The PI, together with his collaborators and students, will develop new models and numerical algorithms for the solution of a number of fundamental problems in image processing and computer vision. The models will be based on the calculus of variations and partial differential equations (PDE) that describe curve and surface evolutions. A main goal of the project will be to devise new models that incorporate prior shape information into existing variational image segmentation techniques such as the Mumford-Shah model and its variants. The new models will be designed to find in given images objects resembling a specified shape regardless of the objects' location and orientation in the image. In addition, they will have convenient numerical implementations using techniques that have already proven their utility in related vision applications, such as the level set method. A second area of research will be to develop novel, efficient numerical algorithms for the solution of PDE that arise in a number of computer vision models and in other fields such as material science. Specifically, the investigator will explore new computational techniques for the solution of high order PDE that describe geometric motion of interfaces, such as the Willmore flow and motion by surface diffusion. These evolutions are computationally very expensive using current techniques. The new approach will be to reduce the computation of these motions to alternating simple operations for which efficient algorithms are already available. Also in this vein, the project will develop new numerical algorithms inspired by models and techniques in image processing for the computation of energy driven dynamics of multiple phases and junctions.
Image segmentation is a fundamental procedure of computer vision. It is a necessary preliminary step whenever useful information is to be extracted from digital images automatically. Its goal is to identify parts of the image that belong to distinct objects, often without knowing what objects might be present in the image. In many practical applications, however, a specific object of known shape is sought in the images. For example, in aerial imagery, the object of interest might be a certain vehicle that has a distinctive outline. Or, in a medical application, it might be desired to identify automatically the individual vertebrae in x-ray images of the spine. It such settings, it would help the success rate of the segmentation procedure if the algorithms could be made aware of what is being sought. This project will develop models and numerical techniques that incorporate prior shape information about objects of interest into the segmentation process, thereby leading to better segmentation methods.
