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

Wavelet based similarity measurement algorithm for seafloor morphology

Thesis (S.M. in Naval Architecture and Marine Engineering and S.M. in Mechanical Engineering)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2006.Includes bibliographical references (leaves 71-73).The recent expansion of systematic seafloor exploration programs such as geophysical research, seafloor mapping, search and survey, resource assessment and other scientific, commercial and military applications has created a need for rapid and robust methods of processing seafloor imagery. Given the existence of a large library of seafloor images, a fast automated image classifier algorithm is needed to determine changes in seabed morphology over time. The focus of this work is the development of a robust Similarity Measurement (SM) algorithm to address the above problem. Our work uses a side-scan sonar image library for experimentation and testing. Variations of an underwater vehicle's height above the sea floor and of its pitch and roll angles cause distortion in the data obtained, such that transformations to align the data should include rotation, translation, anisotropic scaling and skew. In order to deal with these problems, we propose to use the Wavelet transform for similarity detection. Wavelets have been widely used during the last three decades in image processing. Since the Wavelet transform allows a multi-resolution decomposition, it is easier to identify the similarities between two images by examining the energy distribution at each decomposition level.(cont.) The energy distribution in the frequency domain at the output of the high pass and low pass filter banks identifies the texture discrimination. Our approach uses a statistical framework, involving fitting the Wavelet coefficients into a generalized Gaussian density distribution. The next step involves use of the Kullback-Leibner entropy metric to measure the distance between Wavelet coefficient distributions. To select the top N most likely matching images, the database images are ranked based on the minimum Kullback-Leibner distance. The statistical approach is effective in eliminating rotation, mis-registration and skew problems by working in the Wavelet domain. It's recommended that further work focuses on choosing the best Wavelet packet to increase the robustness of the algorithm developed in this thesis.by Ilkay Darilmaz.S.M.in Naval Architecture and Marine Engineering and S.M.in Mechanical Engineerin

Rotation invariant texture characterization and retrieval using steerable wavelet-domain hidden Markov models

We present a new statistical model for characterizing texture images based on wavelet-domain hidden Markov models. With a small number of parameters, the new model captures both the subband marginal distributions and the dependencies across scales and orientations of the wavelet descriptors. Applying to the steerable pyramid, once it is trained for an input texture image, the model can be easily steered to characterize that texture at any other orientation. Furthermore, after a diagonalization operation, we obtain a rotation-invariant model of the texture image. We also propose a fast algorithm to approximate the Kullback–Leibler distance between two wavelet-domain hidden Markov models. We demonstrate the effectiveness of the new texture models in re- trieval experiments with large image databases, where significant improvements are shown

Wavelet-based texture retrieval using generalized Gaussian density and Kullback-Leibler distance

We present a statistical view of the texture retrieval problem by combining the two related tasks, namely feature extraction (FE) and similarity measurement (SM), into a joint modeling and classification scheme. We show that using a con- sistent estimator of texture model parameters for the FE step followed by computing the Kullback–Leibler distance (KLD) between estimated models for the SM step is asymptotically optimal in term of retrieval error probability. The statistical scheme leads to a new wavelet-based texture retrieval method that is based on the accurate modeling of the marginal distribution of wavelet coefficients using generalized Gaussian density (GGD) and on the existence a closed form for the KLD between GGDs. The proposed method provides greater accuracy and flexibility in capturing texture information, while its simplified form has a close resemblance with the existing methods which uses energy distribution in the frequency domain to identify textures. Ex- perimental results on a database of 640 texture images indicate that the new method significantly improves retrieval rates, e.g., from 65% to 77%, compared with traditional approaches, while it retains comparable levels of computational complexity

Multi-Date Divergence Matrices for the Analysis of SAR Image Time Series

International audienceThe paper provides a spatio-temporal change detection framework for the analysis of image time series. In this framework, the detection of changes in time is addressed at the image level by using a matrix of cross-dissimilarities computed upon wavelet and curvelet image features. This makes possible identifying the acquisitions-of-interest: the acquisitions that exhibit singular behavior with respect to their neighborhood in the time series and those that are representatives of some stationary behavior. These acquisitions-of-interest are compared at the pixel level in order to detect spatial changes characterizing the evolution of the time series. Experiments carried out over ERS and TerraSAR-X time series highlight the relevancy of the approach for analyzing SAR image time series