Skip to main content

Mathematics enters the picture

  • Chapter
Mathknow

Part of the book series: MS&A ((MS&A,volume 3))

Abstract

Can one of the most important Italian Renaissance frescoes reduced to hundreds of thousands of framents 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 short paper we want to exemplify, hopefully effectively by taking advantage of the seduction of art, how mathematics today can be applied to real-life problems which were considered unsolvable only few years ago.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aubert, G., Kornprobst, P.: Mathematical Problems in Image Processing. Partial Differential Equations and the Calculus of Variation. Springer, Heidelberg (2002)

    Google Scholar 

  2. Arsenault, H.H., Hsu, Y.N., Chalasinska-Macukow, K.: Rotation-invariant pattern recognition. Opt. Eng. 23, 705–709 (1984)

    Google Scholar 

  3. Brandi, C.: Il Mantegna Ricostituito. L’Immagine I, 179–180 (1947)

    Google Scholar 

  4. Cazzato, R.: Un Metodo per la Ricolorazione di Immagini e Altri Strumenti per il Restauro. Il Progetto Mantegna e gli Affreschi nella Chiesa degli Eremitani (Italian). Laurea thesis, University of Padua (2007)

    Google Scholar 

  5. Cazzato, R., Costa, G. Dal Farra, A., Fornasier, M., Toniolo, D., Tosato, D., Zanuso, C.: Il Progetto Mantegna: storia e risultati. In: Spiazzi, A.M., De Nicolò Salmazo, A., Tiniolo, D. (eds.) Andrea Mantegna. La Cappella Ovetari a Padova. Skira (2006)

    Google Scholar 

  6. Daubechies, I.: Ten Lectures on Wavelets. SIAM (1992)

    Google Scholar 

  7. De Nicolò Salmazo, A.: Le „Storie dei santi Giacomo e Cristoforo“ nella chiesa degli Eremitani. In: Il soggiorno padovano di Andrea Mantegna, pp. 31–86. Cittadella, Padova (1993)

    Google Scholar 

  8. Fornasier, M.: Faithful recovery of vector valued functions from incomplete data. Recolorization and art restoration. In: Sgallari, F., Murli, A., Paragios, N. (eds.) Proceedings of the First International Conference on Scale Space Methods and Variational Methods in Computer Vision. Lecture Notes in Computer Science 4485, 116–127 (2007)

    Google Scholar 

  9. Fornasier, M.: Function spaces inclusions and rate of convergence of Riemanntype sums in numerical integration. Numer. Funct. Anal. Opt. 24(1–2), 45–57 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  10. Fornasier, M.: Nonlinear projection recovery in digital inpainting for color image restoration. J. Math. Imaging Vis. 24(3), 359–373 (2006)

    Article  MathSciNet  Google Scholar 

  11. Fornasier, M., March, R.: Restoration of color images by vector valued BV functions and variational calculus. SIAM J. Appl. Math. 68(2) 437–460 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  12. Fornasier, M., Ramlau, R., Teschke, G.: A comparison of joint sparsity and total variation minimization algorithms in a real-life art restoration problem, to appear in Adv. Comput. Math. (2008) doi:10.1007/s10444-008-9103-6

    Google Scholar 

  13. Fornasier, M., Toniolo, D.: Fast, robust, and efficient 2D pattern recognition for re-assembling fragmented images. Pattern Recognition 38, 2074–2087 (2005)

    Article  Google Scholar 

  14. Galeazzi, G., Toniolo, D.: I frammenti della Chiesa degli Eremitani: un approccio matematico alla soluzione del problema, Atti del convengo „Filosofia e Tecnologia del restauro“ gli ‘Emblémata’, Abbazia di Praglia, 89–97 (1994)

    Google Scholar 

  15. Galeazzi, G., Toniolo, D.: Il problema della ricostruzione degli affreschi della Chiesa degli Eremitani in Padova. (Italian), Atti del convegno „Il complesso basilicale di San Francesco di Assisi ad un anno dal terremoto“, Assisi (1998)

    Google Scholar 

  16. Wolf, K.B.: Integral Transforms in Science and Engineering. Mathematical Concepts and Methods in Science and Engineering. vol. 11, XIII. Plenum Press, New York, London (1979)

    MATH  Google Scholar 

  17. Watson, G.N.: Theory of Bessel Functions. Cambridge University Press, Cambridge (1966)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Italia, Milan

About this chapter

Cite this chapter

Fornasier, M. (2009). Mathematics enters the picture. In: Emmer, M., Quarteroni, A. (eds) Mathknow. MS&A, vol 3. Springer, Milano. https://doi.org/10.1007/978-88-470-1122-9_17

Download citation

Publish with us

Policies and ethics