Generalized fuzzy clustering for segmentation of multi-spectral magnetic resonance images.

An integrated approach for multi-spectral segmentation of MR images is presented. This method is based on the fuzzy c-means (FCM) and includes bias field correction and contextual constraints over spatial intensity distribution and accounts for the non-spherical cluster's shape in the feature space. The bias field is modeled as a linear combination of smooth polynomial basis functions for fast computation in the clustering iterations. Regularization terms for the neighborhood continuity of intensity are added into the FCM cost functions. To reduce the computational complexity, the contextual regularizations are separated from the clustering iterations. Since the feature space is not isotropic, distance measure adopted in Gustafson-Kessel (G-K) algorithm is used instead of the Euclidean distance, to account for the non-spherical shape of the clusters in the feature space. These algorithms are quantitatively evaluated on MR brain images using the similarity measures.

A LAPLACE TRANSFORM PAIR MODEL TO DETERMINE BREMSSTRAHLUNG SPECTRA FROM ATTENUATION DATA (RADIATION, X-RAY, SPECTRAL MODELING)

Every x-ray attenuation curve inherently contains all the information necessary to extract the complete energy spectrum of a beam. To date, attempts to obtain accurate spectral information from attenuation data have been inadequate.^ This investigation presents a mathematical pair model, grounded in physical reality by the Laplace Transformation, to describe the attenuation of a photon beam and the corresponding bremsstrahlung spectral distribution. In addition the Laplace model has been mathematically extended to include characteristic radiation in a physically meaningful way. A method to determine the fraction of characteristic radiation in any diagnostic x-ray beam was introduced for use with the extended model.^ This work has examined the reconstructive capability of the Laplace pair model for a photon beam range of from 50 kVp to 25 MV, using both theoretical and experimental methods.^ In the diagnostic region, excellent agreement between a wide variety of experimental spectra and those reconstructed with the Laplace model was obtained when the atomic composition of the attenuators was accurately known. The model successfully reproduced a 2 MV spectrum but demonstrated difficulty in accurately reconstructing orthovoltage and 6 MV spectra. The 25 MV spectrum was successfully reconstructed although poor agreement with the spectrum obtained by Levy was found.^ The analysis of errors, performed with diagnostic energy data, demonstrated the relative insensitivity of the model to typical experimental errors and confirmed that the model can be successfully used to theoretically derive accurate spectral information from experimental attenuation data. ^

Detecting the signature of natural selection with microsatellites

Natural selection is one of the major factors in the evolution of all organisms. Detecting the signature of natural selection has been a central theme in evolutionary genetics. With the availability of microsatellite data, it is of interest to study how natural selection can be detected with microsatellites. ^ The overall aim of this research is to detect signatures of natural selection with data on genetic variation at microsatellite loci. The null hypothesis to be tested is the neutral mutation theory of molecular evolution, which states that different alleles at a locus have equivalent effects on fitness. Currently used tests of this hypothesis based on data on genetic polymorphism in natural populations presume that mutations at the loci follow the infinite allele/site models (IAM, ISM), in the sense that at each site at most only one mutation event is recorded, and each mutation leads to an allele not seen before in the population. Microsatellite loci, which are abundant in the genome, do not obey these mutation models, since the new alleles at such loci can be created either by contraction or expansion of tandem repeat sizes of core motifs. Since the current genome map is mainly composed of microsatellite loci and this class of loci is still most commonly studied in the context of human genome diversity, this research explores how the current test procedures for testing the neutral mutation hypothesis should be modified to take into account a generalized model of forward-backward stepwise mutations. In addition, recent literature also suggested that past demographic history of populations, presence of population substructure, and varying rates of mutations across loci all have confounding effects for detecting signatures of natural selection. ^ The effects of the stepwise mutation model and other confounding factors on detecting signature of natural selection are the main results of the research. ^