This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
The investigator and his colleagues will continue the study on diffeomorphic deformation of shapes. This framework supplies a rigorous mathematical metric on the shape space, a valuable quantitative measurement of the similarities between shapes. In the proposed project, the investigator and his colleagues will investigate diffeomorphic deformations of textured shapes. This study is to address the problems caused by boundary conditions in the current setup and response to the need of matching regions of interest directly in medical applications. Two problems will be studied: one is to build a rigorous mathematical framework for diffeomorphic deformations of textured shapes, another is to develop computational efficient algorithms for finding the shortest path connecting the textured shapes through the space of diffeomorphisms.
Changes in the anatomical structures occur during the development and aging process, as well as during many disease and injury process. Detecting and monitoring the anatomy changes are crucial in disease diagnosis, treatment and prevention. The results of this research will provide new image analysis tools for quantitative studies of variations of biological shapes, detecting and tracking changes of individual anatomy structures. They can also be applied to computer vision in object tracking, recognition and classification.
