This research project has three parts; the first is to develop a general class of models and inferential techniques for shape analysis. The second aspect is the development of a theory for the case when the least-squares estimate of mean shape can be written as the principal eigenvector of a certain matrix. Then highly interactive software can be written for visualization of shape spaces and shape differences. The shape of a physical object is defined as whatever remains after the position of the object, its size and its orientation are accounted for. In many fields including medicine, biology, imaging, computer vision, industrial engineering, psychology, much of the data is spatial and is often in the form of images. This research will develop statistical and high-performance graphical methods for analyzing and visualizing shapes when these are of principal interest.
