Non-Linear Gaussian Filters Performing Edge Preserving Diffusion
Mustererkennung 1995, 17. DAGM-Symposium
Curvature-Driven PDE Methods for Matrix-Valued Images
International Journal of Computer Vision
Median and related local filters for tensor-valued images
Signal Processing
Morphology for matrix data: Ordering versus PDE-based approach
Image and Vision Computing
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Two major problems in MR Diffusion Tensor Imaging, regularization and tracking are addressed. Regularization is performed on a variance homogenizing transformation of the tensor field via a nonlinear filter chain to preserve discontinuities. The suitability of the smoothing procedure is validated by Monte Carlo simulations. For tracking, the tensor field is diagonalized and a local bilinear interpolation of the corresponding direction field is performed. The track curves, which are not restricted to the measured grid, are modeled by following stepwise the interpolated directions. The presented methods are illustrated by applications to measured data.