## Stefano Brocchi's academic homepage

Stefano Brocchi has been a PhD student, a post-doc and then a researcher for the University of Florence from 2007 to 2015, under the Department of Mathematics and Computer Science. This site describes his academic research and the courses he held. His main research interests involved lossless image compression, discrete tomography and bidimensional languages. He held several courses on basic computer science under the University of Florence, and a course on measurement and error theory at the same university; previously he also held a course of network programming at the University of Siena.

## Research

Stefano Brocchi's research concerns various areas of computer science and mathematics.
One of his main research interest is **discrete tomography**, the discipline that studies the
reconstruction of discrete images from a limited number of projections, modeling some applications regarding x-ray
scans. One of his first works studies how through a pseudo polynomial algorithm
we may solve several reconstruction
problems where the number of rows (i.e. the horizontal resolution) is a fixed number; this may result very useful in
cases where the general problem is NP-complete, as this is a common feature as shown in this paper. Several studies of
Dr. Brocchi concern the 2-color problem, of primary importance in this discipline but proven to be NP-complete. This
problem has been tackled both by searching for families of solvable instances,
both by developing heuristic and approximation algorithms.
The results seems to suggest that the NP-complete core of the problem is small, allowing us
to solve the problem in many of its cases.

Another research field studied by Dr. Brocchi is **lossless image compression**.
In his master thesis
he developed the PCIF compression algorithm , a method to compress true color
images losslessy by the usage of properties of convex polyominoes, structures extensively studied in discrete
tomography. The algorithm has been enhanced and evolved in the
BCIF compression algorithm, actually one of the best
free and open source application-oriented image compressors. More details can be found at the
BCIF website.

Finally, studies on L-convex polyominoes deriving from discrete tomography brought Stefano Brocchi to
interesting results in the field of **bidimensional languages**. By giving a tiling system
defining the class of L-convex polyominoes, considered by some author at the boundary between recognizable and
non recognizable languages, these studies gave useful insight were brought
to this field. Recently, Dr. Brocchi also gave contribution to the studies on **sand pile models**
by proposing a new model that could describe more realistically some cases of application.

The articles deriving from this research can be found in the publications webpage. These works were developed mainly in collaboration with researchers and professor of the universities of Florence and Siena, namely Elena Barcucci, Andrea Frosini, Rinaldi Pinzani and Simone Rinaldi. Collaborations with other academics of international fame include Srecko Brlek, Paolo Massazza and Cristophe Picouleau.