On characterizing and analyzing diffusion tensor images by learning their underlying manifold structure

Parmeshwar Khurd, Ragini Verma, Christos Davatzikos

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The growing importance of diffusion tensor imaging (DTI) in studying the white matter architecture in normal and pathologic states necessitates the development of tools for comprehensive analysis of diffusion tensor data. Operations such as multivariate statistical analysis and hypothesis testing, interpolation and filtering, must now be performed on tensor data, and must overcome challenges introduced by the non-linearity and high dimensionality of the tensors. In this paper, we present a novel approach to performing these computations by modeling the underlying manifold structure of the tensors, using a combination of two manifold learning techniques, isometric mapping (ISOMAP) and local tangent space alignment (LTSA). While ISOMAP identifies the dimensionality of the manifold of the tensors and embeds the tensors into a linear space, facilitating statistical computations therein, operations like interpolation and filtering, integral to the process of normalization, require the reconstruction of the tensor in the tensor domain. To obtain this reverse mapping from the linear space to the tensor domain, i.e. to the domain of the original tensor data, we use LTSA. The modeling of the underlying manifold structure renders our approach better applicable to tensor data than existing methods that may not always be able to capture the non-linearity present in the tensors under consideration. In various simulations with known ground truth, we demonstrate the effectiveness of our framework based on ISOMAP and LTSA in performing a comprehensive analysis of DTI data.

Original languageEnglish (US)
Title of host publication2006 Conference on Computer Vision and Pattern Recognition Workshop
DOIs
StatePublished - 2006
Event2006 Conference on Computer Vision and Pattern Recognition Workshops - New York, NY, United States
Duration: Jun 17 2006Jun 22 2006

Publication series

NameProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Volume2006
ISSN (Print)1063-6919

Other

Other2006 Conference on Computer Vision and Pattern Recognition Workshops
CountryUnited States
CityNew York, NY
Period6/17/066/22/06

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition

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