Manifold learning and representations for image analysis and visualization
2006 (English)Licentiate thesis, comprehensive summary (Other academic)
We present a novel method for manifold learning, i.e. identification of the low-dimensional manifold-like structure present in a set of data points in a possibly high-dimensional space. The main idea is derived from the concept of Riemannian normal coordinates. This coordinate system is in a way a generalization of Cartesian coordinates in Euclidean space. We translate this idea to a cloud of data points in order to perform dimension reduction. Our implementation currently uses Dijkstra's algorithm for shortest paths in graphs and some basic concepts from differential geometry. We expect this approach to open up new possibilities for analysis of e.g. shape in medical imaging and signal processing of manifold-valued signals, where the coordinate system is learned from experimental high-dimensional data rather than defined analytically using e.g. models based on Lie-groups.
We propose a novel post processing method for visualization of fiber traces from DT-MRI data. Using a recently proposed non-linear dimensionality reduction technique, Laplacian eigenmaps (Belkin and Niyogi, 2002), we create a mapping from a set of fiber traces to a low dimensional Euclidean space. Laplacian eigenmaps constructs this mapping so that similar traces are mapped to similar points, given a custom made pairwise similarity measure for fiber traces. We demonstrate that when the low-dimensional space is the RGB color space, this can be used to visualize fiber traces in a way which enhances the perception of fiber bundles and connectivity in the human brain.
Place, publisher, year, edition, pages
Institutionen för medicinsk teknik , 2006. , 116 p.
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1235
manifold learning, image analysis, signal processing, diffusion tensor mri
Biomedical Laboratory Science/Technology
IdentifiersURN: urn:nbn:se:liu:diva-7559ISBN: 91-85497-33-9OAI: oai:DiVA.org:liu-7559DiVA: diva2:22566
2006-03-10, Seminarierummet plan 13, Institutionen för medicinsk teknik, 581 85 LINKÖPING, LINKÖPING, 10:00 (English)
Lenz, Reiner, Ass. Prof.
Knutsson, HansHerberthson, MagnusWestin, Carl-Fredrik
Report code: LIU-TEK-LIC-2006:162006-10-162006-10-162013-08-28