Journals

[For a personal copy of these papers please send me an e-mail]

(Selected papers are displayed in red)

• Lucia Ferrari, Patrizio Frosini, Nicola Quercioli, Francesca Tombari,
  A topological model for partial equivariance in deep learning and data analysis,
  Frontiers in Artificial Intelligence, 6 (2023). DOI: 10.3389/frai.2023.1272619. OPEN ACCESS URL: https://www.frontiersin.org/articles/10.3389/frai.2023.1272619 .


• Faraz Ahmad, Massimo Ferri, Patrizio Frosini,
  Generalized Permutants and Graph GENEOs,
  Machine Learning and Knowledge Extraction, 5(4) (2023), 1905-1920. DOI: 10.3390/make5040092. OPEN ACCESS URL: https://www.mdpi.com/2504-4990/5/4/92 .


• Patrizio Frosini, Ivan Gridelli, Andrea Pascucci,
  A probabilistic result on impulsive noise reduction in topological data analysis through group equivariant non-expansive operators,
  Special issue "Topological Data Analysis Meets Information Theory. New Perspectives for the Analysis of Higher-Order Interactions in Complex Systems."
  Entropy, vol. 25 (2023), Issue 8, 1150. OPEN ACCESS URL: https://www.mdpi.com/1099-4300/25/8/1150 .


• Marc Ethier, Patrizio Frosini, Nicola Quercioli, Francesca Tombari,
  Geometry of the matching distance for 2D filtering functions,
  Journal of Applied and Computational Topology, vol. 7 (2023), 815–830. DOI: 10.1007/s41468-023-00128-7. OPEN ACCESS URL: https://link.springer.com/article/10.1007/s41468-023-00128-7 .


• Giovanni Bocchi, Stefano Botteghi, Martina Brasini, Patrizio Frosini and Nicola Quercioli,
  On the finite representation of linear group equivariant operators via permutant measures,
  Annals of Mathematics and Artificial Intelligence, vol. 91 (2023), n. 4, 465–487. DOI: 10.1007/s10472-022-09830-1. OPEN ACCESS URL: https://link.springer.com/article/10.1007/s10472-022-09830-1 . Full-text access to a view-only version of the paper: https://rdcu.be/c5Obw .


• Francesco Conti, Patrizio Frosini, Nicola Quercioli,
  On the Construction of Group Equivariant Non-Expansive Operators via Permutants and Symmetric Functions,
  Frontiers in Artificial Intelligence, vol. 5 (2022), 1-11. DOI: 10.3389/frai.2022.786091. OPEN ACCESS URL: https://www.frontiersin.org/article/10.3389/frai.2022.786091.


• Andrea Cerri, Patrizio Frosini,
  A new approximation algorithm for the matching distance in multidimensional persistence,
  Journal of Computational Mathematics, vol. 38 (2020), n. 2, 291-309. DOI: 10.4208/jcm.1809-m2018-0043.
  Preprint available at http://amsacta.unibo.it/2971/. WARNING! The first pdf file of this paper that was made available for download from the website of the Journal of Computational Mathematics was not the correct one and contained many misprints. In case you are interested in this paper, please download the last version from this webpage: https://www.global-sci.org/intro/article_detail/jcm/14518.html.


• Mattia G. Bergomi, Patrizio Frosini, Daniela Giorgi, Nicola Quercioli,
  Towards a topological-geometrical theory of group equivariant non-expansive operators for data analysis and machine learning, Nature Machine Intelligence, vol. 1, n. 9, pages 423–433 (2 September 2019). DOI: 10.1038/s42256-019-0087-3
  Full-text access to a view-only version of this paper is available at the link https://rdcu.be/bP6HV .


• Andrea Cerri, Marc Ethier, Patrizio Frosini,
  On the geometrical properties of the coherent matching distance in 2D persistent homology,
  Journal of Applied and Computational Topology, vol. 3 (2019), n. 4, 381–422. DOI: 10.1007/s41468-019-00041-y
  Preprint available at arXiv:1801.06636.


