Contributions to 3D Image Analysis using Discrete Methods and Fuzzy Techniques With Focus on Images from Cryo-Electron Tomography

Abstract: With the emergence of new imaging techniques, researchers are always eager to push the boundaries by examining objects either smaller or further away than what was previously possible. The development of image analysis techniques has greatly helped to introduce objectivity and coherence in measurements and decision making. It has become an essential tool for facilitating both large-scale quantitative studies and qualitative research. In this Thesis, methods were developed for analysis of low-resolution (in respect to the size of the imaged objects) three-dimensional (3D) images with low signal-to-noise ratios (SNR) applied to images from cryo-electron tomography (cryo-ET) and fluorescence microscopy (FM). The main focus is on methods of low complexity, that take into account both grey-level and shape information, to facilitate large-scale studies. Methods were developed to localise and represent complex macromolecules in images from cryo-ET. The methods were applied to Immunoglobulin G (IgG) antibodies and MET proteins. The low resolution and low SNR required that grey-level information was utilised to create fuzzy representations of the macromolecules. To extract structural properties, a method was developed to use grey-level-based distance measures to facilitate decomposition of the fuzzy representations into sub-domains. The structural properties of the MET protein were analysed by developing a analytical curve representation of its stalk. To facilitate large-scale analysis of structural properties of nerve cells, a method for tracing neurites in FM images using local path-finding was developed. Both theoretical and implementational details of computationally heavy approaches were examined to keep the time complexity low in the developed methods. Grey-weighted distance definitions and various aspects of their implementations were examined in detail to form guidelines on which definition to use in which setting and which implementation is the fastest. Heuristics were developed to speed up computations when calculating grey-weighted distances between two points. The methods were evaluated on both real and synthetic data and the results show that the methods provide a step towards facilitating large-scale studies of images from both cryo-ET and FM.