knowledge assumed on an image.

Słowa kluczowe

EN

image reconstruction; discrete tomography; ring theory; information theory; computational complexity; coordinates

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2014
• Tom: Vol. 135, nr 1/2
• Strony: 43--57
• Opis fizyczny: Bibliogr. 21 poz., rys., tab., wykr.

Twórcy

autor

Brocchi S.

• Dipartimento di Matematica e Informatica ’U. Dini’, Università degli Studi di Firenze, Viale Morgagni 65, 50134 Firenze, Italy

Bibliografia

• [1] P. Balazs, M. Gara, An Evolutionary Approach for Object-Based Image Reconstruction Using Learnt Priors, SCIA 2009, Lecture Notes in Computer Science, vol. 5575, pp. 520-529, 2009
• [2] E. Barcucci, S. Brlek, S. Brocchi, PCIF: an algorithm for lossless true color image compression, Proceedings of the 13th International Workshop on Combinatorial Image Analysis 2009, Lecture Notes in Computer Science, Vol. 5852, pp. 224-237, 2009
• [3] E. Barcucci, S. Brocchi, Solving multicolor discrete tomography problems by using prior knowledge, Fundamenta Informaticae, Vol. 125, pp. 313-328, 2013
• [4] E. Barcucci, S. Brocchi, A. Frosini, Solving the two color problem - An heuristic algorithm, Proceedings of the 14th International Workshop on Combinatorial Image Analysis, Lecture Notes in Computer Science, Vol. 6636, 2011
• [5] E. Barcucci, A. Del Lungo, M. Nivat, R. Pinzani, Reconstructing convex polyominoes from horizontal and vertical projections, Theoretical Computer Science, Vol. 155, pp. 321-347, 1996
• [6] K. J. Batenburg, J. Sijbers, DART: A Practical Reconstruction Algorithm for Discrete Tomography, IEEE Transactions on Image Processing vol. 20 (9), pp. 2542-2553, 2011
• [7] K. J. Batenburg, W. A. Kosters, A discrete tomography approach to Japanese puzzles, Proceedings of the 16th Belgium-Netherlands Conference on Artificial Intelligence (BNAIC), 2004
• [8] S. Brocchi, An Object-Based Tomographic Reconstruction Algorithm Exploiting Interest Points in Image Projections, 8th International Symposium on Image and Signal Processing and Analysis (ISPA 2013), Proceedings, 2013
• [9] S. Brocchi, A. Frosini, C. Picouleau, Reconstruction of binary matrices under fixed size neighborhood constraints, Theoretical Computer Science, Vol. 406, pp. 43-54, 2008
• [10] S. Brunetti, A. Del Lungo, F. Del Ristoro, A. Kuba, M. Nivat, Reconstruction of 4- and 8-connected convex discrete sets from row and column projections, Linear Algebra and its Applications, Vol. 339, pp. 37-57, 2001
• [11] C. Dürr, E. Goles Ch., I. Rapaport, E. Remila, Tiling with bars under tomographic constraints, Theoretical Computer Science, vol. 290(3), pp. 1317-1329, 2003
• [12] C. Dürr, F. Guiñez, M. Matamala, Reconstructing 3-Colored Grids from Horizontal and Vertical Projections is NP-Hard, A Solution to the 2-Atom Problem in Discrete Tomography, SIAM J. Discrete Math. 26(1), pp. 330-352, 2012
• [13] R.J. Gardner, P. Gritzmann, D. Pranenberg, On the computational complexity of reconstructing lattice sets from their X-rays, Discrete Mathematics Vol. 202, Issues 1-3, pp. 45-71, May 1999
• [14] N. Hantos, P. Balazs, A Uniqueness Result for Reconstructing hv-Convex Polyominoes From Horizontal and Vertical Projections and Morphological Skeleton, 8th International Symposium on Image and Signal Processing and Analysis (ISPA 2013), Proceedings, 2013
• [15] N. Hantos, P. Balazs, K. Palagyi, Binary Image Reconstruction From Two Projections and Skeletal Information, Proceedings of IWCIA 2012, Lecture Notes in Computer Science, vol. 7655, pp 263-273, 2012
• [16] G. Herman, A. Kuba, Discrete tomography: foundations, algorithms, and applications, Springer, 1999
• [17] G. Herman, A. Kuba, Advances in discrete tomography and its applications, Birkhauser, Boston, 2007
• [18] Z. Kiss, L. Rodek, A. Kuba, Image reconstruction and correction methods in neutron and X-ray tomography, Acta Cybernetica, vol 17 (3), 2006
• [19] A. Kuba, L. Rodek, Z. Kiss, L. Ruskó, A. Nagy, M. Balaskó, Discrete tomography in neutron radiography, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol 542(1), pp. 376-382, 2005
• [20] C. Picouleau, S. Brunetti, A. Frosini, Reconstructing a binary matrix under timetabling constraints, Electronic Notes in Discrete Mathematics, vol. 20, pp. 99-112, 2005
• [21] H. J. Ryser, Combinatorial properties of matrices of zeros and ones, Canadian Journal of Mathematics, Vol. 9, pp. 371-377, 1957