• Patrizio Frosini, Claudia Landi and Facundo Mémoli,
  The persistence homotopy type distance,
  Homology, Homotopy and Applications, vol. 21 (2019), n. 2, 231-259. Preprint available at https://arxiv.org/pdf/1702.07893.pdf.


• Patrizio Frosini, Grzegorz Jabłoński,
  Combining persistent homology and invariance groups for shape comparison,
  Discrete & Computational Geometry, vol. 55 (2016), n. 2, pages 373-409. DOI: 10.1007/s00454-016-9761-y. Preprint available at http://arxiv.org/pdf/1312.7219v4.pdf. Paper available at http://link.springer.com/article/10.1007/s00454-016-9761-y.


• Patrizio Frosini,
  G-invariant persistent homology,
  Mathematical Methods in the Applied Sciences, vol. 38 (2015), n. 6, pages 1190-1199. DOI: 10.1002/mma.3139. Preprint available at arXiv:1212.0655.


• Andrea Cerri, Patrizio Frosini,
  Necessary conditions for discontinuities of multidimensional persistent Betti numbers,
  Mathematical Methods in the Applied Sciences, vol. 38 (2015), n. 4, pages 617-629. DOI: 10.1002/mma.3093. Preprint available here.


• Niccolò Cavazza, Marc Ethier, Patrizio Frosini, Tomasz Kaczynski, Claudia Landi,
  Comparison of persistent homologies for vector functions: from continuous to discrete and back,
  Computers and Mathematics with Applications, vol. 66 (2013), 560-573. DOI:10.1016/j.camwa.2013.06.004, preprint available at http://arxiv.org/abs/1201.3217.


• Barbara Di Fabio, Patrizio Frosini,
  Filtrations induced by continuous functions,
  Topology and its Applications, vol. 160 (2013), 1413-1422. DOI:10.1016/j.topol.2013.05.013, preprint available at arXiv:1304.1268.


• Patrizio Frosini, Claudia Landi,
  Persistent Betti numbers for a noise tolerant shape-based approach to image retrieval,
  Pattern Recognition Letters, vol. 34 (2013), 863-872. DOI: 10.1016/j.patrec.2012.10.015 (Table 1 and Figure 3 corrected in Corrigendum to "Persistent Betti numbers for a noise tolerant shape-based approach to image retrieval",
  Pattern Recognition Letters, vol. 34 (2013), 1320-1321. DOI: 10.1016/j.patrec.2013.04.001)


• Andrea Cerri, Barbara Di Fabio, Massimo Ferri, Patrizio Frosini, Claudia Landi,
  Betti numbers in multidimensional persistent homology are stable functions,
  Mathematical Methods in the Applied Sciences, vol. 36 (2013), 1543-1557. DOI: 10.1002/mma.2704, preprint also available at http://amsacta.unibo.it/2923/.


• Patrizio Frosini,
  Stable comparison of multidimensional persistent homology groups with torsion,
  Acta Applicandae Mathematicae, vol. 124 (2013), n. 1, 43-54. DOI: 10.1007/s10440-012-9769-0


• Massimo Ferri, Patrizio Frosini, Claudia Landi,
  Stable shape comparison by persistent homology,
  Atti Semin. Mat. Fis. Univ. Modena Reggio Emilia, vol. 58 (2011), 143-162.


• Patrizio Frosini, Claudia Landi,
  Uniqueness of models in persistent homology: the case of curves,
  Inverse Problems, vol. 27 (2011) 124005. DOI: 10.1088/0266-5611/27/12/124005, preprint available at http://arxiv.org/abs/1012.5783.


• Silvia Biasotti, Andrea Cerri, Patrizio Frosini, Daniela Giorgi,
  A new algorithm for computing the 2-dimensional matching distance between size functions,
  Pattern Recognition Letters, vol. 32 (2011), n. 14, 1735-1746. DOI: 10.1016/j.patrec.2011.07.014, preprint available at http://amsacta.unibo.it/2821/2/mmd100804ElsarticleBis.pdf.


