An efficient reconstruction of 2D-tiling with t 1,2 , t 2,1 , t 1,1 tiles
19 Jun 2006-pp 474-480
TL;DR: An efficient algorithm is given to tile a 2D-square grid with only t1,2, t2,1, t 1,1 tiles such that the projection of this tiling is the same as the given projection.
Abstract: We define the projection of a tiling as a matrix P = (pij) where pi1 is number of t1,2 tiles in row i and pi2 is the number of t2,1 tiles in row i. We give an efficient algorithm to tile a 2D-square grid with only t1,2, t2,1, t1,1 tiles such that the projection of this tiling is the same as the given projection.
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01 Jan 1999
TL;DR: In this paper, Kuba, Gabor T. Herman, Eilat Vardi, and Cun-Hui Zhang present an algebraic solution for Discrete Tomography.
Abstract: Preface Contributors Part I. Foundations Discrete Tomography: A Historical Overview \ Attila Kuba, Gabor T. Herman Sets of Uniqueness and Additivity in Integer Lattices \ Peter C. Fishburn, Lawrence A. Shepp Tomopgraphic Equivalence and Switching Operations \ T. Yung Kong, Gabor T. Herman Uniqueness and Complexity in Discrete Tomography \ Richard J. Gardner, Peter Gritzmann Reconstruction of Plane Figures from Two Projections \ Akira Kaneko, Lei Huang Reconstruction of Two-Valued Functions and Matrices \ Attila Kuba Reconstruction of Connected Sets from Two Projections \ Alberto Del Lungo, Maurice Nivat Part II. Algorithms Binary Tomography Using Gibbs Priors \ Samuel Matej, Avi Vardi, Gabor T. Herman, Eilat Vardi Probabilistic Modeling of Discrete Images \ Michael T. Chan, Gabor T. Herman, Emanuel Levitan Multiscale Bayesian Methods for Discrete Tomography \ Thomas Frese, Charles A. Bouman, Ken Sauer An Algebraic Solution for Discrete Tomography \ Andrew E. Yagle Binary Steering of Nonbinary Iterative Algorithms \ Yair Censor, Samuel Matej Reconstruction of Binary Images via the EM Algorithm \ Yehuda Vardi, Cun-Hui Zhang Part III. Applications CT-Assisted Engineering and Manufacturing \ Jolyon A. Browne, Mathew Koshy 3D Reconstruction from Sparse Radiographic Data \ James Sachs, Jr., Ken Sauer Heart Chamber Reconstruction from Biplane Angiography \ Dietrich G.W. Onnasch, Guido P.M. Prause Discrete Tomography in Electron Microscopy \ J.M. Carazo, C.O. Sorzano, E. Rietzel, R. Schroeder, R. Marabini Tomopgraphy on the 3D-Torus and Crystals \ Pablo M. Salzberg, Raul Figueroa A Recursive Algorithm for Diffuse Planar Tomography \ Sarah K. Patch From Orthogonal Projections to Symbolic Projections \ Shi-KuoChang Index
480 citations
TL;DR: In this paper, the authors present results for particular instances and for a more general problem, while leaving open the initial problem, for tile a rectangle or torus with only vertical and horizontal bars of a given length.
22 citations
TL;DR: In this note, progress is made toward a comprehensive classification of various tiling reconstruction problems, by proving NP-completeness results for several sets of tiles.
20 citations