Biomedical subjects

Philippe Réfrégier

Publications and source records attributed to Philippe Réfrégier.

At least 19 recordsLinked to original sources

PubMed2006

Cramer-Rao lower bound for the estimation of the degree of polarization in active coherent imagery at low photon levels.

The degree of polarization (DOP) is an important tool in many optical measurement and imaging applications. We address the problem of its estimation in images that are perturbed with both speckle and photon noise, by determining the Cramer-Rao lower bounds (CRLBs) when the illuminated materials are purely depolarizing. We demonstrate that the CRLBs are simply the sum of the CRLBs due to speckle noise and Poisson noise. We use this result to analyze the influence of different optical parameters on DOP estimation.

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PubMed2006

Linear relations of partially polarized and coherent electromagnetic fields.

We show that having a Wolf degree of coherence of unit modulus or having intrinsic degrees of coherence of unit modulus imply different relations between the electric fields of the light. The mean square meaning of such relations is discussed. On the one hand, we demonstrate that if the intrinsic degrees of coherence are equal to 1, then there is a linear relation between the electrical fields. On the other hand, we show that a Wolf degree of coherence of unit modulus corresponds to a stronger property that implies that the fields have to be proportional.

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PubMed2006

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.

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PubMed2006

Nonparametric statistical snake based on the minimum stochastic complexity.

We propose a nonparametric statistical snake technique that is based on the minimization of the stochastic complexity (minimum description length principle). The probability distributions of the gray levels in the different regions of the image are described with step functions with parameters that are estimated. The segmentation is thus obtained by minimizing a criterion that does not include any parameter to be tuned by the user. We illustrate the robustness of this technique on various types of images with level set and polygonal contour models. The efficiency of this approach is also analyzed in comparison with parametric statistical techniques.

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PubMed2006

Minimal stochastic complexity image partitioning with unknown noise model.

We present a generalization of a new statistical technique of image partitioning into homogeneous regions to cases where the family of the probability laws of the gray-level fluctuations is a priori unknown. For that purpose, the probability laws are described with step functions whose parameters are estimated. This approach is based on a polygonal grid which can have an arbitrary topology and whose number of regions and regularity of its boundaries are obtained by minimizing the stochastic complexity of the image. We demonstrate that efficient homogeneous image partitioning can be obtained when no parametric model of the probability laws of the gray levels is used and that this approach leads to a criterion without parameter to be tuned by the user. The efficiency of this technique is compared to a statistical parametric technique on a synthetic image and is compared to a standard unsupervised segmentation method on real optical images.

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PubMed2006

Invariant polarimetric contrast parameters of light with Gaussian fluctuations in three dimensions.

We propose a rigorous definition of the minimal set of parameters that characterize the difference between two partially polarized states of light whose electric fields vary in three dimensions with Gaussian fluctuations. Although two such states are a priori defined by eighteen parameters, we demonstrate that the performance of processing tasks such as detection, localization, or segmentation of spatial or temporal polarization variations is uniquely determined by three scalar functions of these parameters. These functions define a "polarimetric contrast" that simplifies the analysis and the specification of processing techniques on polarimetric signals and images. This result can also be used to analyze the definition of the degree of polarization of a three-dimensional state of light with Gaussian fluctuations in comparison, with respect to its polarimetric contrast parameters, with a totally depolarized light. We show that these contrast parameters are a simple function of the degrees of polarization previously proposed by Barakat [Opt. Acta 30, 1171 (1983)] and Setälä et al. [Phys. Rev. Lett. 88, 123902 (2002)]. Finally, we analyze the dimension of the set of contrast parameters in different particular situations.

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PubMed2006

Kullback relative entropy and characterization of partially polarized optical waves.

Different properties of partially polarized light are discussed using the Kullback relative entropy, which provides a physically meaningful measure of proximity between probability density functions (PDFs). For optical waves with a Gaussian PDF, the standard degree of polarization is a simple function of the Kullback relative entropy between the considered optical light and a totally depolarized light of the same intensity. It is shown that the Kullback relative entropies between different PDFs allow one to define other properties such as a degree of anisotropy and a degree of non-Gaussianity. It is also demonstrated that, in dimension three, the Kullback relative entropy between a partially polarized light and a totally depolarized light can lead to natural definitions of two degrees of polarization needed to characterize the polarization state. These analyses enlighten the physical meaning of partial polarization of light waves in terms of a measure of disorder provided by the Shannon entropy.

