Geodesics on the Manifold of Multivariate Generalized Gaussian Distributions with an Application to Multicomponent Texture Discrimination

Data-Weighted Multivariate Generalized Gaussian Mixture Model: Application to Point Cloud Robust Registration

In this paper, a weighted multivariate generalized Gaussian mixture model combined with stochastic optimization is proposed for point cloud registration. The mixture model parameters of the target scene and the scene to be registered are updated iteratively by the fixed point method under the framework of the EM algorithm, and the number of components is determined based on the minimum message length criterion (MML). The KL divergence between these two mixture models is utilized as the loss function for stochastic optimization to find the optimal parameters of the transformation model. The self-built point clouds are used to evaluate the performance of the proposed algorithm on rigid registration. Experiments demonstrate that the algorithm dramatically reduces the impact of noise and outliers and effectively extracts the key features of the data-intensive regions.

Multisensor Estimation Fusion on Statistical Manifold

In the paper, we characterize local estimates from multiple distributed sensors as posterior probability densities, which are assumed to belong to a common parametric family. Adopting the information-geometric viewpoint, we consider such family as a Riemannian manifold endowed with the Fisher metric, and then formulate the fused density as an informative barycenter through minimizing the sum of its geodesic distances to all local posterior densities. Under the assumption of multivariate elliptical distribution (MED), two fusion methods are developed by using the minimal Manhattan distance instead of the geodesic distance on the manifold of MEDs, which both have the same mean estimation fusion, but different covariance estimation fusions. One obtains the fused covariance estimate by a robust fixed point iterative algorithm with theoretical convergence, and the other provides an explicit expression for the fused covariance estimate. At different heavy-tailed levels, the fusion results of two local estimates for a static target display that the two methods achieve a better approximate of the informative barycenter than some existing fusion methods. An application to distributed estimation fusion for dynamic systems with heavy-tailed process and observation noises is provided to demonstrate the performance of the two proposed fusion algorithms.

Multivariate Statistical Approach to Image Quality Tasks

Many existing natural scene statistics-based no reference image quality assessment (NR IQA) algorithms employ univariate parametric distributions to capture the statistical inconsistencies of bandpass distorted image coefficients. Here, we propose a multivariate model of natural image coefficients expressed in the bandpass spatial domain that has the potential to capture higher order correlations that may be induced by the presence of distortions. We analyze how the parameters of the multivariate model are affected by different distortion types, and we show their ability to capture distortion-sensitive image quality information. We also demonstrate the violation of Gaussianity assumptions that occur when locally estimating the energies of distorted image coefficients. Thus, we propose a generalized Gaussian-based local contrast estimator as a way to implement non-linear local gain control, which facilitates the accurate modeling of both pristine and distorted images. We integrate the novel approach of generalized contrast normalization with multivariate modeling of bandpass image coefficients into a holistic NR IQA model, which we refer to as multivariate generalized contrast normalization (MVGCN). We demonstrate the improved performance of MVGCN on quality-relevant tasks on multiple imaging modalities, including visible light image quality prediction and task success prediction on distorted X-ray images.

Transformation of the Multivariate Generalized Gaussian Distribution for Image Editing

Multivariate generalized Gaussian distributions (MGGDs) have aroused a great interest in the image processing community thanks to their ability to describe accurately various image features, such as image gradient fields. However, so far their applicability has been limited by the lack of a transformation between two of these parametric distributions. In this paper, we propose a novel transformation between MGGDs, consisting of an optimal transportation of the second-order statistics and a stochastic-based shape parameter transformation. We employ the proposed transformation between MGGDs for a color transfer and a gradient transfer between images. We also propose a new simultaneous transfer of color and gradient, which we apply for image color correction.

Fractional Brownian Motion and Rao Geodesic Distance for Bone X-Ray Image Characterization

Osteoporosis diagnosis has attracted particular attention in recent decades. Textured images from the microarchitecture of osteoporotic and healthy subjects show a high degree of similarity, increasing the difficulty of classifying such textures. Thus, the evaluation of osteoporosis from the bone X-ray images presents a major challenge for pattern recognition and medical applications. The purpose of this paper is to use the fractional Brownian motion (fBm) model and the probability density function of its increments to compute a similarity measure with the Rao geodesic distance to classify trabecular bone X-ray images. When evaluated on synthetic fBm images (test vectors) with the well-known Hurst parameter H, the proposed method met our expectations in which a good classification of the synthetic images was achieved. A clinical study was conducted on textured bone X-ray images from two different female populations of osteoporotic patients (fracture cases) and control subjects. Using the proposed method, an area under curve rate of 97% was achieved.

Gaussian Copula multivariate modeling for texture image retrieval using wavelet transforms

In the framework of texture image retrieval, a new family of stochastic multivariate modeling is proposed based on Gaussian Copula and wavelet decompositions. We take advantage of the copula paradigm, which makes it possible to separate dependence structure from marginal behavior. We introduce two new multivariate models using, respectively, generalized Gaussian and Weibull densities. These models capture both the subband marginal distributions and the correlation between wavelet coefficients. We derive, as a similarity measure, a closed form expression of the Jeffrey divergence between Gaussian copula-based multivariate models. Experimental results on well-known databases show significant improvements in retrieval rates using the proposed method compared with the best known state-of-the-art approaches.

Wavelet domain multifractal analysis for static and dynamic texture classification

In this paper, we propose a new texture descriptor for both static and dynamic textures. The new descriptor is built on the wavelet-based spatial-frequency analysis of two complementary wavelet pyramids: standard multiscale and wavelet leader. These wavelet pyramids essentially capture the local texture responses in multiple high-pass channels in a multiscale and multiorientation fashion, in which there exists a strong power-law relationship for natural images. Such a power-law relationship is characterized by the so-called multifractal analysis. In addition, two more techniques, scale normalization and multiorientation image averaging, are introduced to further improve the robustness of the proposed descriptor. Combining these techniques, the proposed descriptor enjoys both high discriminative power and robustness against many environmental changes. We apply the descriptor for classifying both static and dynamic textures. Our method has demonstrated excellent performance in comparison with the state-of-the-art approaches in several public benchmark datasets.

A probabilistic model for the identification of confinement regimes and edge localized mode behavior, with implications to scaling laws

Pattern recognition is becoming an important tool in fusion data analysis. However, fusion diagnostic measurements are often affected by considerable statistical uncertainties, rendering the extraction of useful patterns a significant challenge. Therefore, we assume a probabilistic model for the data and perform pattern recognition in the space of probability distributions. We show the considerable advantage of our method for identifying confinement regimes and edge localized mode behavior, and we discuss the potential for scaling laws.

Wavelet modeling using finite mixtures of generalized gaussian distributions: application to texture discrimination and retrieval

This paper addresses statistical-based texture modeling using wavelets. We propose a new approach to represent the marginal distribution of the wavelet coefficients using finite mixtures of generalized Gaussian (MoGG) distributions. The MoGG captures a wide range of histogram shapes, which provides better description and discrimination of texture than using single probability density functions (pdf's), as proposed by recent state-of-the-art approaches. Moreover, we propose a model similarity measure based on Kullback-Leibler divergence (KLD) approximation using Monte Carlo sampling methods. Through experiments on two popular texture data sets, we show that our approach yields significant performance improvements for texture discrimination and retrieval, as compared with recent methods of statistical-based wavelet modeling.