Statistical image and functional data analysis

This work develops Statistical techniques for image analysis with special focus on bio-images from confocal microscopes. Taking a cue from image processing techniques, statistical features are developed to analyze these images. The central idea is to think of a gray image as a 2-d distribution on the mxn lattice of pixels and extract relevant features of interest. These features are used in particular, to analyze the relationships between protein distributions in the retinal images.;A closely related topic to image analysis is functional data analysis, since a gray image is essentially a 2-d function. Two functional data analysis techniques namely, Growth curve modeling and Functional mixture modeling are studied. Growth curve modeling is developed with B-spline basis functions to model the mean growth curves for various treatments. Mean growth curves are fitted and statistical tests carried out for relevant Biological hypotheses regarding microtubule dynamicity in living cells. These analyses and conclusions have potentially important biological significance.;A scheme to detect non-convex shaped clusters in sparsely sampled functional data is developed. This is based on first fitting a Functional mixture model to the entire data and then performing hierarchical clustering of components using the mixture parameters. Non-convex clusters can be obtained from the original data by graph-theoretic methods but these are computationally intensive. The method developed here performs graph-theoretic clustering on the mixture components which are far fewer, rather than on the whole functional data and hence is fast. This is implemented on a microtubule data set.