Multi-Label Segmentation Propagation for Materials Science Images Incorporating Topology and Interactivity

Segmentation propagation is the problem of transferring the segmentation of an image to a neighboring image in a sequence. This problem is of particular importance to materials science, where the accurate segmentation of a series of 2D serial-sectioned images of multiple, contiguous 3D structures has important applications. Such structures may have prior-known shape, appearance, and/or topology among the underlying structures which can be considered to improve segmentation accuracy. For example, some materials images may have structures with a specific shape or appearance in each serial section slice, which only changes minimally from slice to slice; and some materials may exhibit specific topology which constrains their structure or neighboring relations. In this work, we develop a framework for materials image segmentation that segments a variety of materials image types by repeatedly propagating a 2D segmentation from one slice to another, and we formulate each step of this propagation as an optimal labeling problem that can be efficiently solved using the graph-cut algorithm. During this propagation, we propose novel strategies to enforce the shape, appearance, and topology of the segmented structures, as well as handling local topology inconsistency. Most recent works on topology-constrained image segmentation focus on binary segmentation, where the topology is often described by the connectivity of both foreground and background. We develop a new multi-labeling approach to enforce topology in multiple-label image segmentation. In this case, we not only require each segment to be a connected region (intra-segment topology), but also require specific adjacency relations between each pair of segments (inter-segment topology). Finally, we integrate an interactive approach into the proposed framework that improves the segmentation by allowing minimal and simplistic human annotations. We justify the effectiveness of the proposed framework by testing it on various 3D materials images, and we compare its performance against several existing image segmentation methods

Self-organising maps : statistical analysis, treatment and applications.

This thesis presents some substantial theoretical analyses and optimal treatments of Kohonen's self-organising map (SOM) algorithm, and explores the practical application potential of the algorithm for vector quantisation, pattern classification, and image processing. It consists of two major parts. In the first part, the SOM algorithm is investigated and analysed from a statistical viewpoint. The proof of its universal convergence for any dimensionality is obtained using a novel and extended form of the Central Limit Theorem. Its feature space is shown to be an approximate multivariate Gaussian process, which will eventually converge and form a mapping, which minimises the mean-square distortion between the feature and input spaces. The diminishing effect of the initial states and implicit effects of the learning rate and neighbourhood function on its convergence and ordering are analysed and discussed. Distinct and meaningful definitions, and associated measures, of its ordering are presented in relation to map's fault-tolerance. The SOM algorithm is further enhanced by incorporating a proposed constraint, or Bayesian modification, in order to achieve optimal vector quantisation or pattern classification. The second part of this thesis addresses the task of unsupervised texture-image segmentation by means of SOM networks and model-based descriptions. A brief review of texture analysis in terms of definitions, perceptions, and approaches is given. Markov random field model-based approaches are discussed in detail. Arising from this a hierarchical self-organised segmentation structure, which consists of a local MRF parameter estimator, a SOM network, and a simple voting layer, is proposed and is shown, by theoretical analysis and practical experiment, to achieve a maximum likelihood or maximum a posteriori segmentation. A fast, simple, but efficient boundary relaxation algorithm is proposed as a post-processor to further refine the resulting segmentation. The class number validation problem in a fully unsupervised segmentation is approached by a classical, simple, and on-line minimum mean-square-error method. Experimental results indicate that this method is very efficient for texture segmentation problems. The thesis concludes with some suggestions for further work on SOM neural networks