## COLLOQUIA PATAVINA |

Prof. Massimo Fornasier (Univ. di Monaco)

From Mantegna's frescoes to variational methods for the inpainting of images

(Colloquia Prodi) - Talk in memory of Vicent Caselles

May 13, 2014

From Mantegna's frescoes to variational methods for the inpainting of images

(Colloquia Prodi) - Talk in memory of Vicent Caselles

May 13, 2014

Abstract

Can one of the most important Italian Renaissance frescoes reduced in
hundreds of thousand fragments by a bombing during the Second World War be re-composed after more than 60 years from its damage? Can we reconstruct the missing parts and can we say something about their original color?
In this talk we want to exemplify, hopefully effectively by taking advantage of the seduction of art, how mathematics today can be applied
in real-life problems which were considered unsolvable only few years ago.
Using the mathematical methods mentioned for the fresco restoration
problem, we introduce and analyze nonlocal variational models
for the rotation invariant exemplar-based inpainting of images,
generalizing the work of Vicent Caselles; this talk is dedicated to his memory.

Related work:

* Rotation Invariance in Exemplar-based Image Inpainting (Master Thesis, M. Eller), Technical University of Munich, August 31 2013. http://www-m15.ma.tum.de/foswiki/pub/M15/Allgemeines/PublicationsEN/masterthesis_martin.pdf

* P. Arias, G. Facciolo, V. Caselles, and G. Sapiro. A variational framework for exemplar-based image inpainting. International Journal of Computer Vision, 93:319-347, 2011.

* Mathematics enters the picture (M. Fornasier), Proceedings of the conference Mathknow 2008 http://www.ricam.oeaw.ac.at/people/page/fornasier/mathsinpict.pdf

* Restoration of color images by vector valued BV functions and variational calculus (M. Fornasier and R. March), SIAM J. Appl. Math., Vol. 68 No. 2, 2007, pp. 437-460. http://www.ricam.oeaw.ac.at/people/page/fornasier/SIAM_Fornasier_March_067187.pdf

* Il Progetto Mantegna: storia e risultati (Italian) (R. Cazzato, G. Costa, A. Dal Farra, M. Fornasier, D. Toniolo, D. Tosato, C. Zanuso), in "Andrea Mantegna. La Cappella Ovetari a Padova" (Anna Maria Spiazzi, Alberta De Nicolo' Salmazo, Domenico Toniolo eds.), Skira, 2006. http://www.ricam.oeaw.ac.at/people/page/fornasier/libro.pdf

* Fast, robust, and efficient 2D pattern recognition for re-assembling fragmented images (M. Fornasier and D. Toniolo), Pattern Recognition, Vol. 38, 2005, pp. 2074-2087. http://www.ricam.oeaw.ac.at/people/page/fornasier/Pubblicazione.pdf

* Un metodo per la rappresentazione e il confronto di immagini a meno di rotazioni. Un contributo alla ricostruzione virtuale degli affreschi della Chiesa degli Eremitani in Padova (Italian) (M. Fornasier), Laurea thesis, Department of Pure and Applied Mathematics, University of Padua, Oct. 1999.

Related work:

* Rotation Invariance in Exemplar-based Image Inpainting (Master Thesis, M. Eller), Technical University of Munich, August 31 2013. http://www-m15.ma.tum.de/foswiki/pub/M15/Allgemeines/PublicationsEN/masterthesis_martin.pdf

* P. Arias, G. Facciolo, V. Caselles, and G. Sapiro. A variational framework for exemplar-based image inpainting. International Journal of Computer Vision, 93:319-347, 2011.

* Mathematics enters the picture (M. Fornasier), Proceedings of the conference Mathknow 2008 http://www.ricam.oeaw.ac.at/people/page/fornasier/mathsinpict.pdf

* Restoration of color images by vector valued BV functions and variational calculus (M. Fornasier and R. March), SIAM J. Appl. Math., Vol. 68 No. 2, 2007, pp. 437-460. http://www.ricam.oeaw.ac.at/people/page/fornasier/SIAM_Fornasier_March_067187.pdf

* Il Progetto Mantegna: storia e risultati (Italian) (R. Cazzato, G. Costa, A. Dal Farra, M. Fornasier, D. Toniolo, D. Tosato, C. Zanuso), in "Andrea Mantegna. La Cappella Ovetari a Padova" (Anna Maria Spiazzi, Alberta De Nicolo' Salmazo, Domenico Toniolo eds.), Skira, 2006. http://www.ricam.oeaw.ac.at/people/page/fornasier/libro.pdf

* Fast, robust, and efficient 2D pattern recognition for re-assembling fragmented images (M. Fornasier and D. Toniolo), Pattern Recognition, Vol. 38, 2005, pp. 2074-2087. http://www.ricam.oeaw.ac.at/people/page/fornasier/Pubblicazione.pdf

* Un metodo per la rappresentazione e il confronto di immagini a meno di rotazioni. Un contributo alla ricostruzione virtuale degli affreschi della Chiesa degli Eremitani in Padova (Italian) (M. Fornasier), Laurea thesis, Department of Pure and Applied Mathematics, University of Padua, Oct. 1999.

Short bio

Massimo Fornasier obtained his Laurea degree at the University of Padua with a thesis on the mathematical based restoration of the Mantegna frescoes in the Eremitani Church (the topic of this Colloquium talk).
He received his doctoral degree in Computational Mathematics
at the same University and, under co-supervision, at the University of Vienna. Later he worked at several international Universities, including the University of Rome "La Sapienza", the University of Vienna, and Princeton University. In 2006 he got a position as a Senior Scientist at the Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences in Linz and since April 2011 he leads as Full Professor (with a "Lighthouse Professorship") the Chair of Applied
Numerical Analysis at the Technical University of Munich. He additionally received several honors and awards, including the START-award of the Austrian research fund (2008), the rix de Boelpaepe" of the Royal Academy of Sciences of Belgium (2009), the Heisenberg Professorship of the German research fund (2010), the Biannual
Prize of the Italian Society of Applied and Industrial Mathematics (2011), and a Starting Grant of the European Research Council (2012).