Analytic Expressions for Stochastic Distances Between Relaxed Complex Wishart Distributions

Frery, Alejandro C.; Nascimento, Abraão D. C.; Cintra, Renato J.

doi:10.1109/tgrs.2013.2248737

Cited by 79 publications

(47 citation statements)

References 47 publications

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“…Proposition 1 is a test for the null hypothesis θ 1 = θ 2 based on Lemma 1. Frery et al [27] presented closed expressions for d KL when the random matrices X and Y follow the Wishart distribution:…”

Section: B the Kullback-leibler Distancementioning

confidence: 99%

Detecting Changes in Fully Polarimetric SAR Imagery With Statistical Information Theory

Nascimento

Frery

Cintra

2019

IEEE Trans. Geosci. Remote Sensing

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Images obtained from coherent illumination processes are contaminated with speckle. A prominent example of such imagery systems is the polarimetric synthetic aperture radar (PolSAR). For such remote sensing tool the speckle interference pattern appears in the form of a positive definite Hermitian matrix, which requires specialized models and makes change detection a hard task. The scaled complex Wishart distribution is a widely used model for PolSAR images. Such distribution is defined by two parameters: the number of looks and the complex covariance matrix.The last parameter contains all the necessary information to characterize the backscattered data and, thus, identifying changes in a sequence of images can be formulated as a problem of verifying whether the complex covariance matrices differ at two or more takes. This paper proposes a comparison between a classical change detection method based on the likelihood ratio and three statistical methods that depend on information-theoretic measures: the Kullback-Leibler distance and two entropies. The performance of these four tests was quantified in terms of their sample test powers and sizes using simulated data. The tests are then applied to actual PolSAR data. The results provide evidence that tests based on entropies may outperform those based on the Kullback-Leibler distance and likelihood ratio statistics. PUBLISHED IN THE IEEE TGRS 2 follow the Gaussian law. Thus, analyzing PolSAR images requires tailored image processing based on the statistical properties of speckled data.PolSAR theory prescribes that the returned (backscattered) signal of distributed targets is adequately represented by its complex covariance matrix. Under the assumption that the complex scattering coefficients are jointly circular Gaussian, the Wishart distribution is the statistical model for multilook PolSAR data. This paper adopts the assumption that a PolSAR image is well described by such distribution.Change detection methods aim at identifying differences in the scene configuration at distinct observation instants. Such procedures have achieved a prominent position in recent decades [2]. Indeed, literature reports several approaches for change detection problems, among them: (i) image ratioing [3]-[6], (ii) multitemporal coherence analysis [7], (iii) spatiotemporal contextual classification [8], [9], (iv) Hotelling-Lawley and likelihood ratio tests [10]-[19] and robust tests [20], (v) combination of image ratioing and the generalized minimum-error method [21], (vi) detection algorithms based on Lagrange optimization [22], (vii) information-theoretic measures for change detection [9], [23]-[30] and (viii) change detection with post-classification [31]. This paper advances points (iv) and (vii) above. The change detection process is theoretically rooted in the hypothesis test theory and the proposal of statistical similarity measures [32]. In particular, hypothesis tests based on the complex covariance matrix have been sought for PolSAR data analysis. Many statistical approaches hav...

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Section: B the Kullback-leibler Distancementioning

confidence: 99%

Detecting Changes in Fully Polarimetric SAR Imagery With Statistical Information Theory

Nascimento

Frery

Cintra

2019

IEEE Trans. Geosci. Remote Sensing

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“…Last but not least, for better confirming and validating our choice of Riemannian distance, we will provide in Section 4.3.4 a detailed comparison (i.e., in terms of retrieval performance and computation time) of this metric not only with the mentioned Mahalanobis and Kullback-Leibler metrics but also against some other distance measures of covariance matrices such as the log-Euclidean, the Wishart-like and the Bartlett distances [42,43].…”

Section: Dissimilarity Measure For Retrievalmentioning

confidence: 99%

Color Texture Image Retrieval Based on Local Extrema Features and Riemannian Distance

2017

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A novel efficient method for content-based image retrieval (CBIR) is developed in this paper using both texture and color features. Our motivation is to represent and characterize an input image by a set of local descriptors extracted from characteristic points (i.e., keypoints) within the image. Then, dissimilarity measure between images is calculated based on the geometric distance between the topological feature spaces (i.e., manifolds) formed by the sets of local descriptors generated from each image of the database. In this work, we propose to extract and use the local extrema pixels as our feature points. Then, the so-called local extrema-based descriptor (LED) is generated for each keypoint by integrating all color, spatial as well as gradient information captured by its nearest local extrema. Hence, each image is encoded by an LED feature point cloud and Riemannian distances between these point clouds enable us to tackle CBIR. Experiments performed on several color texture databases including Vistex, STex, color Brodazt, USPtex and Outex TC-00013 using the proposed approach provide very efficient and competitive results compared to the state-of-the-art methods.

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“…The comparison is made through a goodness-of-fit test, and the p-value of the test statistic is used to define the convolution matrix which will define the filter: the higher the p-value the larger the confidence and, thus, the importance, each observation will have in the convolution. In Torres et al's proposal, the tests are derived from h-/ divergences between multi-look scaled complex Wishart distributions for fully PolSAR data [21]. Their results are competitive with classical and advanced polarimetric filters, with respect to usual quantitative measures of quality.…”

Section: Related Workmentioning

confidence: 99%

Optical images-based edge detection in Synthetic Aperture Radar images

Silva

Frery

Sandri

et al. 2015

Knowledge-Based Systems

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We address the issue of adapting optical images-based edge detection techniques for use in Polarimetric Synthetic Aperture Radar (PolSAR) imagery. We modify the gravitational edge detection technique (inspired by the Law of Universal Gravity) proposed by Lopez-Molina et al, using the non-standard neighbourhood configuration proposed by Fu et al, to reduce the speckle noise in polarimetric SAR imagery. We compare the modified and unmodified versions of the gravitational edge detection technique with the well-established one proposed by Canny, as well as with a recent multiscale fuzzy-based technique proposed by Lopez-Molina et Alejandro We also address the issues of aggregation of gray level images before and after edge detection and of filtering. All techniques addressed here are applied to a mosaic built using class distributions obtained from a real scene, as well as to the true PolSAR image; the mosaic results are assessed using Baddeley's Delta Metric. Our experiments show that modifying the gravitational edge detection technique with a non-standard neighbourhood configuration produces better results than the original technique, as well as the other techniques used for comparison. The experiments show that adapting edge detection methods from Computational Intelligence for use in PolSAR imagery is a new field worthy of exploration.Comment: Accepted for publication in Knowledge-Based System

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Analytic Expressions for Stochastic Distances Between Relaxed Complex Wishart Distributions

Cited by 79 publications

References 47 publications

Detecting Changes in Fully Polarimetric SAR Imagery With Statistical Information Theory

Detecting Changes in Fully Polarimetric SAR Imagery With Statistical Information Theory

Color Texture Image Retrieval Based on Local Extrema Features and Riemannian Distance

Optical images-based edge detection in Synthetic Aperture Radar images

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