Image Analysis Using Directional Multiscale Representations and Applications for Characterization of Neuronal Morphology

Recent advances in high-resolution fluorescence microscopy have enabled the systematic study of morphological changes in large populations of cells induced by chemical and genetic perturbations, facilitating the discovery of signaling pathways underlying diseases and the development of new pharmacological treatments. In these studies, though, quantification and analysis of morphological features are for the vast majority processed manually, slowing data processing significantly and limiting the information gained to a descriptive level. As an example, automated identification of the primary components of a neuron and extraction of its features are essential steps in many quantitative studies of neuronal networks. Recent advances in applied harmonic analysis, especially in the area of multiscale representations, offer a variety of techniques and ideas which have potential to impact this field of scientific investigation. Motivated by the properties of directional multiscale representations, the focus of this thesis is to introduce a new notion, directional ratio, which is a multiscale quantitative measure, capable of distinguishing isotropic from anisotropic structures and the characterization of local isotropy. Another part of the dissertation illustrates the application of directional ratio. In particular, we present an algorithm for automated soma extraction and separation of contiguous somas. Our numerical experiments show that this approach is reliable and efficient to detect and segment somas.