Geodesics on the manifold of multivariate generalized Gaussian distributions with an application to multicomponent texture discrimination

We consider the Rao geodesic distance (GD) based on the Fisher information as a similarity measure on the manifold of zero-mean multivariate generalized Gaussian distributions (MGGD). The MGGD is shown to be an adequate model for the heavy-tailed wavelet statistics in multicomponent images, such as color or multispectral images. We discuss the estimation of MGGD parameters using various methods. We apply the GD between MGGDs to color texture discrimination in several classification experiments, taking into account the correlation structure between the spectral bands in the wavelet domain. We compare the performance, both in terms of texture discrimination capability and computational load, of the GD and the Kullback-Leibler divergence (KLD). Likewise, both uni- and multivariate generalized Gaussian models are evaluated, characterized by a fixed or a variable shape parameter. The modeling of the interband correlation significantly improves classification efficiency, while the GD is shown to consistently outperform the KLD as a similarity measure

Using the Dual-Tree Complex Wavelet Transform for Improved Fabric Defect Detection

Published ArticleThe dual-tree complex wavelet transform (DTCWT) solves the problems of shift variance and low directional selectivity in two and higher dimensions found with the commonly used discrete wavelet transform (DWT). It has been proposed for applications such as texture classification and content-based image retrieval. In this paper, the performance of the dual-tree complex wavelet transform for fabric defect detection is evaluated. As experimental samples, the fabric images from TILDA, a textile texture database from the Workgroup on Texture Analysis of the German Research Council (DFG), are used. The mean energies of real and imaginary parts of complex wavelet coefficients taken separately are identified as effective features for the purpose of fabric defect detection. Then it is shown that the use of the dual-tree complex wavelet transform yields greater performance as compared to the undecimated wavelet transform (UDWT) with a detection rate of 4.5% to 15.8% higher depending on the fabric type

A Graph-based approach to derive the geodesic distance on Statistical manifolds: Application to Multimedia Information Retrieval

In this paper, we leverage the properties of non-Euclidean Geometry to define the Geodesic distance (GD) on the space of statistical manifolds. The Geodesic distance is a real and intuitive similarity measure that is a good alternative to the purely statistical and extensively used Kullback-Leibler divergence (KLD). Despite the effectiveness of the GD, a closed-form does not exist for many manifolds, since the geodesic equations are hard to solve. This explains that the major studies have been content to use numerical approximations. Nevertheless, most of those do not take account of the manifold properties, which leads to a loss of information and thus to low performances. We propose an approximation of the Geodesic distance through a graph-based method. This latter permits to well represent the structure of the statistical manifold, and respects its geometrical properties. Our main aim is to compare the graph-based approximation to the state of the art approximations. Thus, the proposed approach is evaluated for two statistical manifolds, namely the Weibull manifold and the Gamma manifold, considering the Content-Based Texture Retrieval application on different databases

Dual-tree Complex Wavelet Transform based Local Binary Pattern Weighted Histogram Method for Palmprint Recognition

In the paper, we improve the Local Binary Pattern Histogram (LBPH) approach and combine it with Dual-Tree Complex Wavelet Transform (DT-CWT) to propose a Dual-Tree Complex Wavelet Transform based Local Binary Pattern Weighted Histogram (DT-CWT based LBPWH) method for palmprint representation and recognition. The approximate shift invariant property of the DT-CWT and its good directional selectively in 2D make it a very appealing choice for palmprint representation. LBPH is a powerful texture description method, which considers both shape and texture information to represent an image. To enhance the representation capability of LBPH, a weight set is computed and assigned to the finial feature histogram. Here we needn't construct a palmprint model by a train sample set, which is not like some methods based on subspace discriminant analysis or statistical learning. In the approach, a palmprint image is first decomposed into multiple subbands by using DT-CWT. After that, each subband in complex wavelet domain is divided into non-overlapping sub-regions. Then LBPHs are extracted from each sub-region in each subband, and lastly, all of LBPHs are weighted and concatenated into a single feature histogram to effectively represent the palmprint image. A Chi square distance is used to measure the similarity of different feature histograms and the finial recognition is performed by the nearest neighborhood classifier. A group of optimal parameters is chosen by 20 verification tests on our palmprint database. In addition, the recognition results on our palmprint database and the database from the Hong Kong Polytechnic University show the proposed method outperforms other methods

Dual-Tree Complex Wavelet Transform in the Frequency Domain and an Application to Signal Classification

We examine Kingsbury's dual-tree complex wavelet transform in the frequency domain, where it can be formulated for standard wavelet filters without special filter design and apply the method to the classification of signals. The obtained transforms achieve low shift sensitivity and better directionality compared to the real discrete wavelet transform while retaining the perfect reconstruction property