Smoothing in magnetic resonance image analysis and a hybrid loss for support vector machine

This dissertation consists of three parts. The first two parts are related to magnetic resonance (MR) image analysis. And the third part is on the hybrid loss support vector machine (SVM).; In the first part, a novel segmentation method is proposed. We fit thin plate splines with different knot configuration to overlapping blocks of the MR image, with the optimal knot configuration found by a modified generalized cross-validation (GCV) criterion for each block. We predict the spline on a fine grid laid on every block. Subsequent thresholding with K-means and blending with a smooth weighting function are then performed. The results show that our method generates good segmentation compared to manual segmentation and those by other methods. Also the new method produces subpixel (or subvoxel) results and smoother boundaries. It handles image inhomogeneity and partial volume effects quite well.; The second part is on functional magnetic resonance image (fMRI) analysis. We propose applying the partial spline model to fMRI analysis. The corresponding hypothesis testing procedure is given. The simulations show that the partial spline approach performs very well compared to commonly used model in fMRI analysis when the underlying covariance structure on time is unknown.; In the last part, a hybrid loss function for support vector machine is studied. The new loss function has the advantages of both the hinge loss and the logistic loss, i.e., their sparseness and estimation of probability respectively. Simulation results corroborate our derivation. And application shows that the new loss does good classification.