Segmentation of DTI based on tensorial morphological gradient

Abstract

This paper presents a segmentation technique for diffusion tensor imaging (DTI). This technique is based on a tensorial morphological gradient (TMG), defined as the maximum dissimilarity over the neighborhood. Once this gradient is computed, the tensorial segmentation problem becomes an scalar one, which can be solved by conventional techniques, such as watershed transform and thresholding. Similarity functions, namely the dot product, the tensorial dot product, the J-divergence and the Frobenius norm, were compared, in order to understand their differences regarding the measurement of tensor dissimilarities. The study showed that the dot product and the tensorial dot product turned out to be inappropriate for computation of the TMG, while the Frobenius norm and the J-divergence were both capable of measuring tensor dissimilarities, despite the distortion of Frobenius norm, since it is not an affine invariant measure. In order to validate the TMG as a solution for DTI segmentation, its computation was performed using distinct similarity measures and structuring elements. TMG results were also compared to fractional anisotropy. Finally, synthetic and real DTI were used in the method validation. Experiments showed that the TMG enables the segmentation of DTI by watershed transform or by a simple choice of a threshold. The strength of the proposed segmentation method is its simplicity and robustness, consequences of TMG computation. It enables the use, not only of well-known algorithms and tools from the mathematical morphology, but also of any other segmentation method to segment DTI, since TMG computation transforms tensorial images in scalar ones.