Sharpening fibers in diffusion weighted MRI via erosion

T.C.J. Dela Haije, R. Duits, C.M.W. Tax

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

6 Citations (Scopus)


In this chapter erosion is generalized to the space of diffusion weighted MRI data. This is done effectively by solving a Hamilton-Jacobi-Bellman (HJB) system (erosion) on the coupled space of three dimensional positions and orientations, embedded as a quotient in the group of three dimensional rigid body motions. The solution to the HJB equations is given by a well-posed morphological convolution. We present two numerical approaches to solve the HJB equations: analytical kernels, and finite differences. Proof of concept is given by showing improved visibility of major fiber bundles in both artificial and human data. Furthermore, the method is shown to significantly improve the output of a probabilistic tractography algorithm used to extract the optic radiation.
Original languageEnglish
Title of host publicationVisualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data, part II
EditorsC.-F. Westin, A. Vilanova, B. Burgeth
ISBN (Print)978-3-642-54300-5
Publication statusPublished - 2014

Publication series

NameMathematics and Visualization
ISSN (Print)1612-3786


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