Hyperspectral image unmixing using a multiresolution sticky HDP

This paper is concerned with joint Bayesian endmember extraction and linear unmixing of hyperspectral images using a spatial prior on the abundance vectors.We propose a generative model for hyperspectral images in which the abundances are sampled from a Dirichlet distribution (DD) mixture model, whose parameters depend on a latent label process. The label process is then used to enforces a spatial prior which encourages adjacent pixels to have the same label. A Gibbs sampling framework is used to generate samples from the posterior distributions of the abundances and the parameters of the DD mixture model. The spatial prior that is used is a tree-structured sticky hierarchical Dirichlet process (SHDP) and, when used to determine the posterior endmember and abundance distributions, results in a new unmixing algorithm called spatially constrained unmixing (SCU). The directed Markov model facilitates the use of scale-recursive estimation algorithms, and is therefore more computationally efficient as compared to standard Markov random field (MRF) models. Furthermore, the proposed SCU algorithm estimates the number of regions in the image in an unsupervised fashion. The effectiveness of the proposed SCU algorithm is illustrated using synthetic and real data

Unsupervised calibrated sonar imaging for seabed observation using hidden Markov random fields

International audienceThis paper deals with seabed imaging issued from sonar systems. Such imaging systems produce images of backscattering (BS) strength relative to physical seabed characteristics. However, these Bs measurements are not only seabed-related but also dependent on the incident angle. Therefore, to enhance the quality of such seabed imaging systems, we develop an unsupervised approach to compensate for these seabed-related angular dependencies. Our approach combines robust estimation and hidden Markov random fields. Results on real data demonstrate the relevance of our approach to improve seabed observation

Adaptive Markov random fields for joint unmixing and segmentation of hyperspectral image

Linear spectral unmixing is a challenging problem in hyperspectral imaging that consists of decomposing an observed pixel into a linear combination of pure spectra (or endmembers) with their corresponding proportions (or abundances). Endmember extraction algorithms can be employed for recovering the spectral signatures while abundances are estimated using an inversion step. Recent works have shown that exploiting spatial dependencies between image pixels can improve spectral unmixing. Markov random fields (MRF) are classically used to model these spatial correlations and partition the image into multiple classes with homogeneous abundances. This paper proposes to define the MRF sites using similarity regions. These regions are built using a self-complementary area filter that stems from the morphological theory. This kind of filter divides the original image into flat zones where the underlying pixels have the same spectral values. Once the MRF has been clearly established, a hierarchical Bayesian algorithm is proposed to estimate the abundances, the class labels, the noise variance, and the corresponding hyperparameters. A hybrid Gibbs sampler is constructed to generate samples according to the corresponding posterior distribution of the unknown parameters and hyperparameters. Simulations conducted on synthetic and real AVIRIS data demonstrate the good performance of the algorithm

The EM Algorithm

The Expectation-Maximization (EM) algorithm is a broadly applicable approach to the iterative computation of maximum likelihood (ML) estimates, useful in a variety of incomplete-data problems. Maximum likelihood estimation and likelihood-based inference are of central importance in statistical theory and data analysis. Maximum likelihood estimation is a general-purpose method with attractive properties. It is the most-often used estimation technique in the frequentist framework; it is also relevant in the Bayesian framework (Chapter III.11). Often Bayesian solutions are justified with the help of likelihoods and maximum likelihood estimates (MLE), and Bayesian solutions are similar to penalized likelihood estimates. Maximum likelihood estimation is an ubiquitous technique and is used extensively in every area where statistical techniques are used. --

Adaptive segmentation of textured images by using the coupled Markov random field model

Author name used in this publication: (David) Dagan FengCentre for Multimedia Signal Processing, Department of Electronic and Information Engineering2006-2007 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Bayesian Fusion of Multi-Band Images

International audienceThis paper presents a Bayesian fusion technique for remotely sensed multi-band images. The observed images are related to the high spectral and high spatial resolution image to be recovered through physical degradations, e.g., spatial and spectral blurring and/or subsampling defined by the sensor characteristics. The fusion problem is formulated within a Bayesian estimation framework. An appropriate prior distribution exploiting geometrical considerations is introduced. To compute the Bayesian estimator of the scene of interest from its posterior distribution, a Markov chain Monte Carlo algorithm is designed to generate samples asymptotically distributed according to the target distribution. To efficiently sample from this high-dimension distribution, a Hamiltonian Monte Carlo step is introduced within a Gibbs sampling strategy. The efficiency of the proposed fusion method is evaluated with respect to several state-of-the-art fusion techniques

Multiscale representations of Markov random fields

Caption title. "December 1992."Includes bibliographical references (leaf [4]).Supported by the Draper Laboratory IR&D Program. DL-H-418524 Supported by the Office of Naval Research. N00014-91-J-1004 Supported by the Army Research Office. DAAL03-92-G-0115 Supported by the Air Force Office of Scientific Research. AFOSR-92-J-0002 F49620-91-C-0047Mark R. Luettgen ... [et al.]

Models and methods for Bayesian object matching

This thesis is concerned with a central aspect of computer vision, the object matching problem. In object matching the aim is to detect and precisely localize instances of a known object class in a novel image. Factors complicating the problem include the internal variability of object classes and external factors such as rotation, occlusion, and scale changes. In this thesis, the problem is approached from the feature-based point of view, in which objects are considered to consist of certain pertinent features, which are then located in the perceived image. The methodological framework applied in this thesis is probabilistic Bayesian inference. Bayesian inference is a branch of statistics which assigns a great role to the mathematical modeling of uncertainty. After describing the basics of Bayesian statistics the object matching problem problem is formulated as a Bayesian probability model and it is shown how certain necessary sampling algorithms can be applied to analyze the resulting probability distributions. The Bayesian approach to the problem partitions it naturally into two submodels; a feature appearance model and an object shape model. In this thesis, feature appearance is modeled statistically via a type of bandpass filters known as Gabor filters, whereas two different shape models are presented: a simpler hierarchical model with uncorrelated feature location variations, and a full covariance model containing the interdependeces of the features. Furthermore, a novel model for the dynamics of object shape changes is introduced. The most important contributions of this thesis are the proposed extensions to the basic matching model. It is demonstrated how it is very straightforward to adjust the Bayesian probability model when difficulties such as scale changes, occlusions and multiple object instances arise. The changes required to the sampling algorithms and their applicability to the changed conditions are also discussed. The matching performance of the proposed system is tested with different datasets, and capabilities of the extended model in adverse conditions are demonstrated. The results indicate that the proposed model is a viable alternative to object matching, with performance equal or superior to existing approaches.reviewe