Reconstruction and Enumeration of hv-Convex Polyominoes with Given Horizontal Projection

The Reconstruction of Polyominoes from Approximately Orthogonal Projections

The reconstruction of discrete two-dimensional pictures from their projection is one of the central problems in the areas of medical diagnostics, computer-aided tomography, pattern recognition, image processing, and data compression. In this note, we determine the computational complexity of the problem of reconstruction of polyominoes from their approximately orthogonal projections. We will pr...

Reconstruction of 2-convex polyominoes

There are many notions of discrete convexity of polyominoes (namely hvconvex [1], Q-convex [2], L-convex polyominoes [5]) and each one has been deeply studied. One natural notion of convexity on the discrete plane leads to the definition of the class of hv-convex polyominoes, that is polyominoes with consecutive cells in rows and columns. In [1] and [6], it has been shown how to reconstruct in ...

Random Generation of hv-Convex Polyominoes with Given Horizontal Projection

Reconstruction of convex polyominoes from orthogonal projections of their contours

The problem of reconstructing a convex polyominoes from its horizontal and vertical projections when the projections are defined as the number of cells of the polyomino in the different lines and columns was studied by Del Lungo and M. Nivat (cf [7]). In this paper we study the reconstruction of any convex polyomino when the orthogonal projections are defined as the contour length of the object...

Two Subclasses of 2-convex Polyominoes: Properties for Reconstruction

A polyomino P is called 2-convex if for every two cells there exists a monotone path included in P with at most 2 changes of direction. This paper studies the tomographical aspects of two subclasses of 2-convex polyominoes called η2L and η′ 2L. In the first part, the uniqueness results of the two subclasses of HV convex polyominoes η and η′ are investigated using the switching components (that ...