TY - JOUR T1 - Algorithms, automata, complexity and games Preface JF - THEORETICAL COMPUTER SCIENCE Y1 - 2008 A1 - Joost K Batenburg A1 - Antal Nagy A1 - Maurice Nivat VL - 406 SN - 0304-3975 IS - 1-2 N1 - UT: 000260289400001doi: 10.1016/j.tcs.2008.07.010 JO - THEOR COMPUT SCI ER - TY - JOUR T1 - In Memoriam Attila Kuba (1953-2006) JF - THEORETICAL COMPUTER SCIENCE Y1 - 2008 A1 - Joost K Batenburg A1 - Antal Nagy A1 - Maurice Nivat CY - KUBA A, PUBLICATION LIST VL - 406 SN - 0304-3975 IS - 1-2 N1 - UT: 000260289400002doi: 10.1016/j.tcs.2008.07.011 JO - THEOR COMPUT SCI ER - TY - JOUR T1 - A sufficient condition for non-uniqueness in binary tomography with absorption JF - Theoretical Computer Science Y1 - 2005 A1 - Attila Kuba A1 - Maurice Nivat AB -

A new kind of discrete tomography problem is introduced: the reconstruction of discrete sets from their absorbed projections. A special case of this problem is discussed, namely, the uniqueness of the binary matrices with respect to their absorbed row and column sums when the absorption coefficient is n=log((1+5^0.5)/2). It is proved that if a binary matrix contains a special structure of 0s and 1s, called alternatively corner-connected component, then this binary matrix is non-unique with respect to its absorbed row and column sums. Since it has been proved in another paper [A. Kuba, M. Nivat, Reconstruction of discrete sets with absorption, Linear Algebra Appl. 339 (2001) 171–194] that this condition is also necessary, the existence of alternatively corner-connected component in a binary matrix gives a characterization of the non-uniqueness in this case of absorbed projections.

VL - 346 ER - TY - JOUR T1 - Reconstruction of 4- and 8-connected convex discrete sets from row and column projections JF - Linear Algebra and its Applications Y1 - 2001 A1 - Sara Brunetti A1 - Alberto DelLungo A1 - F. DelRistoro A1 - Attila Kuba A1 - Maurice Nivat AB -

In this paper we examine the problem of reconstructing a discrete two-dimensional set from its two orthogonal projection (H,V) when the set satisfies some convexity conditions. We show that the algorithm of the paper [Int. J. Imaging Systems and Technol. 9 (1998) 69] is a good heuristic algorithm but it does not solve the problem for all (H,V) instances. We propose a modification of this algorithm solving the problem for all (H,V) instances, by starting to build the ``spine''. The complexity of our reconstruction algorithm is O(mnˇlog(mn)ˇmin{m2,n2}) in the worst case. However, according to our experimental results, in 99% of the studied cases the algorithm is able to reconstruct a solution without using the newly introduced operation. In such cases the upper bound of the complexity of the algorithm is O(mnˇlog(mn)). A systematic comparison of this algorithm was done and the results show that this algorithm has the better average complexity than other published algorithms. The way of comparison and the results are given in a separate paper [Linear Algebra Appl. (submitted)]. Finally we prove that the problem can be solved in polynomial time also in a class of discrete sets which is larger than the class of convex polyominoes, namely, in the class of 8-connected convex sets.

VL - 339 ER - TY - JOUR T1 - Reconstruction of discrete sets with absorption JF - Linear Algebra and its Applications Y1 - 2001 A1 - Attila Kuba A1 - Maurice Nivat AB -

The uniqueness problem is considered when binary matrices are to be reconstructed from their absorbed row and column sums. Let the absorption coefficient n be selected such that en = (1+5^0.5)/2. Then it is proved that if a binary matrix is non-uniquely determined, then it contains a special pattern of 0s and 1s called composition of alternatively corner-connected components. In a previous paper [Discrete Appl. Math. (submitted)] we proved that this condition is also sufficient, i.e., the existence of such a pattern in the binary matrix is necessary and sufficient for its non-uniqueness.

VL - 339 UR - http://www.sciencedirect.com/science/article/B6V0R-44CHW26-C/2/e4cd2b3dc91dbb828db15e331a6230cc ER -