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The Mumford-Shah Functional and its Applications in Image Processing: the Image Registration Case

Technical report


Ioana Gheta


Technical report IES-2009-02. In: Jürgen Beyerer, Marco Huber (eds.), Proceedings of the 2009 Joint Workshop of Fraunhofer IOSB and Institute for Anthropomatics, Vision and Fusion Laboratory, KIT Scientific Publishing, 2009.



This contribution presents a short overview of the development of the Mumford-Shah functional (MSF) and its applications in image processing with emphasis on image registration. MSF has been primarily developed for image segmentation having the main advantage of not requiring prior information. Its main disadvantages are the ill-posedness and the need of discretization when employing the continuous formulation.

Despite these disadvantages MSF is meanwhile also employed for object detection, image registration and inpainting. The known methods for image registration of stereo series perform a pairwise registration mostly based on grey values. If the image series are combined image series (e.g., stereo and spectral image series) a registration method invariant with regard to the grey values is necessary. This contribution presents new ideas of how MSF can be used to perform an edge based registration of such combined image series.