• Patrizio Frosini, Claudia Landi,
  No embedding of the automorphisms of a topological space into a compact metric space endows them with a composition that passes to the limit,
  Applied Mathematics Letters, vol. 24 (2011), n. 10, 1654-1657. DOI:10.1016/j.aml.2011.04.007, preprint available at http://arxiv.org/abs/1005.0921.


• Daniela Giorgi, Patrizio Frosini, Michela Spagnuolo, Bianca Falcidieno,
  3D relevance feedback via multilevel relevance judgements,
  The Visual Computer, vol. 26 (2010), 1321-1338.


• Andrea Cerri, Patrizio Frosini,
  Advances in multidimensional Size Theory,
  Image Analysis and Stereology, vol. 29 (2010), 19-26.


• Michele d'Amico, Patrizio Frosini, Claudia Landi,
  Natural pseudo-distance and optimal matching between reduced size functions,
  Acta Applicandae Mathematicae, vol. 109 (2010), n. 2, 527-554.
  (Some results in this paper, including the proof of stability of persistence diagrams in degree 0, had already appeared in this technical report:
• Michele d'Amico, Patrizio Frosini, Claudia Landi,
  Optimal matching between reduced size functions,
  Technical report no. 35 (2003), DISMI, University of Modena and Reggio Emilia, Italy.)


• Patrizio Frosini,
  Does intelligence imply contradiction?,
  Cognitive Systems Research, vol. 10 (2009), n. 4, 297-315.
  (A beautiful slideshow by Mattia G. Bergomi illustrating this paper can be found here: https://mgbergomi.github.io/Contradiction/)


• Pietro Donatini, Patrizio Frosini,
  Natural pseudo-distances between closed curves,
  Forum Mathematicum, vol. 21 (2009), Issue 6, 981–999.


• Andrea Cerri, Patrizio Frosini, Claudia Landi,
  Stability in multidimensional size theory. Preprint


• Patrizio Frosini, Claudia Landi,
  Reparametrization invariant norms,
  Transactions of the American Mathematical Society, vol. 361 (2009), 407-452.


• Silvia Biasotti, Leila De Floriani, Bianca Falcidieno, Patrizio Frosini, Daniela Giorgi, Claudia Landi, Laura Papaleo, Michela Spagnuolo,
  Describing shapes by geometrical-topological properties of real functions,
  ACM Computing Surveys, vol. 40 (2008), n. 4, 12:1-12:87.


• Silvia Biasotti, Andrea Cerri, Patrizio Frosini, Daniela Giorgi, Claudia Landi,
  Multidimensional size functions for shape comparison,
  Journal of Mathematical Imaging and Vision, vol. 32 (2008), n. 2, 161-179.


• Massimo Ferri, Patrizio Frosini,
  VC-dimension on manifolds: a first approach,
  Mathematical methods in the applied sciences, vol. 31 (2008), n. 5, 589-605.


• Andrea Cerri, Massimo Ferri, Patrizio Frosini, Daniela Giorgi
  Keypics: free-hand drawn iconic keywords,
  International Journal of Shape Modeling, vol. 13 (2007), n. 2, 1-13.


• Pietro Donatini, Patrizio Frosini,
  Natural pseudodistances between closed surfaces,
  Journal of the European Mathematical Society, vol. 9 (2007), n. 2, 331–353.


• Michele d'Amico, Patrizio Frosini, Claudia Landi,
  Using matching distance in size theory: a survey,
  International Journal of Imaging Systems and Technology, vol. 16 (2006) , n. 5, 154–161. Preprint


• Andrea Cerri, Patrizio Frosini, Claudia Landi,
  A global reduction method for multidimensional size graphs,
  Electronic Notes in Discrete Mathematics, n. 26 (2006), 21-28.


• Patrizio Frosini,
  A note on the linearity of real-valued functions with respect to suitable metrics,
  Geometriae Dedicata, vol. 108 (2004), n. 1, 105-110.


• Pietro Donatini, Patrizio Frosini,
  Natural pseudodistances between closed manifolds,
  Forum Mathematicum, vol. 16 (2004), n. 5, 695-715.


