Characterization of hv-Convex Sequences

Reconstructing hv-convex polyominoes with multiple colours

This thesis examines the problem of reconstructing multiple discrete 2D objects, represented by a set of cells arranged in an m×n grid, from their projections. The objects being constructed are disjoint, hv-convex polyominoes, each of which has a separate colour. The main results presented here are two algorithms for unordered C-colour reconstruction that have time complexities of O(Cnm) and O(...

Reconstructing hv-Convex Polyominoes from Orthogonal Projections

Tomography is the area of reconstructing objects from projections. In discrete tomography an object T we wish to reconstruct may be a set of cells of a multidimensional grid. We perform measurements of T , each one involving a projection that determines the number of cells in T on all lines parallel to the projection’s direction. Given a finite number of such measurements, we wish to reconstruc...

Generation and Empirical Investigation of hv -Convex Discrete Sets

One of the basic problems in discrete tomography is the reconstruction of discrete sets from few projections. Assuming that the set to be reconstructed fulfils some geometrical properties is a commonly used technique to reduce the number of possibly many different solutions of the same reconstruction problem. Since the reconstruction from two projections in the class of so-called hv-convex sets...

Random Generation of hv-Convex Polyominoes with Given Horizontal Projection

On the Number of hv-Convex Discrete Sets

One of the basic problems in discrete tomography is the reconstruction of discrete sets from few projections. Assuming that the set to be reconstructed fulfills some geometrical properties is a commonly used technique to reduce the number of possibly many different solutions of the same reconstruction problem. The class of hv-convex discrete sets and its subclasses have a well-developed theory....