General Departmental Seminar Series
Spatially adaptive anisotropic kernel smoothing and
its application to diffusion tensor images of the
Moo K. Chung, Ph.D., Assistant Professor
Department of Statistics
Department of Biostatistics & Medical Informatics
W.M. Keck Laboratory for Functional Brain Imaging and Behavior
University of Wisconsin-Madison
Friday, September 12, 2003, 12:00 - 1:00 p.m.
G5/136-142 Clinical Sciences Center, 600 Highland Ave.
Diffusion tensor imaging technique provides us directional information of water molecule diffusion in the white matter of the brain as 3 by 3 symmetric positive definite matrix called diffusion coefficients. The diffusion coefficients can be used to estimate the pattern of the white fiber connection.
We present a new probabilistic approach to represent the pattern of the white fiber connectivity based on the transition probability of random walk. By realizing that the Chapman-Kolmogorov equation can be approximately formulated as an isotropic Gaussian kernel smoothing locally, estimating the transition probability of random walks can be done as an image smoothing operation.
Smoothing can be viewed as reassigning data values according to the (Riemannian) metric structures of data. Following this view, we can match the covariance matrix of Gaussian kernel to the Riemannian metric tensor of data locally to generate spatially adaptive kernel. It enables us to smooth more along the principal eigenvectors of diffusion coefficient matrix.
Combining these two ideas together, the transition probability of random walk can be approximated as the spatially adaptive Gaussian kernel smoothing.
This is the joint work with Andrew Alexender of the department of the medical physics and Mariana Lazar, Yuefeng Lu and Richard Davidson.