Patrizio Frosini received the PhD degree in Mathematics from the University of Florence in 1991. From the 16th of January 1993 to the 14th of September 2014 he has been an assistant professor in the Faculty of Engineering/School of Engineering and Architecture at the University of Bologna. From the 15th September 2014 he is an associate professor at the Department of Mathematics of the University of Bologna (MAT/03 - Geometry).
He is mainly interested in the study of the topological and metric properties concerning topological spaces and manifolds endowed with R^n-valued functions. He has introduced the concept of size function, precursor of the concept of persistent homology. As for this line of research, he is interested in the extension of the theory in the presence of the action of a subgroup G of the topological group of all self-homeomorphisms of the considered space, and in the study of the natural pseudodistance associated with G. He is also interested in multidimensional persistent topology and homology, and in the use of group equivariant non-expansive operators for topological data analysis, machine learning and artificial intelligence. He also studies the applications of the previous concepts to shape, image and data comparison.
* Senior grant bestowed by the National Institute for High Mathematics “Francesco Severi” for the period 1/10/1990-30/9/1991.
* Post-doc grant bestowed by the University of Bologna for a research on “Topological techniques in computer vision” (4/5/1002-3/5/1993).
* Senior NATO-CNR grant for Mathematical Sciences for a research on “Topological and geometrical methods for computer vision” at the Computer Vision Research Laboratory (University of Massachussets at Amherst, 1/7/96-31/8/96).
INVITED LECTURES AT CONFERENCES
* International Workshop on Computer Vision, Institute for Studies in Theoretical Physics and Mathematics (Tehran, Iran, 2004).
* Gilles Fournier Memorial Conference on Classical and Computational Topological Methods (Sherbrooke, Québec, Canada, 2006).
* Discrete geometry and topology in low dimensions (Banff International Research Station for Mathematical Innovation and Discovery, Banff, Alberta, Canada, 2007).
* Computational Methods in Graphics, Imaging and Technology (National-Louis University, Nowy Sacz, Poland, 2007).
* Shape and Size in Medicine, Biotechnology and Materials Science (University of Milan, Italy, 2008).
* Dynamics, Topology and Computations, (Bedlewo, Poland, 2009).
* Geometric and Topological Methods in Computer Science (Aalborg, Denmark, 2010).
* Minisymposium on Metric and Riemannian Methods in Shape Analysis - SIAM Conference on Imaging Science (Chicago, IL, USA, 2010).
* HOVACOP 2010 - Visual Attention in Robotics, Combinatorial Structures and Homology (Sevilla, Spain, 2010).
* Third International Conference on Scale Space and Variational Methods in Computer Vision (Ein Gedi Resort, Dead Sea, Israel, 2011)
* Applied Algebraic Topology (ETH Zürich, Switzerland, 2011)
* Workshop on Computational Topology (Fields Institute, Toronto, Canada, 2011)
* Dagstuhl Seminar ``Applications of Combinatorial Topology to Computer Science'' (LZI Schloss Dagstuhl, Germany, 2012
* Mini-symposium on Applied and Computational Algebraic Topology (6ECM, Kraków, Poland, 2012)
* Fifth Workshop on Non-Rigid Shape Analysis and Deformable Image Alignment (in conjunction with ECCV 2012) (Florence, Italy, 2012)
* ACA 2013 - Special Session on Computer algebra in algebraic topology and its applications (Málaga, Spain, 2013)
* Applied and Computational Algebraic Topology (Brema, Germany, 2013)
* Geometric and Topological Methods in Computer Science (Aalborg, Denmark, 2015)
* Segunda Escuela/Conferencia de Análisis Topológico de Datos, (Querétaro, Mexico, 2015)
* SIAM Conference on Imaging Science, minisymposium on Geometry-based Models in Image Processing, (Albuquerque, USA, 2016)
* Workshop on Homotopy Probability Theory, Universität des Saarlandes, (Saarbrücken, Germany, 2017)
* XXI BRAZILIAN TOPOLOGY MEETING, Satellite conference of ICM 2018, Universidade Federal Fluminense (Niterói, Rio de Janeiro, Brazil, 2018) (I could not attend the conference but the video of my talk has been shown at the meeting)
* 10th Conference on Geometric and Topological Methods in Computer Science, (Oaxaca, Mexico, 2018)
* International Workshop and Conference on Topology & Applications, Rajagiri School of Engineering & Technology, (Kochi, Kerala, INDIA, 2018)
* Topological data analysis and deep learning: theory and signal applications, 9th International Congress on Industrial and Applied Mathematics, (Valencia, Spain, 2019)
* Complex Simplex: Topological and Network Data Science Workshop, Politecnico di Torino, (Torino, 2019)
INVITED TALKS AT UNIVERSITIES AND INTERNATIONAL SCHOOLS
* University of Perugia (Italy)
* Università of L’Aquila (Italy)
* University of Messina (Italy)
* University of Massachussets at Amherst (USA)
* University of Salerno (Italy)
* Ecole Normale Supérieure de Cachan (France)
* University of Plovdiv (Bulgaria)
* The Abdus Salam International Centre for Theoretical Physics (Italy)
* Université Pierre et Marie Curie (France)
* Institute for Studies in Theoretical Physics and Mathematics (Iran)
* Universitat Pompeu Fabra (Spain)
* CNR-Genova (Italy)
* University of Milan (Italy)
* Université Paris 13 (France)
* Technische Universität Wien (Austria)
* Jagiellonian University (Poland)
* Summer School on Computational Methods for Shape Modelling and Analysis (2004, CNR, Genoa) (Italy)
* International school on "Homology: Theoretical and Computational Aspects" (2015, University of Genoa) (Italy)
* Ohio State University (USA)
* Università di Camerino
* Politecnico di Torino
PARTICIPATION TO SCIENTIFIC, PROGRAM OR ORGANIZING COMMITTEES OF CONFERENCES AND INTERNATIONAL SCHOOLS
* Shape Modeling International (MIT, Cambridge, USA, 2005)
* Shape Modeling International (Tohoku University, Sendai, Japan, 2006)
* Metodi Geometrici nelle Applicazioni e nell’Industria (Bologna, Italy, 2006)
* Shape Modeling International (Lyon, France, 2007).
