Day 5: Optimal mass transport has become an essential tool in medical imaging analysis. We will show how it may be used for various purposes such as elastic image registration as well as visualization. Topics include prediction of outcomes for left atial fibrillation ablation and traumatic brain injury.
Creator:
Tannenbaum, Allen (State University of New York, Stony Brook (SUNY))
Created:
2014-06-13
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Day 3: We describe several possible approaches to extending the classical theory of OMT to the multivariate (matrix-valued) case. Some applications to spectral analysis will be given.
Creator:
Tannenbaum, Allen (State University of New York, Stony Brook (SUNY))
Created:
2014-06-11
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Day 1: We introduce the Monge-Kantorovich (MK) problem and then give a brief overview of the calculus of variations, and how this may be used to treat Monge-Kantorovich, that is, the Optimal Transport problem.
Creator:
Tannenbaum, Allen (State University of New York, Stony Brook (SUNY))
Created:
2014-06-09
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In this talk, we will review some key inverse problems in medical imaging and vision, in particular, segmentation and registration. The approach will be via energy minimization through the calculus of variations as well Bayesian. We will also show how these techniques made be made interactive through the use of feedback. This will allow us to ma...
Creator:
Tannenbaum, Allen (State University of New York, Stony Brook (SUNY))
Created:
2016-03-15
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Day 2: Using ideas from fluid dynamics, we derive a partial differential equation (pde) whose asymptotic solution solves the optimal transport problem in L2. Numerical schemes are then described allowing one to implement the pde on computer to be used in real-world applications.
Creator:
Tannenbaum, Allen (State University of New York, Stony Brook (SUNY))
Created:
2014-06-10
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Day 4: Transport theory leads to a natural metric of the space of probability densities that in turn leads to a natural Riemannian structure. We will describe some of the basic geometric concepts such as Ricci curvature, and see how this methodology allows one to define a notion of curvature on rather general metric spaces. We will describe appl...
Creator:
Tannenbaum, Allen (State University of New York, Stony Brook (SUNY))
Created:
2014-06-12
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Allen Tannenbaum will be speaking on the theme of Optimal Mass Transport for Problems in Systems, Control, and Signal Processing. The lectures will be based on a number of published papers as well as lecture notes. He will lead participants through basic methods in the calculus of variations for the classical solution of the Monge-Kantorovich pr...
Creator:
Rachev, Svetlozar (Zari) (State University of New York, Stony Brook (SUNY)); Tannenbaum, Allen (State University of New York, Stony Brook (SUNY))
Created:
2014-06-09
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.