Algorithms

• Computational complexity, efficient algorithms, and uniqueness issues for problems in Discrete Tomography;
• definition of shape descriptors for digital image analysis;
• design of efficient algorithms for problems in Bioinformatics;
• protocols based on majority-rules in distributed systems, and dynamic multicolored monopolies

Area: Discrete Tomography
Discrete Tomography focuses on the problem of reconstruction of binary images from a small number of their projections.
In general, tomography deals with the problem of determining shape and dimensional information of an object from a set of projections. In "continuous" tomography when a large number of projections is available, accurate reconstructions can be made by many different algorithms. It is typical for discrete tomography that only a few projections (line sums) are used. In this case, conventional techniques fail. A special case of discrete tomography deals with the problem of the reconstruction of a binary image. Discrete tomography has strong connections with other mathematical fields, such as number theory, discrete mathematics, complexity theory and combinatorics.

• Study of reconstruction algorithms for special binary images
• Study of instability/stability problems
• Study of uniqueness from set of directions (for bounded sets)

Area: Shape representation and digital image analysis
Shape representation is a current topic in digital image analysis, for example, for object recognition and classification issues. Suitable approaches for handling the problems consist in the design of new shape descriptors and measures for descriptors sensitive to distinguish the shapes but robust to noise. Many shape properties like shape convexity, ellipticity, elongation, compactness, linearity, are suitable for a numerical evaluation and give rise to shape descriptors. The measures which do relate to a certain shape property have a well understood and predictable behavior.

Among common feature we are going to focus on convexity, and in particular to a special two-dimensional convexity so called Quadrant-convexity.

• Study of multiple measures
• Study of complex spatial relations
• Ranking of images
• Classification issues

Area: Algorithms and data structure for problems in Bioinformatics, and Distributed protocols for dynamic monopolies.

Sara Brunetti