Improving PSF modelling for weak gravitational lensing using new methods in model selection

A simple theoretical framework for the description and interpretation of spatially correlated modelling residuals is presented, and the resulting tools are found to provide a useful aid to model selection in the context of weak gravitational lensing. The description is focused upon the specific problem of modelling the spatial variation of a telescope point spread function (PSF) across the instrument field of view, a crucial stage in lensing data analysis, but the technique may be used to rank competing models wherever data are described empirically. As such it may, with further development, provide useful extra information when used in combination with existing model selection techniques such as the Akaike and Bayesian Information Criteria, or the Bayesian evidence. Two independent diagnostic correlation functions are described and the interpretation of these functions demonstrated using a simulated PSF anisotropy field. The efficacy of these diagnostic functions as an aid to the correct choice of empirical model is then demonstrated by analyzing results for a suite of Monte Carlo simulations of random PSF fields with varying degrees of spatial structure, and it is shown how the diagnostic functions can be related to requirements for precision cosmic shear measurement. The limitations of the technique, and opportunities for improvements and applications to fields other than weak gravitational lensing, are discussed.Comment: 18 pages, 12 figures. Modified to match version accepted for publication in MNRA

Detecting Similarity of Rational Plane Curves

A novel and deterministic algorithm is presented to detect whether two given rational plane curves are related by means of a similarity, which is a central question in Pattern Recognition. As a by-product it finds all such similarities, and the particular case of equal curves yields all symmetries. A complete theoretical description of the method is provided, and the method has been implemented and tested in the Sage system for curves of moderate degrees.Comment: 22 page

Shape analysis of the corpus callosum of autistic and normal subjects in neuroimaging.

Early detection of human disease in today’s society can have an enormous impact on the severity of the disease that is manifested. Disease such as Autism and Dyslexia, which have no current cure or proven mechanism as to how they develop, can often have an adverse physical and physiological impact on the lifestyle of a human being. Although these disease are not fully curable, the severity handicaps that accompany them can be significantly reduced with the proper therapy, and thus the earlier that the disease is detected the faster therapy can be administered. The research in this thesis is an attempt at studying discriminatory shape measures of some brain structures that are known to carry changes from autistics to normal individuals. The focus will be on the corpus callosum. There has been considerable research done on the brain scans (MRI, CT) of autistic individuals vs. control (normal) individuals to observe any noticeable discrepancies through statistical analysis. The most common and powerful tool to analyze structures of the brain, once a specific region has been segmented, is using Registration to match like structures and record their error. The ICP algorithm (Iterative Closest Point) is commonly used to accomplish this task. Many techniques such as level sets and statistical methods can be used for segmentation. The Corpus Callosum (CC) and the cortical surface of the brain are currently where most Autism analysis is performed. It has been observed that the gyrification of the cortical surface is different in the two groups, and size as well as shape of the CC. An analysis approach for autism MRI is quite extensive and involves many steps. This thesis is limited to examination of shape measures of the CC that lend discrimination ability to distinguish between normal and autistic individuals from T1-weigheted MRI scans. We will examine two approaches for shape analysis, based on the traditional Fourier Descriptors (FD) method and shape registration (SR) using the procrustes technique. MRI scans of 22 autistic and 16 normal individuals are used to test the approaches developed in this thesis. We show that both FD and SR may be used to extract features to discriminate between the two populations with accuracy levels over 80% up to 100% depending on the technique