Geometric Level Set Methods in Imaging, Vision, and Graphics

Introduction Imageprocessing,computervisionandcomputergraphicsarenowestablished - search areas. Pattern recognition and arti?cial intelligence were the origins of the explorationofthespace ofimages.Simplistic digitaltechniquesusedatthe beg- ning of 60’s for gray image processing operations have been now replaced with a complex mathematical framework that aims to exploit and understand images in two and three dimensions. Advances in computing power continue to make the use and processing of visual information an important part of our lives. The evolution of these techniques was a natural outcome of the need to p- cess an emerging informationspace, the space of natural images. Images in space and time are now a critical part of many human activities. First, pictures and now video streams were used to eternalize small and signi?cant moments of our life. Entertainment including movies, TV-programs and video games are part of our every-day life where capturing, editing, understanding and transmitting images are issues to be dealt with. The medical sector is also a major area for the use of images. The evolution of the acquisition devices led to new ways of capturing information, not visible by the human eye. Medical imaging is probably the most established market for processing visual information[405]. Visualization of c- plex structures and automated processing towards computer aided diagnosis is used more and more by the physicians in the diagnostic process. Safety and se- rity are also important areas where images and video play a signi?cant role [432].

* Level set methods * Deformable models * Fast methods for implicit active contour models * Fast edge integration * Variational snake theory * Multiplicative denoising and deblurring * Total varation minimization for scalar/vector regularization * Morphological global reconstruction and levelings * Fast marching techniques for visual grouping and segmentation * Multiphase object detection and image segmentation * Adaptive segmentation of vector-valued images * Mumford-Shah for segmentation and stereo * Shape analysis toward model-based segmentation * Joint image registration and segmentation * Image alignment * Variational principles in optical flow estimation and tracking * Region matching and tracking under deformations or occlusions * Computational stereo * Visualization, analysis and shape reconstruction of sparse data * Variational problems and partial differential equations on implicit surfaces * Knowledge-based segmentation of medical images * Topology preserving geometric deformable models for brain reconstruction * Editing geometric models * Simulating natural phenomena