Tensorial Morphological Gradient (TMG)

The TMG transforms the tensorial information into a scalar map, retaining border information. This allows one to use the resulting scalar map, together with the watershed transform, to segment DTI. In summary, the computed TMG in a neighborhood given by an structuring element is the maximum dissimilarity among all pairwise dissimilarities.

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Figura 1: TMG computation

Segmentation experiments showed that the method based on the TMG and the watershed transform are able to delineated brain structures from diffusion tensor data. Two main concepts here are crucial to a good segmentation result:

  • the dissimilarity measure used in the TMG computation;
  • the markers for the watershed transform.

Main challenges:

  • The first experiments were conducted using popular dissimilarity measures: Dot product, Tensorial dot product, Frobenius Norm, J-divergence, Riemannian metric, etc. But theoretical and experimental analysis indicate that none of the used measures are ideal for segmenting purpose and better results could be obtained if we use a more adequate dissimilarity measure.
  • The watershed markers are automatically selected using the dynamics of the regional minima. A distinct criteria for marker selection could also improve the segmentation results.

Related publications: