Prof. Dr. Anuj Srivastava
Fellow, Inst. of Electrical and Electronic Engineers (IEEE)
Fellow, American Statistical Association (ASA)
Fellow, Intern. Assoc. for Pattern Recognition (IAPR)
Professor, Department of Statistics, Distinguished Research Professor
Florida State University, Statistical Shape Analysis and Modeling Group (SSAMG)
Title - Functional and Shape Data Analysis
Functional and shape data analysis are important research areas, due to their broad applications across many disciplines. An essential component in solving them is the registration of points across functional objects. Without proper registration the results are often inferior and difficult to interpret. The current practice in functional data analysis and shape communities is to treat registration as a pre-processing step, using off-the-shelf alignment procedures, and follow it up with statistical analysis of the resulting data. In contrast, an elastic framework is a more comprehensive approach, where one solves for the registration and statistical inferences in a simultaneous fashion. The key idea here is to use Riemannian metrics with appropriate invariance properties, to form objective functions for alignment and to develop statistical models involving functional data. While these elastic metrics are complicated in general, we have developed a family of square-root transformations that map these metrics into simpler Euclidean metrics, thus enabling more standard statistical procedures. Specifically, we have developed techniques for elastic functional PCA and elastic regression models involving functional variables. This course will demonstrate these ideas using imaging data in neuroscience where anatomical structures can often be represented as functions (curves or surfaces) on intervals or spheres. Examples of curves include DTI fiber tracts and sulcal folds while examples of surfaces include subcortical structures (hippocampus, thalamus, putamen, etc). Statistical goals here include shape analysis and modeling of these structures and to use their shapes in medical diagnosis. As an extension, we will also cover shape analysis of 3D objects by considering shapes of their boundaries (surfaces). A prominent example of this kind of data is full body scans of humans, and we will discuss elastic shape analysis of human body shapes.