Abstract: There is a great interest in characterizing populations of objects, such as anatomical parts, human faces, cells, proteins, neurons, etc, based on their structural variability. Quantifying structures to enable statistical inferences requires metrics, especially metrics with certain invariances and also computational tractability. I will describe a family of elastic Riemannian metrics, that allow joint registration and comparison of objects. A set of square-root transformations convert these elastic metrics into Euclidean metrics, thus greatly simplifying ensuing statistical analysis. A typical statistical analysis includes computing means and covariances in shapes space, discovering principal modes of variability in given data, and to test hypotheses associated with given shapes. I will develop this framework starting from similar objects -- real-valued functions on an interval -— and work through objects of increasing complexity. Srivastava will cover curves in Euclidean spaces and on nonlinear manifolds, surfaces of 3D objects, and shapes of certain types of trees.
Bio: Anuj Srivastava is a professor in the Department of Statistics and a Distinguished Research Professor at the Florida State University. His areas of research include statistical analysis on nonlinear manifolds, statisticalcomputer vision, functional data analysis, and statistical shape theory. He has been an associate editor for several statistics and IEEE journals. He is a fellow of the International Association of Pattern Recognition (IAPR), Institute for Electrical and Electronic Engineers (IEEE), and American Statistical Association (ASA). He has held several visiting positions at European universities, including INRIA, France, the University of Lille, France, and Durham University, UK. He has been advisor to more than 20 doctoral students so far in his career. He has authored more than 200 papers in peer-reviewed journals and top-tier conferences, and also several books, including the recent Springer textbook on "Functional and Shape Data Analysis."