caa a22 4500 467914184 CHVBK 20180406152857.0 cr unu---uuuuu 170328e20060801xx s 000 0 eng 10.1007/s11263-006-6854-8 doi (NATIONALLICENCE)springer-10.1007/s11263-006-6854-8 Curvature-Driven PDE Methods for Matrix-Valued Images [Elektronische Daten] [Christian Feddern, Joachim Weickert, Bernhard Burgeth, Martin Welk] Matrix-valued data sets arise in a number of applications including diffusion tensor magnetic resonance imaging (DT-MRI) and physical measurements of anisotropic behaviour. Consequently, there arises the need to filter and segment such tensor fields. In order to detect edge-like structures in tensor fields, we first generalise Di Zenzo's concept of a structure tensor for vector-valued images to tensor-valued data. This structure tensor allows us to extend scalar-valued mean curvature motion and self-snakes to the tensor setting. We present both two-dimensional and three-dimensional formulations, and we prove that these filters maintain positive semidefiniteness if the initial matrix data are positive semidefinite. We give an interpretation of tensorial mean curvature motion as a process for which the corresponding curve evolution of each generalised level line is the gradient descent of its total length. Moreover, we propose a geodesic active contour model for segmenting tensor fields and interpret it as a minimiser of a suitable energy functional with a metric induced by the tensor image. Since tensorial active contours incorporate information from all channels, they give a contour representation that is highly robust under noise. Experiments on three-dimensional DT-MRI data and an indefinite tensor field from fluid dynamics show that the proposed methods inherit the essential properties of their scalar-valued counterparts. Springer Science + Business Media, LLC, 2006 DT-MRI nationallicence denoising nationallicence segmentation nationallicence edge detection nationallicence structure tensor nationallicence mean curvature motion nationallicence self-snakes nationallicence active contours nationallicence Feddern Christian Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Building E11, 66041, Saarbrücken, Germany aut Weickert Joachim Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Building E11, 66041, Saarbrücken, Germany aut Burgeth Bernhard Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Building E11, 66041, Saarbrücken, Germany aut Welk Martin Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Building E11, 66041, Saarbrücken, Germany aut International Journal of Computer Vision Kluwer Academic Publishers 69/1(2006-08-01), 93-107 0920-5691 69:1<93 2006 69 11263 https://doi.org/10.1007/s11263-006-6854-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11263-006-6854-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Feddern Christian Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Building E11, 66041, Saarbrücken, Germany aut NATIONALLICENCE 700 1- Weickert Joachim Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Building E11, 66041, Saarbrücken, Germany aut NATIONALLICENCE 700 1- Burgeth Bernhard Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Building E11, 66041, Saarbrücken, Germany aut NATIONALLICENCE 700 1- Welk Martin Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Building E11, 66041, Saarbrücken, Germany aut NATIONALLICENCE 773 0- International Journal of Computer Vision Kluwer Academic Publishers 69/1(2006-08-01), 93-107 0920-5691 69:1<93 2006 69 11263 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer