Manifold learning and representations for image analysis and visualization

• 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.

Subject headings

MEDICIN OCH HÄLSOVETENSKAP  -- Medicinsk bioteknologi -- Biomedicinsk laboratorievetenskap/teknologi (hsv//swe)

MEDICAL AND HEALTH SCIENCES  -- Medical Biotechnology -- Biomedical Laboratory Science/Technology (hsv//eng)

Keyword

manifold learning

image analysis

signal processing

diffusion tensor mri

Medical informatics

Medicinsk informatik

Publication and Content Type

vet (subject category)

lic (subject category)