Evaluation of Sharpness Measures and Proposal of a Stop Criterion for Reverse Diffusion in the Context of Image Deblurring

Pol Moreno, Felipe Calderero

Abstract

The heat equation can be used to model the diffusion process shown in a defocused (blurry) region of a picture taken with conventional camera lens. The original focused image can be recovered by reverting the heat equation, that is, by reverse diffusion. However, the main difficulty with this technique is that it becomes unstable very quickly due to the finite precision of pixel values and the image values blow up. For that reason, detecting the exact time when the reverse diffusion process should stop is crucial. The goal of this work it to evaluate the behavior of different non-reference state-of-the-art sharpness measures (that is, when a perfectly focused image is not available) for the forward and inverse diffusion processes and to propose a robust stop criterion to reliably detect the moment before each region becomes unstable. To find out a good stop criterion, we carry out a set of experiments with test and real images. The results in this paper can be valuable not only to estimate monocular depth from blur cues, but also to any other image processing fields that require image deblurring.

References

  1. Aydin, T. and Akgul, Y. (2008). A new adaptive focus measure for shape from focus. In Proceedings of the British Machine Vision Conference, pages 8.1-8.10.
  2. Batten, C. (2000). Autofocusing and astigmatism correction in the scanning electron microscope. PhD thesis, University of Cambridge.
  3. Blanchet, G. and Moisan, L. (2012). An explicit sharpness index related to global phase coherence. In Acoustics, Speech and Signal Processing (ICASSP), 2012 IEEE International Conference on, pages 1065 -1068.
  4. Blanchet, G., Moisan, L., and Rougé, B. (2008). Measuring the global phase coherence of an image. In Image Processing, 2008. ICIP 2008. 15th IEEE International Conference on, pages 1176-1179. IEEE.
  5. Dimiccoli, M. and Salembier, P. (2009). Exploiting tjunctions for depth segregation in single images. In Acoustics, Speech and Signal Processing, 2009. ICASSP 2009. IEEE International Conference on, pages 1229-1232. IEEE.
  6. Favaro, P., Soatto, S., Burger, M., and Osher, S. (2008). Shape from defocus via diffusion. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 30(3):518 -531.
  7. Ferzli, R. and Karam, L. (2009). A no-reference objective image sharpness metric based on the notion of just noticeable blur (jnb). Image Processing, IEEE Transactions on, 18(4):717-728.
  8. Forsyth, D. and Ponce, J. (2002). Computer vision: a modern approach. Prentice Hall Professional Technical Reference.
  9. Hoiem, D., Efros, A., and Hebert, M. (2011). Recovering occlusion boundaries from an image. International Journal of Computer Vision, 91(3):328-346.
  10. Horn, R. and Johnson, C. (1990). Matrix analysis. Cambridge university press.
  11. Lindeberg, T. (1993). Detecting salient blob-like image structures and their scales with a scale-space primal sketch: a method for focus-of-attention. International Journal of Computer Vision, 11(3):283-318.
  12. Mandelbrot, B. and Wallis, J. (1969). Some long-run properties of geophysical records. Water resources research, 5(2):321-340.
  13. Moisan, L. (2011). Periodic plus smooth image decomposition. Journal of Mathematical Imaging and Vision, 39(2):161-179.
  14. Namboodiri, V. and Chaudhuri, S. (2008). Recovery of relative depth from a single observation using an uncalibrated (real-aperture) camera. In Computer Vision and Pattern Recognition, 2008. CVPR 2008. IEEE Conference on, pages 1-6. IEEE.
  15. Palou, G. and Salembier, P. (2011). Occlusion-based depth ordering on monocular images with binary partition tree. In Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on, pages 1093-1096. IEEE.
  16. Rajagopalan, A., Chaudhuri, S., and Mudenagudi, U. (2004). Depth estimation and image restoration using defocused stereo pairs. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 26(11):1521 - 1525.
  17. Saxena, A., Chung, S., and Ng, A. (2008). 3-d depth reconstruction from a single still image. International Journal of Computer Vision, 76(1):53-69.
  18. Shaked, D. and Tastl, I. (2005). Sharpness measure: Towards automatic image enhancement. In Image Processing, 2005. ICIP 2005. IEEE International Conference on, volume 1, pages I-937. IEEE.
  19. Sporring, J. and Weickert, J. (1999). Information measures in scale-spaces. Information Theory, IEEE Transactions on, 45(3):1051 -1058.
Download


Paper Citation


in Harvard Style

Moreno P. and Calderero F. (2013). Evaluation of Sharpness Measures and Proposal of a Stop Criterion for Reverse Diffusion in the Context of Image Deblurring . In Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2013) ISBN 978-989-8565-47-1, pages 69-77. DOI: 10.5220/0004271200690077


in Bibtex Style

@conference{visapp13,
author={Pol Moreno and Felipe Calderero},
title={Evaluation of Sharpness Measures and Proposal of a Stop Criterion for Reverse Diffusion in the Context of Image Deblurring},
booktitle={Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2013)},
year={2013},
pages={69-77},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004271200690077},
isbn={978-989-8565-47-1},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2013)
TI - Evaluation of Sharpness Measures and Proposal of a Stop Criterion for Reverse Diffusion in the Context of Image Deblurring
SN - 978-989-8565-47-1
AU - Moreno P.
AU - Calderero F.
PY - 2013
SP - 69
EP - 77
DO - 10.5220/0004271200690077