* Computational and Geometric Topology (Bertinoro, Italy, 2010)
* International Conference on Computer Analysis of Images and Patterns (Siviglia, Spain, 2011)
* Applied and Computational Algebraic Topology - Advanced School (Bologna, Italy, 2012)
* International Workshop on Computational Topology in Image Context (Bertinoro, Italy, 2012)
* International Workshop on Computational Topology in Image Context (Timisoara, Romania, 2014)
* Conference on Geometric Science of Information (Ecole Polytechnique, Paris-Saclay, France, 2015)
* International Workshop on Computational Topology in Image Context (Marseille, France, 2016)
* SIAM Conference on Imaging Science (Bologna, Italy, 2018)
* International Conference on Computer Analysis of Images and Patterns (Salerno, Italy, 2019)
* International Workshop on Applications of Topological Data Analysis (Würzburg, Germania, 2019)
* International Workshop on Computational Topology in Image Context (Retz, Austria, 2020)
COORDINATION OF INTERNATIONAL PROJECTS
In 2003 and 2004 he has been responsible, on the Italian side, of the project “Fast shape search in large databases” within the program of scientific cooperation between Italy and France GALILEO (responsible on the French side: Jean-Michel Morel, Ecole Normale Supérieure de Cachan).
ACTIVITY AS REFEREE AND REVIEWER FOR JOURNAL AND CONFERENCES
He has exerted his activity as referee for these journals:
* Applicable Algebra in Engineering, Communication and Computing
* International Journal of Shape Modeling
* IEE Proceedings - Vision, Image & Signal Processing
* Computer-Aided Design
* Computers & Graphics
* Pattern Recognition
* Computers & Mathematics with Applications
* International Journal of Computer Vision
* IEEE Transactions on Pattern Analysis and Machine Intelligence
* Computer Vision and Image Understanding
* Pattern Recognition Letters
* Topological Methods in Nonlinear Analysis
* Discrete & Computational Geometry
* IEEE Transactions on Signal Processing
* IEEE Transactions on Image Processing
He has exerted his activity as referee for the conferences:
* International Conference on Shape Modelling and Applications
* Asian Conference on Computer Vision (ACCV)
* International Conference on Discrete Geometry for Computer Imagery
* Conference on Geometric Science of Information
* International Conference on Computer Analysis of Images and Patterns
EDITORIAL BOARDS OF JOURNALS
* From the 4th of March 2011 to the 28th of February 2014 he has been a member of the editorial board of the journal ISRN Geometry.
* From the 1st of March 2014 until the end of 2017 he has been a member of the editorial board of the journal International Scholarly Research Notices - subject area Geometry.
* He has been a Guest Editor for the journal Computer Vision and Image Understanding (Elsevier) (Special section on computational topology in image context, Computer Vision and Image Understanding, vol. 121 (2014), 1).
* He has been an editor for the proceedings of the 4th International Workshop "Computational Topology in Image Context" (Bertinoro, Italy, May 28-30, 2012), (Lecture Notes in Computer Science, Vol. 7309)
He is a member of the Excellence Center of the University of Bologna ''Research Centre on Electronic Systems for the Information and Communication Technology''. He has participated in the Network Interested Researcher Group AIM@SHAPE (a Network of Excellence Project of the European Union's 6 th Framework Programme Thematic Priority 2 - Information Society Technologies). From the 15 May 2013 to the 14 May 2016 he has been an associate research fellow at IMATI-CNR (Genoa).
* He is author of more than sixty articles on journals and conference proceedings.
* He has been supervisor of three PhD students and member of four foreign PhD committees.
