@article {100, title = {Frozen State Hierarchical Annealing}, journal = {IEEE Transactions on Image Processing}, volume = {22}, year = {2013}, pages = {1486-1497}, abstract = {

There is significant interest in the synthesis of discrete-state random fields, particularly those possessing structure over a wide range of scales. However, given a model on some finest, pixellated scale, it is computationally very difficult to synthesize both large and small-scale structures, motivating research into hierarchical methods.
In this paper we propose a frozen-state approach to hierarchical modeling, in which simulated annealing is performed on each scale, constrained by the state estimates at the parent scale. The approach leads to significant advantages in both modelling flexibility and computational complexity. In particular, a complex structure can be realized with very simple, local, scale-dependent models, and by constraining the domain to be annealed at finer scales to only the uncertain portions of coarser scales, the approach leads to huge improvements in computational complexity. Results are shown for a synthesis problem in porous media.

}, keywords = {hierarchical algorithms, image synthesis, random sampling, simulated annealing}, author = {W Campaigne and P Fieguth} } @article {281, title = {Statistical fusion of two-scale images of porous media}, journal = {Advances in Water Resources}, volume = {32}, year = {2009}, pages = {1567 - 1579}, abstract = {

The reconstruction of the architecture of void space in porous media is a challenging task, since porous media contain pore structures at multiple scales. Whereas past methods have been limited to producing samples with matching statistical behavior, the patterns of grey-level values in a measured sample actually say something about the unresolved details, thus we propose a statistical fusion framework for reconstructing high-resolution porous media images from low-resolution measurements. The proposed framework is based on a posterior sampling approach in which information obtained by low-resolution (MRI or X-ray) measurements is combined with prior models inferred from high-resolution microscopic data, typically 2D. In this paper, we focus on two-scale reconstruction tasks in which the measurements resolve only the large scale structures, leaving the small-scale to be inferred. The evaluation of the results generated by the proposed method shows the strong ability of the proposed method in reconstructing fine-scale structures positively correlated with the underlying ground truth. Comparing our method with the recent method of Okabe and Blunt [12], in which the measurements are also used in the reconstruction, we conclude that our method is more robust to the resolution of the measurement, and more closely matches the underlying fine-scale field.

}, keywords = {Data fusion, magnetic resonance imaging, Porous media reconstruction, Posterior sampling, simulated annealing}, issn = {0309-1708}, doi = {http://dx.doi.org/10.1016/j.advwatres.2009.08.005}, url = {http://www.sciencedirect.com/science/article/pii/S0309170809001274}, author = {A Mohebi and P Fieguth and M A. Ioannidis} } @inproceedings {760, title = {Hierarchical annealing for scientific models}, booktitle = {37th IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)}, year = {2004}, address = {Montreal}, abstract = {

The computational complexity of simulated annealing makes it an impractical tool in many applications, particularly for complex, non-local models on very large 2D and 3D domains as desired in many scientific contexts. In particular, it is very difficult to produce large scale structure from a fine, pixellated lattice. Thus a hierarchical approach is intuitively attractive. However, existing approaches are few and limited. Motivated by a current problem in porous media, we develop a hierarchical approach to complex model sampling. In experiments, this approach results in 1-2 orders of magnitude computational gain, and significant gains in convergence as well.

}, keywords = {2D domains, 3D domains, complex model sampling, computational complexity, data visualisation, hierarchical annealing, hierarchical sampling, image resolution, image sampling, pixellated lattice, porous materials, porous media, sampled images, scientific models, simulated annealing}, doi = {http://dx.doi.org/10.1109/ICASSP.2004.1326474}, author = {S K. Alexander and P Fieguth and E Vrscay} } @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} } @inproceedings {650, title = {Parametric contour estimation by simulated annealing}, booktitle = {IEEE International Conference on Image Processing}, year = {2003}, address = {Spain}, abstract = {

Virtually all implementations of simulated annealing are simplified by assuming discrete unknowns, however continuous-parameter annealing has many potential applications to image processing. Widely scattered problems such as formant tracking, boundary estimation and phase- unwrapping can all be approached as the annealed minimizations of continuous B-spline parameters. The benefits of simulated annealing are well known, including an insensitivity to initial conditions and the ability to solve problems with many local minima. Discrete variable annealing has seen broad application, however continuous-variable annealing is limited by the computational challenge of Gibbs sampling. In this paper we develop efficient approaches to sampling, illustrated in the context of contour tracking in noisy images.

}, keywords = {boundary estimation, continuous B-spline parameters, continuous-variable annealing, discrete variable annealing, formant tracking, Gibbs sampling, image processing, image sampling, noisy images, parametric contour estimation, phase-unwrapping, simulated annealing, splines (mathematics), tracking}, doi = {http://dx.doi.org/10.1109/ICIP.2003.1247278}, author = {M Jamieson and P Fieguth and L J. Lee} }