Efficient Computation of the Inverse Gradient on Irregular Domains

The inverse gradient problem, finding a scalar field f with a gradient near a given vector field g on some bounded and connected domain Rn , can be solved by means of a Poisson equation with inhomogeneous Neumann boundary conditions. We present an elementary derivation of this partial differential equation and an efficient multigridbased method to numerically compute the inverse gradient on non-rectangular domains. The utility of the method is demonstrated by a range of important medical applications such as phase unwrapping, pressure computation, inverse deformation fields, and fiber bundle tracking.

• Type: Conference
• Year: 2007
• Where: ICCV
• Authors: Gunnar Farnebäck, Hans Knutsson, Joakim Rydell, Mats T. Andersson, Tino Ebbers
• Keywords: Computer Vision, Fiber Bundle Tracking, ICCV 2007, Inverse Deformation Fields, Inverse Gradient Problem, Neumann Boundary Conditions, Poisson Equation