## Bhattacharyya distance as a contrast parameter for statistical processing of noisy optical images

JOSA A, Vol. 21, Issue 7, pp. 1231-1240 (2004)

http://dx.doi.org/10.1364/JOSAA.21.001231

Enhanced HTML Acrobat PDF (524 KB)

### Abstract

In many imaging applications, the measured optical images are perturbed by strong fluctuations or noise. This can be the case, for example, for coherent-active or low-flux imagery. In such cases, the noise is not Gaussian additive and the definition of a contrast parameter between two regions in the image is not always a straightforward task. We show that for noncorrelated noise, the Bhattacharyya distance can be an efficient candidate for contrast definition when one uses statistical algorithms for detection, location, or segmentation. We demonstrate with numerical simulations that different images with the same Bhattacharyya distance lead to equivalent values of the performance criterion for a large number of probability laws. The Bhattacharyya distance can thus be used to compare different noisy situations and to simplify the analysis and the specification of optical imaging systems.

© 2004 Optical Society of America

**OCIS Codes**

(030.0030) Coherence and statistical optics : Coherence and statistical optics

(030.4280) Coherence and statistical optics : Noise in imaging systems

**History**

Original Manuscript: November 7, 2003

Revised Manuscript: January 29, 2004

Manuscript Accepted: January 29, 2004

Published: July 1, 2004

**Citation**

François Goudail, Philippe Réfrégier, and Guillaume Delyon, "Bhattacharyya distance as a contrast parameter for statistical processing of noisy optical images," J. Opt. Soc. Am. A **21**, 1231-1240 (2004)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-21-7-1231

Sort: Year | Journal | Reset

### References

- J. W. Goodman, “The speckle effect in coherence imaging,” in Statistical Optics (Wiley, New York, 1985), pp. 347–356.
- J. W. Goodman, “Some effects of target-induced scintillation on optical radar performance,” Proc. IEEE 53, 1688–1700 (1965). [CrossRef]
- F. Goudail, N. Roux, Ph. Réfrégier, “Performance parameters for detection in low-flux coherent images,” Opt. Lett. 28, 81–83 (2003). [CrossRef] [PubMed]
- Ph. Réfrégier, F. Goudail, “Invariant polarimetric contrast parameters for coherent light,” J. Opt. Soc. Am. A 19, 1223–1233 (2002). [CrossRef]
- A. O. Hero, C. Guillouet, “Robust detection of SAR/IR targets via invariance,” in Proceedings of the Sixth IEEE International Conference on Image Processing and its Applications (Institute of Electrical and Electronics Engineers, New York, 1997), pp. 472–475.
- J. A. O’Sullivan, R. E. Blahut, D. L. Snyder, “Information-theoretic image formation,” IEEE Trans. Inf. Theory 44, 2094–2123 (1998). [CrossRef]
- A. D. Lanterman, A. J. O’Sullivan, M. I. Miller, “Kullback-Leibler distances for quantifying clutter and models,” Opt. Eng. (Bellingham) 38, 2134–2146 (1999). [CrossRef]
- A. Jain, P. Moulin, M. I. Miller, K. Ramchandran, “Information-theoretic bounds on target recognition performance based on degraded image data,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 1153–1166 (2002). [CrossRef]
- T. M. Cover, J. A. Thomas, Elements of Information Theory (Wiley, New York, 1991).
- H. H. Barrett, C. K. Abbey, E. Clarkson, “Objective assessment of image quality. III. ROC metrics, ideal observers and likelihood generating functions,” J. Opt. Soc. Am. A 15, 1520–1535 (1998). [CrossRef]
- J. Shapiro, “Bounds on the area of the roc curve,” J. Opt. Soc. Am. A 16, 53–57 (1999). [CrossRef]
- E. Clarkson, H. H. Barrett, “Approximations to ideal observer performance on signal detection tasks,” Appl. Opt. 39, 1783–1793 (2000). [CrossRef]
- E. Clarkson, “Bounds on the area under the receiver oper-ating characteristic curve for the ideal observer,” J. Opt. Soc. Am. A 19, 1963–1968 (2002). [CrossRef]
- J. Rissanen, “Modeling by shortest data description,” Automatica 14, 465–471 (1978). [CrossRef]
- S. A. Kassam, “Optimal quantization for signal detection,” IEEE Trans. Commun. 25, 479–484 (1977). [CrossRef]
- H. V. Poor, J. B. Thomas, “Application of Ali-Silvey distance measures in the design of general quantizers for binary decision systems,” IEEE Trans. Commun. 25, 893–900 (1977). [CrossRef]
- H. V. Poor, “Elements of hypothesis testing,” in An Introduction to Signal Detection and Estimation (Springer-Verlag, New York, 1994), pp. 5–39.
- M. Basseville, “Distance measures for signal processing and pattern recognition,” Signal Process. 18, 349–369 (1989). [CrossRef]
- V. Pagé, F. Goudail, Ph. Réfrégier, “Improved robust-ness of target location in nonhomogeneous backgrounds by use of the maximum likelihood ratio test location algorithm,” Opt. Lett. 24, 1383–1385 (1999). [CrossRef]
- S. M. Kay, “Statistical decision theory II,” in Fundamentals of Statistical Signal Processing, Vol. II: Detection Theory (Prentice Hall, Upper Saddle River, N.J., 1998), pp. 186–247.
- T. S. Ferguson, “Exponential families of distributions,” in Mathematical Statistics, a Decision Theoretic Approach (Academic, New York, 1967), pp. 125–132.
- O. Ruch, Ph. Réfrégier, “Minimal-complexity segmentation with a polygonal snake adapted to different optical noise models,” Opt. Lett. 41, 977–979 (2001). [CrossRef]
- J. Rissanen, Stochastic Complexity in Statistical Inquiry (World Scientific, Singapore, 1989).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.