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A New Sandpile Model with Smoothness Assumptions

Brocchi S., Massazza P.

Fundamenta Informaticae

2016

Vol. 143, nr 3/4

261--286

We consider two new granular dynamical systems obtained from the Sand Pile Model SPM(n) by adding a smoothness condition. First, we define the Smooth Sand Pile Model SmSPM(n) and we provide a characterization of the reachable states, together with some interesting properties of the resulting lattice. Then we extend it to SmSPM*(n), a related dynamical system with a more complex lattice structure.

A New Approach for the Reconstruction of Object-Based Images in Discrete Tomography

Brocchi S.

Fundamenta Informaticae

2014

Vol. 135, nr 1/2

43--57

In this paper we tackle the problem of the reconstruction of object based images, specifically formed by a set of circles inside a ring. By analyzing the projections of the image, we are able to determine some coordinates corresponding to interest points that give significant information about features of the image of aid in the reconstruction. Our approach yields promising results in comparison to other methods in literature. Finally, we discuss how a similar approach could be extended to more complex problems deriving from tomographic applications, in order to develop an efficient method exploiting the prior knowledge assumed on an image.

Solving Multicolor Discrete Tomography Problems by Using Prior Knowledge

Barcucci E., Brocchi S.

Fundamenta Informaticae

2013

Vol. 125, nr 3/4

313--328

Discrete tomography deals with the reconstruction of discrete sets with given projections relative to a limited number of directions, modeling the situation where a material is studied through x-rays and we desire to reconstruct an image representing the scanned object. In many cases it would be interesting to consider the projections to be related to more than one distinguishable type of cell, called atoms or colors, as in the case of a scan involving materials of different densities, as a bone and a muscle. Unfortunately the general n-color problem with n > 1 is NP-complete, but in this paper we show how several polynomial reconstruction algorithms can be defined by assuming some prior knowledge on the set to be rebuilt. In detail, we study the cases where the union of the colors form a set without switches, a convex polyomino or a convex 8-connected set. We describe some efficient reconstruction algorithms and in a case we give a sufficient condition for uniqueness.