Hidden Hierarchical Markov Fields for Image Modeling

TitleHidden Hierarchical Markov Fields for Image Modeling
Publication TypeThesis
Year of Publication2011
AuthorsLiu, Y.
Academic DepartmentDepartment of Systems Design Engineering
UniversityUniversity of Waterloo
CityWaterloo, Ontario, Canada
Thesis TypePh.D. Thesis

Random heterogeneous, scale-dependent structures can be observed from many image sources, especially from remote sensing and scientific imaging. Examples include slices of porous media data showing pores of various sizes, and a remote sensing image including small and large sea-ice blocks. Meanwhile, rather than the images of phenomena themselves, there are many image processing and analysis problems requiring to deal with \emph{discrete-state} fields according to a labeled underlying property, such as mineral porosity extracted from microscope images, or an ice type map estimated from a sea-ice image. In many cases, if discrete-state problems are associated with heterogeneous, scale-dependent spatial structures, we will have to deal with complex discrete state fields. Although scale-dependent image modeling methods are common for continuous-state problems, models for discrete-state cases have not been well studied in the literature. Therefore, a fundamental difficulty will arise which is how to represent such complex discrete-state fields. Considering the success of hidden field methods in representing heterogenous behaviours and the capability of hierarchical field methods in modeling scale-dependent spatial features, we propose a Hidden Hierarchical Markov Field (HHMF) approach, which combines the idea of hierarchical fields with hidden fields, for dealing with the discrete field modeling challenge. However, to define a general HHMF modeling structure to cover all possible situations is difficult. In this research, we use two image application problems to describe the proposed modeling methods: one for scientific image (porous media image) reconstruction and the other for remote-sensing image synthesis. For modeling discrete-state fields with a spatially separable complex behaviour, such as porous media images with nonoverlapped heterogeneous pores, we propose a Parallel HHMF model, which can decomposes a complex behaviour into a set of separated, simple behaviours over scale, and then represents each of these with a hierarchical field. Alternatively, discrete fields with a highly heterogeneous behaviour, such as a sea-ice image with multiple types of ice at various scales, which are not spatially separable but arranged more as a partition tree, leads to the proposed Tree-Structured HHMF model. According to the proposed approach, a complex, multi-label field can be repeatedly partitioned into a set of binary/ternary fields, each of which can be further handled by a hierarchical field.