Title :
Efficient Computation of the Inverse Gradient on Irregular Domains
Author :
Farnebäck, Gunnar ; Rydell, Joakim ; Ebbers, Tino ; Andersson, Mats ; Knutsson, Hans
Author_Institution :
Linkoping Univ., Linkoping
Abstract :
The inverse gradient problem, finding a scalar field f with a gradient near a given vector field g on some bounded and connected domain Omega isin 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 multigrid-based 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.
Keywords :
Jacobian matrices; Poisson equation; gradient methods; image registration; inverse problems; medical image processing; vectors; Jacobian matrices; Poisson equation; fiber bundle tracking; image registration; inhomogeneous Neumann boundary conditions; inverse deformation fields; inverse gradient problem; irregular domains; iterative methods; medical imaging applications; multigrid-based method; partial differential equation; phase unwrapping; pressure computation; scalar field; vector field; Biomedical computing; Biomedical engineering; Biomedical imaging; Biomedical informatics; Boundary conditions; Calculus; Partial differential equations; Physiology; Poisson equations; Visualization;
Conference_Titel :
Computer Vision, 2007. ICCV 2007. IEEE 11th International Conference on
Conference_Location :
Rio de Janeiro
Print_ISBN :
978-1-4244-1630-1
Electronic_ISBN :
1550-5499
DOI :
10.1109/ICCV.2007.4409176