@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} } @inproceedings {186, title = {Multi-Scale 3D representation via volumetric quasi-random scale space}, booktitle = {18th IEEE International Conference on Image Processing (ICIP 2011)}, year = {2011}, month = {09/2011}, abstract = {

A novel nonlinear volumetric scale-space framework is proposed for multi-scale volumetric data representation. The problem is formulated as a Bayesian least-squares estimator, and a quasi-random density estimation approach is introduced for estimating the posterior distribution between consecutive volumetric scale space realizations. Experimental results using both synthetic and real MR volumetric data demonstrate the effectiveness of the proposed scale-space framework for three-dimensional representation with significantly better structural separation and localization across all scales when compared to existing volumetric scale-space frameworks such as volumetric anisotropic diffusion and volumetric linear Gaussian scale-space, especially under scenarios with high noise levels.

}, keywords = {multi-scale, random sampling, Scale space, volumetric representation}, author = {A Mishra and A Wong and P Fieguth and D A. Clausi} }