Skip to main content
Log in

A new PDE-based approach for singularity-preserving regularization: application to degraded characters restoration

  • Original Paper
  • Published:
International Journal on Document Analysis and Recognition (IJDAR) Aims and scope Submit manuscript

Abstract

The massive digitization of heritage documents has raised new prospects for research like degraded document image restoration. Degradations harm the legibility of the digitized documents and limit their processing. As a solution, we propose to tackle the problem of degraded text characters with PDE (partial differential equation)-based approaches. Existing PDE approaches do not preserve singularities and edge continuities while smoothing. Hence, we propose a new anisotropic diffusion by adding new constraints to the Weickert coherence-enhancing diffusion filter in order to control the diffusion process and to eliminate the inherent corner rounding. A qualitative improvement in the singularity preservation is thus achieved. Experiments conducted on degraded document images illustrate the effectiveness of the proposed method compared with other anisotropic diffusion approaches. We illustrate the performance with the study of the optical recognition accuracy rates.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Drira, F.: Towards restoring historic documents degraded over time. In: Second IEEE International Conference on Document Image Analysis for Libraries (DIAL’2006), Lyon, France, pp. 350–357. ISBN 0-7695-2531-4 (2006)

  2. Cannon M., Hochberg J., Kelly P.: Quality assessment and restoration of typewritten document images. Int. J. Document Anal. Recogn. 2, 80–89 (1999)

    Article  Google Scholar 

  3. Aurich, V., Weule, J.: Non-linear gaussian filters performing edge preserving diffusion. In: Proceedings of the DAGM Symposium, pp. 538–545. Springer, Berlin (1995)

  4. Rudin L., Osher S.: Nonlinear total variation based noise removal algorithms. Phys. D Nonlinear Phenom. 60, 259–268 (1992)

    Article  MATH  Google Scholar 

  5. Buades, A., Coll, B., Morel, J.: A non local algorithm for image denoising. In: Proceedings of International Conference on Computer Vision and Pattern Recognition (CVPR), vol. 2, pp. 60–65 (2005)

  6. Buades A., Coll B., Morel J.: A review of image denoising algorithms, with a new one. SIAM Interdis. J. Multiscale Model. Simul. 4(2), 290–530 (2005)

    MathSciNet  Google Scholar 

  7. Dauwe, A., Goossens, B., Luong, H., Philips, W.: A fast non-local image denoising algorithm. In: Proceedings of SPIE Electronic Imaging, vol. 6812 (2008)

  8. Coup P., Yger P., Prima S., Hellier P., Kervrann C., Barillot C.: An optimized blockwise nonlocal means denoising filter for 3-D magnetic resonance images. IEEE Trans. Med. Imaging 27(4), 425–441 (2008)

    Article  Google Scholar 

  9. Chatterjee, P., Milanfar, P.: A generalization of non-local means via kernel regression. In: Proceedings of SPIE Electronic Imaging, vol. 6814 (2008)

  10. Zimmer, S., Didas, S., Weickert, J.: A rotationally invariant block matching strategy improving image denoising with non-local means. In: Proceedings of International Workshop on Local andNon-Local Approximation in Image Processing, pp. 135–142 (2008)

  11. Aharon M., Elad M., Bruckstein A.: KSVD: An algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans. Signal Process. 54(11), 4311–4322 (2006)

    Article  Google Scholar 

  12. Nakagaki R., Katsaggelos A.: A VQ-based blind image restoration algorithm. IEEE Trans. Image Process. 12(9), 1044–1053 (2003)

    Article  Google Scholar 

  13. Roth S., Black M.J.: Fields of experts. Int. J. Comput. Vis. 82(2), 205–229 (2009)

    Article  Google Scholar 

  14. Mairal J., Elad M., Sapiro G.: Sparse representation for color image restoration. IEEE Trans. Image Process. 17, 53–69 (2008)

    Article  MathSciNet  Google Scholar 

  15. Nishida, H.: Restoring high-resolution binary images for text enhancement. In: ICIP, pp. 506–509 (2005)

  16. Zheng, Q., Kanungo, T.: Morphological degradation models and their use in document image restoration. In: ICIP’01, pp. I: 193–196 (2001)

  17. Liang, J., Haralick, R.M.: Document image restoration using binary morphological filters. In: SPIE’96, vol. 2660, pp. 274–285 (1996)

  18. Sattar F., Tay D.: Enhancement of document images using multiresolution and fuzzy logic techniques. Signal Process. Lett. 6, 249–252 (1999)

    Article  Google Scholar 

  19. Shi, Z., Govindaraju, V.: Historical Document Image Enhancement Using Background Light Intensity Normalization. In: 17th International Conference on Pattern Recognition (ICPR’04), vol. 1, pp. 473–476 (2004)

