Philippe Réfrégier

Minimum description length synthetic aperture radar image segmentation

We present a new minimum description length (MDL) approach based on a deformable partition--a polygonal grid--for automatic segmentation of a speckled image composed of several homogeneous regions. The image segmentation thus consists in the estimation of the polygonal grid, or, more precisely, its number of regions, its number of nodes and the location of its nodes. These estimations are performed by minimizing a unique MDL criterion which takes into account the probabilistic properties of speckle fluctuations and a measure of the stochastic complexity of the polygonal grid. This approach then leads to a global MDL criterion without an undetermined parameter since no other regularization term than the stochastic complexity of the polygonal grid is necessary and noise parameters can be estimated with maximum likelihood-like approaches. The performance of this technique is illustrated on synthetic and real synthetic aperture radar images of agricultural regions and the influence of different terms of the model is analyzed.

Shannon entropy of partially polarized and partially coherent light with Gaussian fluctuations.

We propose to analyze Shannon entropy properties of partially coherent and partially polarized light with Gaussian probability distributions. It is shown that the Shannon entropy is a sum of simple functions of the intensity, of the degrees of polarization, and of the intrinsic degrees of coherence that have been recently introduced. This analysis clearly demonstrates the contribution of partial polarization and of partial coherence to the characterization of disorder of the light provided by the Shannon entropy, which is a standard measure of randomness. We illustrate these results on two simple examples.

Estimation of the degree of polarization in active coherent imagery by using the natural representation.

We address the problem of degree of polarization estimation in polarization diversity images. We consider active imaging techniques with laser illumination, which have the appealing feature of revealing contrasts that do not appear in conventional intensity images. These techniques provide two images of the same scene that are perturbed with speckle noise. Because of the presence of nonhomogeneity in the reflected intensity, it can be preferable to perform image analysis of the orthogonal-state contrast image, which is a measure of the degree of polarization of the reflected light when the coherency matrix is diagonal. It has been shown that a simple nonlinear transformation of this orthogonal-state contrast image leads to an image perturbed with additive symmetrical noise on which simple and efficient estimation and detection techniques can be applied. We propose to precisely analyze estimation properties of the degree of polarization using this natural representation. In particular, we determine the Cramer-Rao bound of the polarization degree estimation and the variance of the proposed estimator, and we study the estimators efficiency as a function of the speckle order for different measurement strategies.

Coherence polarization filtering and relation with intrinsic degrees of coherence.

It is demonstrated for stationary fields that when the polarization state of the electric field can be modified arbitrarily the maximal value of the modulus of the degree of coherence proposed by Wolf [Phys. Lett. A312, 263 (2003)] is equal to the largest intrinsic degree of coherence. In addition, when the light is a mixing of a coherent light that satisfies the factorization condition in the two spatial variables with a statistically uncorrelated, partially coherent, perfectly polarized light, but with a nonparallel polarization state, we show that the polarization modifications that maximize the modulus of the Wolf degree of coherence lead to a light that also satisfies the factorization condition.

Performance parameters for detection in low-flux coherent images

We analyze the optimization of low-flux coherent active imagery systems for target detection. We demonstrate that, unlike the Fisher ratio, the Bhattacharyya distance is an efficient figure of merit when one uses detection algorithms based on the generalized likelihood ratio test for realistic situations when the target and the background mean values are unknown. For example, we show that detection capabilities can be better if the pulse energy is divided into four shots, whereas using more than ten shots does not significantly improve the results.

Photon-noise effect on detection in coherent active images

We analyze photon-noise effects on target detection performance in low-flux coherent active imagery systems. We show that when photon noise is expected, the performance of classical detection techniques designed for pure and fully developed speckle images can be improved with no increase in algorithm complexity. Furthermore, the mean photon number under which photon noise becomes sensitive is higher when the target and background mean values are unknown than in the idealized case, where they are assumed to be known, and when the reflectivity ratio between the target and the background is low.

Stochastic Complexity based Image Segmentation with unknown Noise Model

We propose a general statistical image segmentation method which does not need any a priori knowledge of the probability density functions (PDF) of the grey levels of the image. This method is based on the minimization of the stochastic complexity (Minimum Description Length principle) which leads to optimize a criterion without parameter to be tuned by the user which is adapted to the PDF of the grey levels of the image. We apply this method to three partition descriptors: a polygonal active contour, a level set implementation and a polygonal active grid. We illustrate the technique on real images.

Non-parametric partitioning of SAR images

We describe and analyse a generalization of a parametric segmentation technique adapted to Gamma distributed SAR images to a simple non parametric noise model. The partition is obtained by minimizing the stochastic complexity of a quantized version on Q levels of the SAR image and lead to a criterion without parameters to be tuned by the user. We analyse the reliability of the proposed approach on synthetic images. The quality of the obtained partition will be studied for different possible strategies. In particular, one will discuss the reliability of the proposed optimization procedure. Finally, we will precisely study the performance of the proposed approach in comparison with the statistical parametric technique adapted to Gamma noise. These studies will be led by analyzing the number of misclassified pixels, the standard Hausdorff distance and the number of estimated regions.

Intrinsic degrees of coherence of partially polarized light

We address the problem of defining degrees of coherence for partially polarized light. We discuss a new theoretical approach that introduces intrinsic degrees of coherence. These parameters make it possible to separate partial polarization and partial coherence and are measurable quantities. We analyze their physical meaning and propose a method to measure them with a finite number of measurement.

Optimal Matching of images at Low Photon Level

Publisher Summary A classical problem in image processing consists in determining the translation from one noisy image to a reference image. For the astronomical application that this chapter considers, the image detector is fastened to a shuttle whose motion blurs the observed images. To preserve the quality of this image, the exposure time of the detector is very small, and as a consequence, very few photons can be present in each observation. All the observed images S p are matched and added together in order to built a final image r . At low photon levels, the observed image S p is mainly corrupted by the discrete nature of the photon which is described by a Poisson statistics. The chapter considers the problem of matching astronomical images with a very low photon level. It also analyzes the performances of the optimal technique when the noise of the moved images is no longer Gaussian, and the classical linear intercorrelation method fails.