* Patrizio Frosini's H-index: 18 (Scopus - 18 October 2019)
* Number of citations of papers authored or coauthored by Patrizio Frosini: 870 (Scopus - 18 October 2019)
* Frosini, P., A distance for similarity classes of submanifolds of a Euclidean space, Bull. Austral. Math. Soc. 42, 3 (1990), 407-416
* Verri, A., Uras, C., Frosini, P., Ferri, M., On the use of size functions for shape analysis, Biol. Cybern. 70, (1993), 99-107
* Frosini, P., Mulazzani, M., Size homotopy groups for computation of natural size distances, Bull. Belg. Math. Soc. 6 (1999), 455-464
* Frosini, P., Landi, C., Intrinsic harmonicity of Morse functions, Mathematika, vol. 50 (2003), 167-170
* Dibos, F., Frosini, P., and Pasquignon, D., The use of size functions for comparison of shapes through differential invariants, Journal of Mathematical Imaging and Vision, vol. 21 (2004), n. 2, 107-118
* Donatini, P., Frosini, P., Natural pseudodistances between closed manifolds, Forum Mathematicum, vol. 16 (2004), n. 5, 695-715
* Frosini, P., A note on the linearity of real-valued functions with respect to suitable metrics, Geometriae Dedicata, vol. 108 (2004), n. 1, 105-110
* Donatini, P., Frosini, P., Natural pseudodistances between closed surfaces, Journal of the European Mathematical Society, vol. 9 (2007), n. 2, 331-353
* Biasotti, S., De Floriani, L., Falcidieno, B., Frosini, P., Giorgi, D., Landi, C., Papaleo, L., Spagnuolo, M., Describing shapes by geometrical-topological properties of real functions, ACM Computing Surveys, vol. 40 (2008), n. 4, 12:1-12:87
* Biasotti, S., Cerri, A., Frosini, P., Giorgi, D., Landi, C., Multidimensional size functions for shape comparison, Journal of Mathematical Imaging and Vision, vol. 32 (2008), n. 2, 161-179
* Frosini, P., Does intelligence imply contradiction?, Cognitive Systems Research, vol. 10 (2009), n. 4, 297-315
* Donatini, P., Frosini, P., Natural pseudodistances between closed curves, Forum Mathematicum, vol. 21 (2009), n. 6, 981-999
* Frosini, P., Landi, C., Reparametrization invariant norms, Transactions of the American Mathematical Society, vol. 361 (2009), 407-452
* Frosini, P., Landi, C., Uniqueness of models in persistent homology: the case of curves, Inverse Problems, vol. 27 (2011) 124005
* Biasotti, S., Cerri, A., Frosini, P., Giorgi, D., A new algorithm for computing the 2-dimensional matching distance between size functions, Pattern Recognition Letters, vol. 32 (2011), n. 14, 1735-1746
* Di Fabio, B., Frosini, P., Filtrations induced by continuous functions, Topology and its Applications, vol. 160 (2013), 1413-1422
* Frosini, P., Landi, C., Persistent Betti numbers for a noise tolerant shape-based approach to image retrieval, Pattern Recognition Letters, vol. 34 (2013), 863-872
* Cerri, A., Di Fabio, B., Ferri, M., Frosini, P., Landi, C., Betti numbers in multidimensional persistent homology are stable functions, Mathematical Methods in the Applied Sciences, vol. 36 (2013), 1543-1557
* Frosini, P., G-invariant persistent homology, Mathematical Methods in the Applied Sciences, vol. 38 (2015), n. 6, pages 1190-1199
* Frosini, P., Jablonski, G., Combining persistent homology and invariance groups for shape comparison, Discrete & Computational Geometry, vol. 55 (2016), n. 2, 373-409
* Frosini, P., Landi, C., Mémoli, F., The persistence homotopy type distance, Homology, Homotopy and Applications, vol. 21, (2019), n. 2, 231-259
* Cerri, A., Frosini, P., A new approximation algorithm for the matching distance in multidimensional persistence, to appear in the Journal of Computational Mathematics
* Bergomi, M.G., Frosini, P., Giorgi, D., Quercioli, N., Towards a topological-geometrical theory of group equivariant non-expansive operators for data analysis and machine learning, Nature Machine Intelligence, vol. 1, n. 9, 423-433 (2 September 2019)
* Cerri, A., Ethier, M., Frosini, P., On the geometrical properties of the coherent matching distance in 2D persistent homology, to appear in the Journal of Applied and Computational Topology
From 1996 to present with the exception of two academic years, each year he has taught a course of Geometry and Algebra for engineering students at the University of Bologna. From 2014 to present, each year he has taught a course of Computational Topology for students in mathematics at the University of Bologna. He has taught two PhD courses and given an invited lecture for the Seminar on “Topics in Mathematics” at the Department of Mathematics of the University of Bologna.
In the academic years 2017/2018 and 2018/2019 he has been a member of the Academic Board of the PhD Programme in Mathematics (University of Bologna).