Medians of discrete sets according to a linear distance

l'URL de l'article publié est http://www.springerlink.com/link.asp?id=9rukhuabxp8abkweIn this paper, we present some results concerning the median points of a discrete set according to a distance defined by means of two directions p and q. We describe a local characterization of the median points and show how these points can be determined from the projections of the discrete set along directions p and q. We prove that the discrete sets having some connectivity properties have at most four median points according to a linear distance, and if there are four median points they form a parallelogram. Finally, we show that the 4-connected sets which are convex along the diagonal directions contain their median points along these directions

The number of convex polyominoes reconstructible from their orthogonal projections

AbstractMany problems of computer-aided tomography, pattern recognition, image processing and data compression involve a reconstruction of bidimensional discrete sets from their projections. [3–5,10,12,16,17]. The main difficulty involved in reconstructing a set Λ starting out from its orthogonal projections (V,H) is the ‘ambiguity’ arising from the fact that, in some cases, many different sets have the same projections (V,H). In this paper, we study this problem of ambiguity with respect to convex polyominoes, a class of bidimensional discrete sets that satisfy some connection properties similar to those used by some reconstruction algorithms. We determine an upper and lower bound to the maximum number of convex polyominoes having the same orthogonal projections (V,H), with V ∈ Nn and H ∈ Nm. We prove that under these connection conditions, the ambiguity is sometimes exponential. We also define a construction in order to obtain some convex polyominoes having the same orthogonal projections

Outils, machines et informatique

Les outils jouent un rôle fondamental dans toutes les sociétés et ce depuis les temps préhistoriques les plus reculés depuis que l'homme est devenu homo faber, l'homme qui fabrique. Un outil, une pioche, une bêche, un marteau, ce n'est pas qu'un objet, c'est le fruit d'une réflexion sur des matières à travailler, des actions que l'on peut effectuer sur cette matière, et une gestuelle pour manier l'outil, pour effectuer les actions nécessaires à l'obtention d'un certain résultat. Même si chez le manieur d'outil l'expérience et l'instinct qu'elle a induit l'emporte souvent sur la réflexion consciente, avant tout maniement de l'outil approprié, il convient de savoir ce que l'on veut faire et concevoir une suite de gestes qui permettrons d'obtenir le résultat voulu. Et rien ne ressemble plus à un programme informatique que la description de la suite des gestes que l'ouvrier (au sens propre, de celui qui oeuvre) doit effectuer

On the interpretation of recursive program schemes

This paper extends a previous paper [8] where we described a semantics for monadic recursive program schemes (also called Scott-de Bakker schemes). The method consists in considering program schemes as rewriting systems which generate subsets of a free magma and defining a mapping of such subsets in a proper domain of functions. In our previous paper, dealing with a simple case, the combinatorial properties on which the whole construction relies were well known or at least immediate corollaries of wellknown results in the theory of context-free languages. In the present case, the rewriting systems which we are led to consider, and which in a very naturalway could be called algebraic rewriting systems or grammars on a free magma, have been little considered in the literature and we need establish first a number of results concerning such systems. This is done in a first part of this paper. Afterwards we establish the link between such rewriting systems and recursive program schemes, define the function computed by such a scheme under a given discrete interpretation and apply the results of part I to show the equivalence of one definition of this function with the classical definitions : the operational semantics as described for example in [3], Kleene\u27s definition of recursive function [2], the fix-point semantics as it can be found in [5], [6] or [10]