Imaging vector fields using line integral convolution
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
International Journal of Computer Vision
Discrete exterior calculus
Journal of Cognitive Neuroscience
Computing - Special Issue on Industrial Geometry
A riemannian framework for the processing of tensor-valued images
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
IEEE Transactions on Image Processing
Anisotropic diffusion of tensor fields for fold shape analysis on surfaces
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
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The exterior surface of the brain is characterized by a juxtaposition of crests and troughs that together form a folding pattern. The majority of the deformations that occur in the normal course of adult human development result in folds changing their length or width. Current statistical shape analysis methods cannot easily discriminate between these two cases. Using discrete exterior calculus and Tikhonov regularization, we develop a method to estimate a dense orientation field in the tangent space of a surface described by a triangulated mesh, in the direction of its folds. We then use this orientation field to distinguish between shape differences in the direction parallel to folds and those in the direction across them. We test the method quantitatively on synthetic data and qualitatively on a database consisting of segmented cortical surfaces of 92 healthy subjects and 97 subjects with Alzheimer's disease. The method estimates the correct fold directions and also indicates that the healthy and diseased subjects are distinguished by shape differences that are in the direction perpendicular to the underlying hippocampi, a finding which is consistent with the neuroscientific literature. These results demonstrate the importance of direction specific computational methods for shape analysis.