Date of Degree


Document Type


Degree Name



Computer Science


Gabor T. Herman

Subject Categories

Applied Mathematics | Biology


component tree, Macromolecule, Rooted tree, Segmentation, structures, Topological descriptor


Understanding the three-dimensional structure of a macromolecular complex is essential for understanding its function. A component tree is a topological and geometric image descriptor that captures information regarding the structure of an image based on the connected components determined by different grayness thresholds. This dissertation presents a novel interactive framework for visual exploration of component trees of the density maps of macromolecular complexes, with the purpose of improved understanding of their structure. The interactive exploration of component trees together with a robust simplification methodology provide new insights in the study of macromolecular structures. An underlying mathematical theory is introduced and then is applied to studying digital pictures that represent objects at different resolutions. Illustrations of how component trees, and their simplifications, can help in the exploration of macromolecular structures include (i) identifying differences between two very similar viruses, (ii) showing how differences between the component trees reflect the fact that structures of mutant virus particles have varying sets of constituent proteins, (ii) utilizing component trees for density map segmentation in order to identify substructures within a macromolecular complex, (iv) showing how an appropriate component tree simplification may reveal the secondary structure in a protein, and (v) providing a potential strategy for docking a high-resolution representation of a substructure into a low-resolution representation of whole structure.