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PubMed2006

Estimation of the degree of polarization of coherent light in the presence of uniform and nonuniform illumination.

We address estimation of the degree of polarization (DOP) in active images acquired under coherent light when the coherency matrix of the backscattered light is diagonal. We consider cases when the illumination intensity is uniform on the scene and when it is not, and we take into account different parametrizations of the DOP. In all cases, we determine the maximum-likelihood (ML) estimators and compare their variances with the Cramer-Rao lower bound for unbiased estimation. When illumination is not uniform, the ML estimators are solutions of equations that have to be solved numerically. We show that simpler estimators based on the trimmed mean make it possible to approach performance of ML estimators at lower computational cost.

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PubMed2006

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.

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PubMed2005

Mutual information-based degrees of coherence of partially polarized light with Gaussian fluctuations.

The spatiotemporal coherence properties of partially polarized light with Gaussian probability distributions are analyzed using the mutual information that is a standard measure of statistical dependence. This approach leads to intrinsic degrees of coherence that have powerful invariance properties and that provide new information in comparison with other recently introduced degrees of coherence.

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PubMed2005

Minimal stochastic complexity snake-based technique adapted to an unknown noise model.

We propose a polygonal snake segmentation technique adapted to objects that can be composed of several regions with gray-level fluctuations described by a priori unknown probability laws. This approach is based on a histogram equalization and on the minimization of a criterion without parameter to be tuned by the user. We demonstrate the efficiency of this approach, which has low computational cost, on synthetic and real images perturbed by different types of optical noise.

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PubMed2005

Polarization degree of optical waves with non-Gaussian probability density functions: Kullback relative entropy-based approach.

The definition of degree of polarization for non-Gaussian partially polarized light is analyzed. A general framework based on the Kullback relative entropy is developed, and properties that enlighten the physical meaning of the degree of polarization are established. In particular, it is shown how the degree of polarization is related to the measure of proximity between probability density functions and to the measure of disorder provided by the Shannon entropy.

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PubMed2005

Cramer-Rao lower bounds on the estimation of the degree of polarization in coherent imaging systems.

We analyze the estimation precision of the parameter of the orthogonal state contrast image (OSCI) under coherent illumination. This parameter represents the degree of polarization of the light if the materials that compose the scene are purely depolarizing. Two different estimation modes are considered, depending on the uniformity of the illumination of the scene. We first determine lower bounds on the estimation precision in both cases by computing the Cramer-Rao lower bounds (CRLBs) for unbiased estimation. This allows us to compare the potential precision that can be reached in each mode. We then consider the estimators based on empirical averaging of the data, and we show that there are cases where they are strongly biased. We thus propose and characterize another estimator based on the natural representation of the OSCI, which is asymptotically unbiased and whose variance is close to the unbiased CRLB.

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PubMed2004

Information-theory-based snake adapted to multiregion objects with different noise models.

We propose a segmentation technique adapted to objects composed of several regions with gray-level fluctuations described by different probability laws. This approach is based on information theory techniques and leads to a multiregion polygonal snake driven by the minimization of a criterion without any parameters to be tuned by the user. We demonstrate the improvements obtained with this approach as well as its low computational cost. This approach is compatible with applications such as object recognition and object tracking with nonrigid deformation in images perturbed by different types of optical noise.

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PubMed2004

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.

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PubMed2004

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

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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PubMed2004

Entropy of partially polarized light and application to statistical processing techniques.

We have analyzed entropy properties of coherent and partially polarized light in an arbitrary number of spatial dimensions. We show that for Gaussian fields, the Shannon entropy is a simple function of the intensity and of the Barakat degree of polarization. In particular, we provide a probabilistic interpretation of this definition of the degree of polarization. Using information theory results, we also deduce some physical properties of partially polarized light such as additivity of the entropy and depolarization effects induced by mixing partially polarized states of light. Finally, we demonstrate that entropy measures can play an important role in segmentation and detection tasks.

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PubMed2004

Speckle removal using a maximum-likelihood technique with isoline gray-level regularization.

We propose a method based on the maximum-likelihood technique for removing speckle patterns that plague coherent images. The proposed method is designed for images whose gray levels vary continuously in space. The image model is based on a lattice of nodes corresponding to vertices of triangles in which the gray level of each pixel is produced by linear interpolation. A constraint on isoline gray levels is introduced to regularize the solution.

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