  20. Sarkar, P., Baird, H., Zhang, X.: Training on severely degraded text-line images. In: Proceedings of the International Conference on Document Analysis and Recognition, pp. 38–43 (2003)

  21. Tonazzini A., Vezzosi S., Bedini L.: Analysis and recognition of highly degraded printed characters. Int. J. Document Anal. Recogn. 6, 236–247 (2004)

    Article  Google Scholar 

  22. Luong, H., Philips, W.: Non-Local text image reconstruction. In: Ninth International Conference on Document Analysis and Recognition (ICDAR’2007), vol. 1, pp. 546–550 (2007)

  23. Banerjee, J., Namboodiri, A.M., Jawahar, C.V.: Contextual restoration of severely degraded document images. In: Proceeding of IEEE International Conference on CVPR, pp. 517–524 (2009)

  24. Tonazzini A., Salerno E., Bedini L.: Fast correction of bleed-through distortion in grayscale documents by a blind source separation technique. Int. J. Doc. Anal. Recogn. 10, 17–25 (2007)

    Article  Google Scholar 

  25. Wolf C.: Document Ink bleed-through removal with two hidden Markov random fields and a single observation field. IEEE Trans. Pattern Anal. Mach. Intell. 32, 431–447 (2010)

    Article  Google Scholar 

  26. Moghaddam R.F., Cheriet M.: RSLDI: restoration of single-sided low-quality document images. Pattern Recogn. Spec. Issue Handw. Recogn. 42, 3355–3364 (2009)

    MATH  Google Scholar 

  27. Nwogu, I., Shi, Z., Govindaraju, V.: PDE-based enhancement of low quality documents. In: Proceedings of the Ninth International Conference on Document Analysis and Recognition, vol. 01, pp. 541–545 (2007)

  28. Drira, F., Lebourgeois, F., Emptoz, H.: Restoring ink bleed-through degraded document images using a recursive unsupervised classification technique. In: DAS’2006, LNCS 3872. Nelson, New Zealand, pp. 38–49 (2006)

  29. Drira, F., Lebourgeois, F., Emptoz, H.: A modified mean shift algorithm for efficient document image restoration. In: Signal processing for image enhancement and multimedia processing. Springer, Berlin (2008). ISBN 978-0-387-72499-7, on-line copy http://www.springerlink.com/content/978-0-387-72499-7

  30. Ledda, A., Luong, H.Q., Philips, W., De Witte, V., Kerre, E.E.: Greyscale image interpolation using mathematical morphology. In: Proceedings of ACIVS (LNCS 4179), pp. 78–90 (2006)

  31. Likforman-Sulem, L., Darbon, J., Barney Smith, E.H.: Pre-processing of degraded printed documents by non-local means and total variation. In: International Conference on Document Analysis and Recognition 2009, pp. 758–762 (2009)

  32. Hobby, J.D., Baird, H.S., Zheng, Q., Kanungo, T.: Morphological degradation models and their use in document image restoration, ICIP’01, Greece, pp. 193–196 (2001)

  33. Hobby, J.D., Baird, H.S.: Degraded character image restoration. In: Proceedings of Document Analysis and Information Retrieval, Las Vegas (1996)

  34. Baird, H.S.: State of the art of document image degradation modeling. In: Proceedings of 4th IAPR International Workshop on Document Analysis Systems, vol. 1, Rio de Janeiro, Brazil (2000)

  35. Hobby, J.D., Ho, T.K.: Enhancing degraded document images via bitmap clustering and averaging. In: Proceeding of the Fourth International Conference on Document Analysis and Recognition, ICDAR’97, Germany, pp. 394–400 (1997)

  36. Whichello A., Yan H.: Linking broken character borders with variable sized masks to improve recognition. Pattern Recogn. 29(8), 1429–1435 (1996)

    Article  Google Scholar 

  37. http://www.impact-project.eu/

  38. Alvarez L., Guichard F., Lions P.L., Morel J.M.: Axioms and fundamental equations of images processing. Arch. Ration. Mech. Anal. 123(3), 199–257 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  39. Weickert, J.: a review of nonlinear diffusion filtering. In: Scale-Space Theory in Computer Vision, Volume 1252 of Lecture Notes in Computer Science, Utrecht, The Netherlands (1997)

  40. Weickert J.: Anisotropic Diffusion in Image Processing. Teubner-Verlag, Stuttgart (1998)

    MATH  Google Scholar 

  41. Alvarez L., Guichard F., Lions P.L., Morel J.M.: Axioms and fundamental equations of images processing. Arch. Ration. Mech. Anal. 123(3), 199–257 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  42. Tikhonov A., Arsenin V.: Solution of Ill-Posed Problems. Winston and Wiley, Washington, DC (1977)

