Algorithms and data structure for component-hypertrees of gray-level images - Morimitsu, Alexandre (2021)
This thesis focuses on the study of component-hypertrees, which are graphs that store gray-level images in a hierarchical way. In such graphs, nodes represent connected components of an image extracted from multiple increasing connectivities, while arcs are used to organize these nodes according to an inclusion relation. In this research, the main goal is to develop efficient algorithms and data structures for component-hypertree construction, storage and manipulation. More specifically, our main contributions can be summarized as follows: (i) the theory behind component-hypertrees is reviewed and expanded, with some important properties being highlighted and proved. Using these properties, optimized algorithms and data structures are developed, resulting in implementations that considerably decrease time consumption and memory usage when compared to previously existing strategies; (ii) the impact of the choice of connectivities used to extract connected component is studied and a new family of neighborhoods based on a hierarchy of partitions is proposed, leading to the development of even faster algorithms; (iii) an efficient way of computing attribute variation is explained, allowing the development of applications that extract nodes comprised of clusters of smaller objects; (iv) an experimental analysis is conducted, to show that the proposed strategy is faster and more efficient than previously existing approaches and (v) a word segmentation tool is developed, to showcase an example of an application where attribute variation is particularly suitable.