ABSTRACT
SHAPE-BASED INTERPOLATION OF MULTIDIMENSIONAL IMAGE DATA:
PRINCIPLES, ALGORITHMS, AND THEIR EVALUATION
George Joseph Grevera
Gabor Herman, Ph.D., Committee Member
Steven Horii, M.D., Committee Member
Dimitris Metaxas, Ph.D., Committee Chairperson
Oleh Tretiak, Ph.D., External Committee Member
Jayaram Udupa, Ph.D., Advisor
Medical image data are typically three-dimensional or higher and are acquired or sampled at different levels of discretization in each of the three or more directions. Display and manipulation of these data, whether it be in a two dimensional slice-by-slice fashion or in three-dimensional surface or volume renditions, requires that the data be estimated at points other than those at which they were originally acquired. This estimation process is usually referred to as interpolation. In this thesis, we present a new interpolation paradigm that is an extension of binary, shape-based interpolation to grey images. The gist of this technique is to convert the original grey scene of n dimensions to a binary scene of n+1 dimensions by projecting the grey values as height in the additional dimension. Then we perform a distance transform on this binary scene to create an n+1 dimensional grey scene. Interpolation of this data set is then performed to arrive at the desired discretization. Then this interpolated data set is thresholded to convert it back into a binary scene. Then finally, we convert the n+1 dimensional projections into grey values. We present a detailed investigation of the algorithm itself and its performance on phantom and medical image data. To evaluate this new method, we present a task-independent investigation by comparing the new method with a variety of established methods using some objective criteria. To further evaluate the new method, we also present a task-dependent investigation for the specific task of Multiple Sclerosis lesion detection. The results of the task-independent evaluation demonstrate that the new method outperforms the established methods. The results of the task-dependent evaluation demonstrate that the new method performs similarly to or better than the established interpolation methods. We conclude that this new method of grey, shape-based interpolation is a viable, superior alternative to established interpolation methods commonly used in tomographic 3D imaging.