    Google Scholar 

  43. Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. In: IEEE Transactions on Pattern Analysis and Machine Intelligence, pp. 629–639 (1990)

  44. Perona P., Shiota T., Malik J.: Anisotropic diffusion. In: Ter Haar Romeny, Bart M. (ed.) Geometry-Driven Diffusion in Computer Vision, pp. 229–254. Kluwer, Dordrecht (1994)

    Google Scholar 

  45. Catté F., Morel J.M., Lions P.L., Coll T.: Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal. 29, 182–193 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  46. Weickert, J.: Scale-space properties of nonlinear diffusion filtering with a diffusion tensor. Report No. 110. Laboratory of Technomathematics, University of Kaiserslautern, Germany (1994)

  47. Weickert J.: Anisotropic Diffusion in Image Processing. Teubner-Verlag, Stuttgart (1998)

    MATH  Google Scholar 

  48. Weickert, J.: Coherence-enhancing diffusion of colour images. In: The 7th National Symposium on Pattern Recognition and Image Analysis, Barcelona, Spain (1997)

  49. Sochen N., Kimmel R., Malladi R.: A geometrical framework for low level vision. IEEE Trans. Image Process., Spec. Issue PDE Based Image Process. 7(3), 310–318 (1998)

    MathSciNet  MATH  Google Scholar 

  50. Kimmel R., Malladi R., Sochen N.: Images as embedded maps and minimal surfaces: movies, color, texture, and volumetric medical images. Int. J. Comput. Vis. 39(2), 111–129 (2000)

    Article  MATH  Google Scholar 

  51. Tschumperlé, D., Deriche, R.: Vector-Valued image regularisation with PDE’s: a common framework for different applications. IEEE Trans. Pattern Anal. Mach. Intell. 27(4) (2005)

  52. Baird, H.S.: The state of the art of document image degradation modeling, in book. In: Digital Document Processing Advances in Pattern Recognition, pp. 261–279. doi:10.1007/978-1-84628-726-8-12 (2007)

  53. Barney Smith, E.H., Andersen, T.: Text degradations and OCR training. In: International Conference on Document Analysis and Recognition 2005, Seoul, Korea, pp. 834–838 (2005)

  54. Hale, C., Barney Smith, E.H.: Human image preference and document degradation models. In: International Conference on Document Analysis and Recognition 2007 (2007)

  55. Les prophéties de M. Michel Nostradamus, Nostradamus, Bibliothèque nationale de France, 1589, http://gallica2.bnf.fr/ark:/12148/bpt6k700592

  56. LE CONSTITUTIONNEL, journal politique et littéraire, exemplaire du Mardi 31 octobre 1815, Paris, ark:/12148/cb327475869/date, ISSN 17706165, Bibliothèque nationale de France, http://gallica.bnf.fr/ark:/12148/bpt6k648239f.pleinepage.langFR

  57. Le bourgeois gentilhomme, comédie-balet faite Chambort, pour le divertissement du Roy, Molière, 1671, Bibliothèque nationale de France, Rés. p-Yf-56, http://gallica2.bnf.fr/ark:/12148/bpt6k70212z

  58. Discours sur les avantages ou les désavantages qui résultent pour l’Europe de la découverte de l’Amérique, objet du prix proposé par M. l’abbé Raynal, Franois-Jean Chastellux, 1787, Bibliothèque nationale de France http://gallica2.bnf.fr/ark:/12148/bpt6k1157109

  59. http://gazettes18e.ish-lyon.cnrs.fr/

  60. Courrier d’Avignon, du 4 juillet 1775, http://gazettes18e.ish-lyon.cnrs.fr/

  61. Drira, F., Lebourgeois, F., Emptoz, H.: Document images restoration by a new tensor based diffusion process: application to the recognition of old printed documents. In: 10th International Conference on Document Analysis and Recognition (ICDAR), IEEE ed. Spain. pp. 321–325 (2009)

  62. An Epitomy of English History,Thomas May, Printed for N. Boddington at the Golden Ball in Duck lane, 1690, University of Michigan, digitized 5 june 2007, http://books.google.fr/books?id=kSE2AAAAMAAJ

  63. A vindication of the truth of Christian religion: against the objections of all modern opposers,Volume 1, Jacques Abbadie, 1694, New York Public Library, digitized 1st december 2005. http://books.google.fr/books?id=5crJcHvTpZcC

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fadoua Drira.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Drira, F., LeBourgeois, F. & Emptoz, H. A new PDE-based approach for singularity-preserving regularization: application to degraded characters restoration. IJDAR 15, 183–212 (2012). https://doi.org/10.1007/s10032-011-0165-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10032-011-0165-5

Keywords

Navigation