• Pietro Donatini, Patrizio Frosini,
  Lower bounds for natural pseudodistances via size functions,
  Archives of Inequalities and Applications, vol. 2 (2004), n. 1, 1-12.


• Françoise Dibos, Patrizio Frosini, Denis Pasquignon,
  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.


• Patrizio Frosini, Claudia Landi,
  Intrinsic harmonicity of Morse functions,
  Mathematika, vol. 50 (2003), 167-170.


• Patrizio Frosini,
  A note on the representability of compact sets by real sequences,
  Applied Mathematics Letters, 15(8) (2002), 931-935.


• Patrizio Frosini, Claudia Landi,
  Size functions and formal series,
  Applicable Algebra in Engineering, Communication and Computing, 12(4) (2001), 327-349.


• Patrizio Frosini, Michele Mulazzani,
  Size homotopy groups for computation of natural size distances,
  Bulletin of the Belgian Mathematical Society - Simon Stevin, 6 (1999), 455-464.


• Patrizio Frosini, Claudia Landi,
  Size theory as a topological tool for computer vision,
  Pattern Recognition And Image Analysis, vol. 9 (4) (1999), 596-603.


• Patrizio Frosini, Massimiliano Pittore,
  New methods for reducing size graphs,
  International Journal of Computer Mathematics, 70 (3) (1999), 505-517.


• Patrizio Frosini,
  Metric homotopies,
  Atti del Seminario Matematico e Fisico dell'Università di Modena, XLVII, 271-292 (1999).


• Patrizio Frosini, Claudia Landi,
  Size functions and morphological transformations,
  Acta Applicandae Mathematicae, vol. 49 (1) (1997), 85-104.


• Patrizio Frosini,
  Connections between size functions and critical points,
  Mathematical Methods In The Applied Sciences, vol. 19 (1996), 555-569.


• Patrizio Frosini,
  Una rapida escursione fra le distanze naturali di taglia,
  Atti Accademia Peloritana dei Pericolanti Cl. Sci. Fis. Mat. Natur., vol. LXXIII (1995), 25-40 (Italian)


• Francesco Domenicucci, Patrizio Frosini, Sara Lazzarini,
  Calcolo della taglia libera di immagini,
  Automazione e Strumentazione, Novembre 1994, 83-87.


• Alessandro Verri, Claudio Uras, Patrizio Frosini, Massimo Ferri,
  On the use of size functions for shape analysis,
  Biological Cybernetics, 70, (1993), 99-107.


• Patrizio Frosini,
  Discrete computation of size functions,
  Journal of Combinatorics, Information & System Sciences, 17, 3-4 (1992), 232-250.


• Patrizio Frosini,
  A distance for similarity classes of submanifolds of a Euclidean space,
  Bulletin of the Australian Mathematical Society, 42, 3 (1990), 407-416.

Conference proceedings

(For a personal copy of these papers please send me an e-mail)

• Patrizio Frosini,
  An introduction to the notion of natural pseudo-distance in topological data analysis,
  In: Devaney R.L., Chan K.C., Vinod Kumar P. (eds) Topological Dynamics and Topological Data Analysis. IWCTA 2018. Springer Proceedings in Mathematics & Statistics, vol. 350 (2021), 203-213. Springer, Singapore. DOI: 10.1007/978-981-16-0174-3_17.
  Paper available at this link.


• Andrea Cerri, Patrizio Frosini,
  A brief introduction to multidimensional persistent Betti numbers,
  In: Devaney R.L., Chan K.C., Vinod Kumar P. (eds) Topological Dynamics and Topological Data Analysis. IWCTA 2018. Springer Proceedings in Mathematics & Statistics, vol. 350 (2021), 215-228. Springer, Singapore. DOI: 10.1007/978-981-16-0174-3_18.
  Paper available at this link.


• Francesco Camporesi, Patrizio Frosini, Nicola Quercioli,
  On a new method to build group equivariant operators by means of permutants,
  Lecture Notes in Computer Science, Proceedings of the International Cross-Domain Conference, CD-MAKE 2018, Hamburg, Germany, August 27-30, 2018, MAKE Topology, Springer, Cham, A. Holzinger et al. (Eds.), LNCS 11015, 265–272, 2018. DOI: 10.1007/978-3-319-99740-7_18. Preprint available here.


