Exploiting Spatial Information to Enhance DTI Segmentations via Spatial Fuzzy c-Means with Covariance Matrix Data and Non-Euclidean Metrics

Safa Elsheikh, Andrew Fish, Diwei Zhou

Research output: Contribution to journalArticlepeer-review


A diffusion tensor models the covariance of the Brownian motion of water at a voxel and is required to be symmetric and positive semi-definite. Therefore, image processing approaches, designed for linear entities, are not effective for diffusion tensor data manipulation, and the existence of artefacts in diffusion tensor imaging acquisition makes diffusion tensor data segmentation even more challenging. In this study, we develop a spatial fuzzy c-means clustering method for diffusion tensor data that effectively segments diffusion tensor images by accounting for the noise, partial voluming, magnetic field inhomogeneity, and other imaging artefacts. To retain the symmetry and positive semi-definiteness of diffusion tensors, the log and root Euclidean metrics are used to estimate the mean diffusion tensor for each cluster. The method exploits spatial contextual information and provides uncertainty information in segmentation decisions by calculating the membership values for assigning a diffusion tensor at one voxel to different clusters. A regularisation model that allows the user to integrate their prior knowledge into the segmentation scheme or to highlight and segment local structures is also proposed. Experiments on simulated images and real brain datasets from healthy and Spinocerebellar ataxia 2 subjects showed that the new method was more effective than conventional segmentation methods.
Original languageEnglish
Article number7003
Number of pages19
JournalApplied Sciences
Issue number15
Publication statusPublished - 29 Jul 2021

Bibliographical note

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Funding Information:
Funding: This research was funded by the Higher Education Innovation Funding-UK and the EPSRC IAA (UK).


  • diffusion tensor
  • fuzzy c-means
  • non-euclidean metrics
  • K-means
  • Corpus Callosum
  • Diffusion tensor
  • Non-euclidean metrics
  • Corpus callosum
  • Fuzzy c-means


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