Jean-Luc Rémy

Detection of the Discrete Convexity of Polyominoes

The convexity of a discrete region is a property used in numerous domains of computational imagery. We study its detection in the particular case of polyominoes. We present a first method, directly relying on its definition. A second method, which is based on techniques for segmentation of curves in discrete lines, leads to a very simple algorithm whose correctness is proven. Correlatively, we obtain a characterisation of lower and upper convex hulls of a discrete line segment. Finally, we evoke some applications of these results to the problem of discrete tomography.

Uniform generation of a Schro¨der tree

We present a simple O(n) algorithm that generates uniformly a Schroder tree of size n. The basic idea is to choose a slightly enlarged probability space where uniformity can be achieved.