• Patrizio Frosini, Nicola Quercioli,
  Some remarks on the algebraic properties of group invariant operators in persistent homology,
  Lecture Notes in Computer Science, Proceedings of the International Cross-Domain Conference, CD-MAKE 2017, Reggio, Italy, August 29–September 1, 2017, MAKE Topology, Springer, Cham, Holzinger A., Kieseberg P., Tjoa A M., Weippl E. (Eds.), LNCS 10410, 14-24, 2017. DOI: 10.1007/978-3-319-66808-6_2. Preprint available here.


• Patrizio Frosini,
  Towards an observer-oriented theory of shape comparison,
  Proceedings of the 8th Eurographics Workshop on 3D Object Retrieval, Lisbon, Portugal, May 7-8, 2016, A. Ferreira, A. Giachetti, and D. Giorgi (Editors), 5-8. DOI: 10.2312/3dor.20161080. Preprint available at http://arxiv.org/pdf/arXiv:1603.02008v1.pdf.


• Andrea Cerri, Marc Ethier, Patrizio Frosini,
  The coherent matching distance in 2D persistent homology,
  Lecture Notes in Computer Science, Proceedings of the 6th International Workshop on Computational Topology in Image Context, Marseille, France, June 15-17, 2016, Springer International Publishing Switzerland, A. Bac and J.-L. Mari (Eds.), LNCS 9667, 216-227, 2016. DOI: 10.1007/978-3-319-39441-1_20. Preprint available at http://arxiv.org/pdf/1603.03886v1.pdf.


• Andrea Cerri, Marc Ethier, Patrizio Frosini, A study of monodromy in the computation of multidimensional persistence, Proceedings of the 17th IAPR International Conference on Discrete Geometry for Computer Imagery, Seville, Spain, March 20-22, 2013, Lecture Notes in Computer Science 7749, 2013, 192-202. Preprint
  Click here if you wish to have more information about this paper and the phenomenon of monodromy in multidimensional persistence.


• Patrizio Frosini, Claudia Landi, Persistent Betti numbers for a noise tolerant shape-based approach to image retrieval, A. Berciano et al. (Eds.): CAIP 2011, LNCS 6854, 294-301. Springer-Verlag Berlin Heidelberg (2011).


• Andrea Cerri, Patrizio Frosini, Walter G. Kropatsch, Claudia Landi, A global method for reducing multidimensional size graphs, X. Jiang et al. (Eds.): GbRPR 2011, LNCS 6658, 1-11. Springer-Verlag Berlin Heidelberg (2011).


• Daniela Giorgi, Patrizio Frosini, Michela Spagnuolo, Bianca Falcidieno, Multilevel relevance feedback for 3D shape retrieval, Proceedings 3DOR'09: Eurographics Workshop on 3D Object Retrieval, The Eurographics Association, 45-52, 2009.


• Silvia Biasotti, Bianca Falcidieno, Patrizio Frosini, Daniela Giorgi, Claudia Landi, Simone Marini, Giuseppe Patanè, Michela Spagnuolo, 3D shape description and matching based on properties of real functions, Eurographics 2007 Tutorial Notes, 1025-1074, The Eurographics Association, 2007.


• Patrizio Frosini, Geometrical shape comparison by size theory, Proceedings in Applied Mathematics and Mechanics, Special Issue: Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Zürich 2007, Volume 7 Issue 1 (December 2007), Pages 1141907 - 1141908.


• Massimo Ferri, Patrizio Frosini, A proposal for image indexing: keypics, plastic graphical metadata, In: Proc. SPIE Vol. 5670, Internet Imaging VI; Simone Santini, Raimondo Schettini, Theo Gevers Eds. (2005), 225-231.


• Claudia Landi, Patrizio Frosini, Size functions as complete invariants for image recognition, Proc. SPIE Vol. 4794, p. 101-109, Vision Geometry XI, Robert A. Melter, Angela Y.Wu, Longin J. Latecki (eds.) (2002).


