author = {Berkels, Benjamin},
  title = {Joint methods in imaging based on diffuse image representations},
  school = {University of Bonn},
  year = {2010},
  type = {Dissertation},
  abstract = {This thesis deals with the application and the analysis of different
	variants of the Mumford-Shah model in the context of image processing.
	In this kind of models, a given function is approximated in a piecewise
	smooth or piecewise constant manner. Especially the numerical treatment
	of the discontinuities requires additional models that are also outlined
	in this work. The main part of this thesis is concerned with four
	different topics.
	Simultaneous edge detection and registration of two images: The image
	edges are detected with the Ambrosio-Tortorelli model, an approximation
	of the Mumford-Shah model that approximates the discontinuity set
	with a phase field, and the registration is based on these edges.
	The registration obtained by this model is fully symmetric in the
	sense that the same matching is obtained if the roles of the two
	input images are swapped.
	Detection of grain boundaries from atomic scale images of metals or
	metal alloys: This is an image processing problem from materials
	science where atomic scale images are obtained either experimentally
	for instance by transmission electron microscopy or by numerical
	simulation tools. Grains are homogenous material regions whose atomic
	lattice orientation differs from their surroundings. Based on a Mumford-Shah
	type functional, the grain boundaries are modeled as the discontinuity
	set of the lattice orientation. In addition to the grain boundaries,
	the model incorporates the extraction of a global elastic deformation
	of the atomic lattice. Numerically, the discontinuity set is modeled
	by a level set function following the approach by Chan and Vese.
	Joint motion estimation and restoration of motion-blurred video: A
	variational model for joint object detection, motion estimation and
	deblurring of consecutive video frames is proposed. For this purpose,
	a new motion blur model is developed that accurately describes the
	blur also close to the boundary of a moving object. Here, the video
	is assumed to consist of an object moving in front of a static background.
	The segmentation into object and background is handled by a Mumford-Shah
	type aspect of the proposed model.
	Convexification of the binary Mumford-Shah segmentation model: After
	considering the application of Mumford-Shah type models to tackle
	specific image processing problems in the previous topics, the Mumford-Shah
	model itself is studied more closely. Inspired by the work of Nikolova,
	Esedoglu and Chan, a method is developed that allows global minimization
	of the binary Mumford-Shah segmentation model by solving a convex,
	unconstrained optimization problem. In an outlook, segmentation of
	flowfields into piecewise affine regions using this convexification
	method is briefly discussed.},
  url = {}