The features based on Markov random field (MRF) models are usually sensitive to the rotation of image textures. The paper develops an anisotropic circular Gaussian MRF (ACGMRF) model for modeling rotated image textures and retrieving rotation-invariant texture features. To overcome the singularity problem of the least squares estimate (LSE) method, an approximate least squares estimate (ALSE) method is proposed to estimate the parameters of ACGMRF model. The rotation-invariant features can be obtained from the parameters of the ACGMRF model by the one-dimensional (1D) discrete Fourier transform (DFT). Significantly improved accuracy can be achieved by applying the rotation-invariant features to classify SAR (synthetic aperture radar) sea ice and Brodatz imagery.

}, keywords = {ACGMRF model, ALSE method, anisotropic circular Gaussian MRF, approximate least squares estimate, Brodatz imagery, discrete Fourier transform, discrete Fourier transforms, Feature Extraction, Gaussian distribution, image classification, image texture rotation, least squares approximation, least squares approximations, Markov processes, Markov random field, one-dimensional DFT, Remote Sensing, remote sensing image classification, rotated image texture modeling, rotation-invariant feature, rotation-invariant texture feature, SAR classification, sea ice, singularity problem, synthetic aperture radar}, doi = {http://dx.doi.org/10.1109/CVPR.2003.1211533}, author = {H Deng and D A. Clausi} } @inproceedings {821, title = {Hierarchical posterior sampling for Gauss-Markov random fields}, booktitle = {2003 International Conference on Image Processing}, year = {2003}, abstract = {The estimation of images and random fields from sparse and/or noisy data is highly-developed, to the point where methods such as least-squares estimation, simulated annealing, and wavelet shrinkage are quite standardized. The key problem, however, is that the estimates are not a realistic version of the random field, and do not represent a typical or representative sample of the system being studied. Instead, what is often desired is that we find a random sample from the posterior distribution, a much more subtle and difficult problem than estimation. Typically this is solved using Markov-Chain Monte-Carlo / simulated annealing approaches, however these may be computationally challenging and slow to converge. In this paper we use hierarchical models to formulate a novel, fast posterior sampler.

}, keywords = {image estimation, image hierarchical posterior sampling, image sampling, least squares approximations, least-squares estimation, Markov processes, Markov-chain, Monte Carlo methods, Monte-Carlo method, noisy data, posterior distribution, random field, simulated annealing, wavelet shrinkage}, doi = {http://dx.doi.org/10.1109/ICIP.2003.1247088}, author = {P Fieguth} } @article {485, title = {An overlapping tree approach to multiscale stochastic modeling and estimation}, journal = {IEEE Transactions on Image Processing}, volume = {6}, year = {1997}, pages = {1517 - 1529}, abstract = {Recently, a class of multiscale stochastic models has been introduced in which random processes and fields are described by scale-recursive dynamic trees. A major advantage of this framework is that it leads to an extremely efficient, statistically optimal algorithm for least-squares estimation. In certain applications, however, estimates based on the types of multiscale models previously proposed may not be adequate, as they have tended to exhibit a visually distracting blockiness. We eliminate this blockiness by discarding the standard assumption that distinct nodes on a given level of the multiscale process correspond to disjoint portions of the image domain; instead, we allow a correspondence to overlapping portions of the image domain. We use these so-called overlapping-tree models for both modeling and estimation. In particular, we develop an efficient multiscale algorithm for generating sample paths of a random field whose second-order statistics match a prespecified covariance structure, to any desired degree of fidelity. Furthermore, we demonstrate that under easily satisfied conditions, we can ldquo;lift rdquo; a random field estimation problem to one defined on an overlapped tree, resulting in an estimation algorithm that is computationally efficient, directly produces estimation error covariances, and eliminates blockiness in the reconstructed imagery without any sacrifice in the resolution of fine-scale detail

}, keywords = {covariance analysis, covariance structure, error analysis, estimation algorithm, estimation error covariances, fine scale detail resolution, image domain, image reconstruction, image resolution, least squares approximations, least squares estimation, multiscale stochastic modeling, overlapping tree, parameter estimation, quadtrees, random field estimation, random processes, scale recursive dynamic trees, second order statistics, statistically optimal algorithm, stochastic processes}, issn = {1057-7149}, author = {W W. Irving and P Fieguth and A S. Willsky} } @inproceedings {490, title = {A general multiresolution approach to the estimation of dense fields in remote sensing}, booktitle = {International Conference on Image Processing}, year = {1996}, address = {Lausanne, Switzerland}, abstract = {A fast multiscale optimal interpolation algorithm has been adapted to the mapping of hydrographic and other oceanographic data. This multiscale algorithm produces solution and error estimates which are consistent with those obtained from exact least-squares methods, but at a small fraction of the computational cost. Problems whose solution would be completely impractical using exact least-squares, that is problems with tens or hundreds of thousands of measurements and estimation grid points, can easily be solved on a small workstation using the multiscale algorithm. Contrary to methods previously proposed for solving large least-squares problems, the multiscale approach provides error statistics while permitting long-range correlations, using all measurements, and permitting arbitrary measurement locations

}, keywords = {arbitrary measurement locations, computational cost, correlation methods, dense fields estimation, error estimates, error statistics, exact least-squares methods, fast multiscale optimal interpolation algorithm, general multiresolution approach, geophysical signal processing, hydrographic data mapping, hydrological techniques, image resolution, interpolation, least squares approximations, long-range correlations, measurements, multiscale algorithm, oceanographic data mapping, oceanographic techniques, Remote Sensing, workstation}, doi = {http://dx.doi.org/10.1109/ICIP.1996.560937}, author = {P Fieguth and A S. Willsky and D Menemenlis and C Wunsch} }