• Aldo Brucale, Fabio Cesari, Michele d'Amico, Massimo Ferri, Patrizio Frosini, Luciano Gualandri, Monica Guerra, Alberto Lovato, Ilaria Pace, Image retrieval through abstract shape indication, Proceedings IAPR Workshop on Machine Vision Applications, University of Tokyo, Japan (2000), 367-370.


• Pietro Donatini, Patrizio Frosini, Claudia Landi, Deformation energy for size functions, Proceedings Second International Workshop EMMCVPR'99, Lecture Notes in Computer Science 1654, E. R. Hancock, M. Pelillo (editors) Springer-Verlag, Berlin Heidelberg (1999), 44-53.


• Claudia Landi, Patrizio Frosini, Algebraic representation of size functions, Pattern Recognition and Image Understanding, 5th open German-Russian workshop, B. Radig et al. (eds.), Infix (1999), 41-46.


• Costantino Collina, Massimo Ferri, Patrizio Frosini, Eleonora Porcellini, SketchUp: Towards qualitative shape data management, Proceedings Third Asian Conference on Computer Vision, Lecture Notes in Computer Science 1351, vol. I, R. Chin, T. Pong (editors) Springer-Verlag, Berlin Heidelberg (1998), 338-345.


• Pietro Donatini, Massimo Ferri, Patrizio Frosini, Applications of size theory to computer vision and pattern recognition, Joint Workshop of the AI*IA - IAPR-IC IAPRVA98 (Ferrara), Universita' di Ferrara, Ferrara (1998), 65-68.


• Pietro Donatini, Patrizio Frosini, Alberto Lovato, Size functions for signature recognition, Proceedings of the SPIE's Workshop ``Vision Geometry VII'', 3454 (1998), 178-183. (This paper can be downloaded from here. Please see also this web page.)


• Massimo Ferri, Patrizio Frosini, Alberto Lovato, Chiara Zambelli, Point selection: A new comparison scheme for size functions (With an application to monogram recognition), Proceedings Third Asian Conference on Computer Vision, Lecture Notes in Computer Science 1351, vol. I, R. Chin, T. Pong (editors) Springer-Verlag, Berlin Heidelberg (1998), 329-337. (Please see also this web page.)


• Claudia Landi, Patrizio Frosini, New pseudodistances for the size function space, Proc. SPIE Vol. 3168, p. 52-60, Vision Geometry VI, Robert A. Melter, Angela Y. Wu, Longin J. Latecki (eds.), 1997. (This paper can be downloaded from here.)


• Claudia Landi, Patrizio Frosini, Connections between size functions and morphological transformations, Proc. SPIE Vol. 2785, p. 24-32, Vision Systems: New Image Processing Techniques, Philippe Refregier; Ed. (1996). (This paper can be downloaded from here.)


• Patrizio Frosini, Massimo Ferri, Range size functions, Proceedings of the SPIE's Workshop ``Vision Geometry III'', 2356 (1994), 243-251. (This paper can be downloaded from here.)


• Patrizio Frosini, Measuring shapes by size functions, Proc. of SPIE, Intelligent Robots and Computer Vision X: Algorithms and Techniques, Boston, MA 1607 (1991), 122-133. (This paper can be downloaded from here.)

Editorships and reviews

• Massimo Ferri, Patrizio Frosini, Claudia Landi, Andrea Cerri, Barbara Di Fabio (Eds.), Computational Topology in Image Context - Proceedings of the 4th International Workshop on Computational Topology in Image Context, CTIC 2012, Bertinoro, Italy, May 28-30, 2012, Lecture Notes in Computer Science 7309, Springer 2012.


• Massimo Ferri, Patrizio Frosini, Claudia Landi, Special section on computational topology in image context, Computer Vision and Image Understanding 121: 1 (2014).


• Patrizio Frosini, A clash of mathematical cultures, Nature Physics. Published online: 13 June 2023. DOI: 10.1038/s41567-023-02124-1.
  Full-text access to a view-only version of this paper is available at the link https://rdcu.be/dfowk .