Introduction

I received my Bachelor and Master degree in Computer Science at the University of Genova, in 2008 and 2010, respectively. I started my PhD in 2011 under the supervision of Professor Leila De FLoriani. During Fall 2012 I've been a visiting PhD student at the University of Maryland collaborating with Kenneth Weiss and, successively, Patricio Simari. In 2014 I got my PhD in Computer Science at the University of Genova defending a thesis on "Multi-resolution shape analysis based on discrete Morse decompositions". Currently, I am a post-doctoral fellow at the University of Maryland at College Park.



My research interesets include geometric modeling, topological analysis, homology computation, multiresolution analysis and visualization.



My CV can be downloaded here.



Projects

Terrain Modeling

my photo Digital Terrain Models (DTMs) and Digital Surface Models (DSMs), provide a detailed geometric representation of a terrain. Terrain analysis requires extracting succinct descriptors that can capture the broader, higher level structures of the terrain. In my research, I focus on the Forman gradient and discrete Morse complexes as abstract morphological descriptions of a terrain. By using the Forman gradient, we can efficiently compute critical points and integral lines used for creating morphological segmentations. I am particularly interested in developing scalable and efficient methods for triangulations and point data of big size. Current mesh data structures are not feasible for very large data especially if parallelize/distribute the computation is required. In my work, I am using the Morse complexes as an intermediate representation for such purposes.


Highlights


Topology Based Visual analytics

my photo Topological Data Analysis relies on tools rooted in computational topology. Based on TDA many visualization tools have been developed for studying the shape of an object or the analyzing the evolution of scalar or vector-valued functions. I am focusing on studying efficient tools for data segmentation, based on persistent homology. The generality of topological tools makes them well suited for any data, either they are scalar fields, point data, multivariate data or vector fields. Recently I have worked on the first algorithm for computing a gradient-based representation on multivariate data. This is the first algorithm capable of extracting a discrete gradient field on real-world data. In my current research, I am studying the relationships between this new gradient based representation and its monodimensional counterpart trying to extend the usefulness of persistent homology to the multidimensional case (i.e., when multiple filtrations are provided).


Highlights


High-dimensional data analysis

my photo While several data structures have been proposed in the literature for both cell and simplicial complexes very few of them scale when working in high dimensions. We are working on a new model for encoding a simplicial complex, that we call a Stellar decomposition. The objective is obtaining a compact representation which scales well with both the size and the dimension of the complex. We are developing dedicated versions of the Stellar decomposition to be included in distributed frameworks, such as Hadoop or Apache Spark. I think that being able to represent a simplicial complex efficiently will boost the efficiency in high-dimensional data analysis, which nowadays is mainly limited to the analysis of point clouds or graphs. By developing structures like the Stellar decomposition, my objective is twofold: (i) overcome the current limitations in representing simplicial complexes when working with big data (ii) improving the efficiency of extracting structural information of high-dimensional data


Highlights