We analyze level set implementation of region snakes based on the maximum likelihood method for different noise models that belong to the exponential family. We show that this approach can improve segmentation results in noisy images and we demonstrate that the regularization term can be efficiently determined using an information theory-based approach, i.e., the minimum description length principle. The criterion to be optimized has no free parameter to be tuned by the user and the obtained segmentation technique is adapted to nonsimply connected objects.

Polar decomposition consists of representing an arbitrary Mueller matrix with a product of three simpler matrices, but, since these matrices do not commute, the result depends on the order in which they are multiplied. We show that the six possible decompositions can be classified into two families and that one of these families always leads to physical elementary matrices, whereas the other does not.

The spatio-temporal properties of partially polarized light are analyzed in order to separate partial polarization and partial coherence. For that purpose we introduce useful invariance properties which allow one to characterize intrinsic properties of the optical light independently of the particular experimental conditions. This approach leads to new degrees of coherence and their relation with measurable quantities is discussed. These results are illustrated on some simple examples.

In many imaging applications, the measured optical images are perturbed by strong fluctuations or boise. 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.

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