Continuous mixture modeling via goodness‐of‐fit cores

This dissertation introduces a novel technique for consistently and accurately modeling the distributions of data. The technique is ideal for representing distributions that arise in a variety of problems including the driving problem of this dissertation, representing the distributions of intensities associated with tissues in medical images containing intensity inhomogeneities. Intensity inhomogeneities arise in MR images due to inhomogeneous fields, in x‐ray CT images due to beam hardening, and in SPECT images due to deficiencies in attenuation compensation. Within regions of such images, a tissue's intensity distribution is Gaussian. Between regions, however, the mean and variance of a tissue's Gaussian may vary as a result of inhomogeneities. That is, a tissue's intensities throughout an inhomogeneous image have a generalized projective Gaussian distribution (GPGD). Traditionally, GPGDs have been modeled using finite Gaussian mixture models (FGMMs). The dissertation demonstrates that GPGDs are better represented by continuous Gaussian mixture models (CGMMs). Gaussian goodness‐of‐fit cores define CGMMs. For GPGDs, Monte Carlo and ROC analysis demonstrate that classifiers utilizing CGMMs provide as consistent labelings as and better true‐positive rates than FGMMs. The CGMM‐based classification of gray and white matter in an inhomogeneous magnetic resonance image is demonstrated.