Seminar Details
2017-03-21 (14:00) : Variational Methods for Manifold Valued Image Processing
At Euler building (room A.002)
Organized by Mathematical Engineering
Speaker :
Ronny Bergmann (University of Kaiserslautern)
Abstract :
In many real life scenarios measured data appears as values from a Riemannian
manifold. For example in interferometric Synthetic Aperture Radar (InSAR) data
is given as a phase, in electron backscattered diffraction (EBSD) as data items
being from a quotient of the orientation group SO(3), and in diffusion tensor
magnetic resonance imaging (DT-MRI) the measured data are symmetric positive
definite matrices. These data items are often measured on a pixel grid like
usual images and they also suffer from the same measurement errors like noisy
or incompleteness.Hence there is a need to perform image processing tasks like
denoising, inpainting or segmentation on these manifold-valued images. Recently
the ROF-Model for TV regularization has been transferred to the setting of
manifold-valued images to perform such image processing tasks.
In this talk we present methods and algorithms to compute the TV regularization
for manifold-valued images efficiently using variational methods. We present
generalizations to second order methods, and to the case, where the data is not
given on a pixel grid, for example when dealing with nonlocal methods.