Reconstructing hv-convex images by tabu research approach Fethi JARRAY 1,2 , Abdessalem DAKHLI 3 and Ghassen TLIG 1 1. Laboratoire CEDRIC- CNAM, Paris, France Fethi.jarray@cnam.fr , Ghassen_tlik@yahoo.fr 2. Al-Imam Mohamed Bin Saud University, Riyadh, Kingdom of Saudi Arabia 3.Institut Supérieur de Gestion Gabes, Tunisie Dakhli-ab@voila.fr Keywords: Discrete tomography, Images reconstruction, Tabu research. Abstract Consider a binary matrix, we call the horizontal projection of row i, the number of ones on this row. Similarly, we call the vertical projection of column j, the number of ones on column j. The standard problem of reconstructing a binary matrix from its orthogonal projections is defined as follows: given the horizontal projection of each row and the vertical projection of each column find a binary matrix such that the ones fit with the prescribed projections (see Figure 1). This problem is polynomial and a polynomial time algorithm is proposed [5]. Figure 1. Reconstruction of a binary matrix from its projections In general, the standard problem is underdetermined and many solutions may exist. To reduce the space of feasible solutions, prior knowledge about the image to reconstruct should be considered. Much real knowledge are considered in literature such as periodicity, convexity, connectedness, etc. In this work we deal with the reconstruction of hv-convex binary matrices from their orthogonal projections. A matrix is called hv-convex if the ones occur consecutively in a single block in each row and in each column. Barcucci et al. show that this problem is NP-complete [1]. May approximate method has been propose to reconstruct nearly hv-convex matrices [1, 2, 3]. Dahl and Flatberg [2] provide approximate solution based on a lagrangean decomposition. Jarray et al. [3] provide an approximate algorithm based on longest path and network flow algorithm. Recently Jarray and Tlig [4] use simulated annealing algorithm to reconstruct hv-convex images. 1