Tomography and Applications

Fundamenta Informaticae, vol. 189, pp. i–x

Abstract

In DiscreteTomography,several classes of binary images presenting different kind of convexity have been considered for their reconstruction from projections. In Digital Image Analysis convexity estimators are among the most important shape descriptors. Shape feature extraction and representation plays an important role in many categories of applications like for example shape retrieval, shape recognition and classification, shape approximation and simplification, and so on. In this talk, we present a multi-level description of a binary image based on a special kind of convexity. In particular, the so called generalized salient pixels provides a decomposition of the image into Q-convex hulls at different levels and they are stored in a matrix called, GS-matrix (where GS stands for GeneralizedSalient). Therefore, there is a one to-one correspondence between the binary image and its GS-matrix. We show how to build the GS-matrix from the binary image and viceversa how to rebuild the binary image from its GS-matrix. Then, we play with GS-matrices to see how changes can modify the rebuild images. In Mathematical Morphology, a wide range of operators permits to process images for edge detection, noise removal, image enhancement and image segmentation, to mention some common usage. Among them, the two most basic operations are erosion and dilation. Virtually all other mathematical morphology operators can be defined in terms of combinations of erosion and dilation along with set operators such as intersection and union. We start by defining a new “erosion”operation based on the interaction of GS-matrix binary image and we investigate some consequences.

Authors 4

1. Paolo Dulio Aachen

   Leiden University · University of Colorado Boulder · University of Florence · Politecnico di Milano

   Affiliation as printed

   Dipartimento di Matematica, Politecnico di Milano, Milano, Italy, paolo.dulio@polimi.it

   Department of Computer Science University of Colorado at Boulder,USA

   Dipartimento di Matematica "F. Brioschi" Politecnico di Milano Piazza Leonardo da Vinci 32, I-20133 Milano, Italy

   Dipartimento di Matematica e Informatica "U.Dini" Viale Morgagni 65, 50134 Firenze, Italy

   LIACS, Leiden University Niels Bohrweg 1, 2333 CA Leiden, The Netherlands

2. Andrea Frosini Aachen

   Leiden University · University of Colorado Boulder · University of Florence · Politecnico di Milano

   Affiliation as printed

   Dipartimento di Matematica e Informatica “U.Dini”, Firenze, Italy, andrea.frosini@unifi.it

   Department of Computer Science University of Colorado at Boulder,USA

   Dipartimento di Matematica "F. Brioschi" Politecnico di Milano Piazza Leonardo da Vinci 32, I-20133 Milano, Italy

   LIACS, Leiden University Niels Bohrweg 1, 2333 CA Leiden, The Netherlands

3. Grzegorz Rozenberg Aachen

   Leiden University · University of Colorado Boulder · University of Florence · Politecnico di Milano

   Affiliation as printed

   Department of Computer Science, University of Colorado at Boulder, USA

   LIACS, Leiden University, Niels Bohrweg, CA Leiden, The Netherlands, grozenberg@gmail.com

   Dipartimento di Matematica "F. Brioschi" Politecnico di Milano Piazza Leonardo da Vinci 32, I-20133 Milano, Italy

   Dipartimento di Matematica e Informatica "U.Dini" Viale Morgagni 65, 50134 Firenze, Italy

4. Lama Tarsissi

   Sorbonne University Abu Dhabi · Laboratoire d'Informatique Gaspard-Monge

   Affiliation as printed

   Sorbonne University Abu Dhabi, Laboratoire Informatiques Gaspard Monges, France, lama.tarsissi@sorbonne.ae