Tensor Field Regularization Using Normalized Convolution and Markov Random Fields in a Bayesian Framework

C.-F. Westin, M. Martin-Fernandez, C. Alberola-Lopez, J. Ruiz-Alzola, H. Knutsson
Visualization and Image Processing of Tensor Fields. Series: Mathematics and Visualization
Pages 381-398,464-467
2006

Download full paper

Abstract

This chapter presents two techniques for regularization of tensor fields. We first present a nonlinear filtering technique based on normalized convolution, a general method for filtering missing and uncertain data. We describe how the signal cerntainty function can be constructed to depend on locally derived certainty information and further combined with a spatially dependent certainty field. This results in a reduced mixing between regions of different signal characteristics, and increased robustness to outliers, compared to the standard approach with a stochastic technique based on a multivariate Gaussian signal model in a Bayesian framework This method uses a Markov random field approach with a 3D neighborhood system for modeling spatial interactions between the tensors locally. Experiments both on synthetic and real data are presented. The driving tensor application for thsi work throughout the chapter is the filtering of diffusion tensor MRI data.

Glyph visualizaion for a coronal slice for the original noisy DT-MRI data from a monkey brain (a) and the same visualization after regularization (b)

Reference

Westin CF, Martin-Fernandez M, Alberola-Lopez C, Ruiz-Alzola J, Knutsson H. Tensor field regularization using normalized convolution and markov random fields in a bayesian framework. In J Weickert, H Hagen, eds., Visualization and Image Processing of Tensor Fields. Series: Mathematics and Visualization. Springer, 2006;381-398,464-467. ISBN:3-540-25032-8.

Bibtex entry

@InCollection{westinTensor06,
  author         = {C.-F. Westin and M. Martin-Fernandez and C. Alberola-Lopez 
                   and J. Ruiz-Alzola and H. Knutsson},                        
  title          = {Tensor Field Regularization Using Normalized Convolution   
                   and Markov Random Fields in a Bayesian Framework},          
  booktitle      = {Visualization and Image Processing of Tensor Fields.       
                   Series: Mathematics and Visualization},                     
  publisher      = {Springer},                                                 
  year           = {2006},                                                     
  pages          = {381--398,464--467},                                        
  editor         = {J. Weickert and H. Hagen},                                 
  note           = {ISBN:3-540-25032-8}
}

Grants

NIH P41-RR13218 (NAC), NIH R01-MH50747, TIC2001-3808-C02, NOE FP6-507609, Fulbright FU2003-0968

Copyright Information

© Springer-Verlag (Berlin - Heidelberg - New York). Copyrights to this PDF document are held by Springer-Verlag. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the Springer-Verlag Publishing.

This material is presented electronically to ensure timely dissemination of scholarly and technical work. Certain rights are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the author and/or copyright holder.