IMAGE COMPLETION USING A DIFFUSION DRIVEN MEAN CURVATURE FLOW IN A SUB-RIEMANNIAN SPACE

Gonzalo Sanguinetti, Giovanna Citti, Alessandro Sarti

Abstract

In this paper we present an implementation of a perceptual completion model performed in the three dimensional space of position and orientation of level lines of an image. We show that the space is equipped with a natural subriemannian metric. This model allows to perform disocclusion representing both the occluding and occluded objects simultaneously in the space. The completion is accomplished by computing minimal surfaces with respect to the non Euclidean metric of the space. The minimality is achieved via diffusion driven mean curvature flow. Results are presented in a number of cognitive relevant cases.

References

  1. Ambrosio, L. and Masnou, S. (2005). On a variational problem arising in image reconstruction.
  2. August, J. and Zucker, S. W. (2003). Sketches with curvature: The curve indicator random field and markov processes. IEEE Trans. Pattern Anal. Mach. Intell, 25(4):387-400.
  3. Ballester, C., Bertalmío, M., Caselles, V., Sapiro, G., and Verdera, J. (2001). Filling-in by joint interpolation of vector fields and gray levels. IEEE Transactions on Image Processing, 10(8):1200-1211.
  4. Ben-Shahar, O. and Zucker, S. W. (2004). Geometrical computations explain projection patterns of longrange horizontal connections in visual cortex. Neural Computation, 16(3):445-476.
  5. Bertalmío, M., Sapiro, G., Caselles, V., and Ballester, C. (2000). Image inpainting. In SIGGRAPH, pages 417- 424.
  6. Chan, T. F. and Shen, J. (2001). Mathematical models for local nontexture inpaintings. Journal of Applied Mathematics, 62(3):1019-1043.
  7. Citti, G. and Sarti, A. (2006). A cortical based model of perceptual completion in the roto-translation space. Journal of Mathematical Imaging and Vision, 24(3):307- 326.
  8. Hladky, R. K. and Pauls, S. D. (2005). Minimal surfaces in the roto-translation group with applications to a neuro-biological image completion model. Comment: 35 pages, 15 figures.
  9. Kanisza, G. (1979). Organization in Vision: Essays on Gestalt Perception. Praeger, New York, NY.
  10. Masnou, S. and Morel, J.-M. (1998). Level lines based disocclusion. In ICIP (3), pages 259-263.
  11. Medioni, G. (2000). Tensor voting: Theory and applications.
  12. Merriman, B., Bence, J. K., and Osher, S. J. (1998). Diffusion generated motion by mean curvature. Computational Crystal Growers Workshop, J. Taylor Sel. Taylor (Ed).
  13. Nitzberg, M. and Mumford, D. (1990). The 2.1-D sketch. In International Conference on Computer Vision, pages 138-144.
  14. Petitot, J. and Tondut, Y. (1999). Vers une neurogéométrie. fibrations corticales, structures de contact et contours subjectifs modaux.
  15. Williams, L. R. and Jacobs, D. W. (1995). Stochastic completion fields: A neural model of illusory contour shape and salience. In ICCV, pages 408-415.
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Paper Citation


in Harvard Style

Sanguinetti G., Citti G. and Sarti A. (2008). IMAGE COMPLETION USING A DIFFUSION DRIVEN MEAN CURVATURE FLOW IN A SUB-RIEMANNIAN SPACE . In Proceedings of the Third International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2008) ISBN 978-989-8111-21-0, pages 46-53. DOI: 10.5220/0001075800460053


in Bibtex Style

@conference{visapp08,
author={Gonzalo Sanguinetti and Giovanna Citti and Alessandro Sarti},
title={IMAGE COMPLETION USING A DIFFUSION DRIVEN MEAN CURVATURE FLOW IN A SUB-RIEMANNIAN SPACE},
booktitle={Proceedings of the Third International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2008)},
year={2008},
pages={46-53},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001075800460053},
isbn={978-989-8111-21-0},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Third International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2008)
TI - IMAGE COMPLETION USING A DIFFUSION DRIVEN MEAN CURVATURE FLOW IN A SUB-RIEMANNIAN SPACE
SN - 978-989-8111-21-0
AU - Sanguinetti G.
AU - Citti G.
AU - Sarti A.
PY - 2008
SP - 46
EP - 53
DO - 10.5220/0001075800460053