A new computational method for image registration is formulated. Registration refers to the task of aligning a pair of images obtained by CT (computed tomography), MR (magnetic resonance), ultra-sound, and other techniques, so that they can be compared both qualitatively and quantitatively. This is an important problem with applications ranging from remote sensing to medicine. In medicine, imaging techniques and analysis have become an important, non-invasive tool for diagnosis and for surgical and radiation treatment planning. Despite advances in this area of research, the challenges posed by registration for three-dimensional images remains an open problem. A new mathematical approach is developed that optimizes any chosen similarity measure of the images, subject to the constraint of a set of differential equations that can generate any differentiable and invertible transformation.
The main intellectual merit of the project is that it significantly enhances our understanding of imagery and shapes and also the accuracy and efficiency of image registration techniques. The main features of the new method are as follows. 1. Similarity measures used to compare images are directly optimized. 2. The method has a landmark matching capacity for large deformations between images. 3. The method is founded on solid mathematical theory; in particular, the admissible space of transformations is the set of all differentiable and invertible transformations. 4. The project is carried out with the use of the software Insight Tool Kit developed by the National Institutes of Health; that software provides an excellent resource for the research activity. The broader impacts of the proposed activity are as follows. 1. Undergraduate and graduate students are educated and trained to apply powerful mathematical techniques to medical and other image processing problems. 2. The new method will impact other areas of the computational sciences. Results are to be presented at conferences and published in scientific journals and through the mass media directed at scientists and the general population as well. 3. New partnerships between medical doctors, biomedical engineers, and mathematicians are established, helping create a favorable environment for further research aimed at improving the health of our citizens.
