Total Bregman divergence and its applications to DTI analysis

Area of Science:

• Mathematics
• Computer Vision
• Medical Imaging

Background:

• Divergence measures quantify dissimilarity between objects like vectors and probability density functions (PDFs).
• Common examples include Kullback-Leibler (KL) divergence and square loss (SL), both Bregman divergences (BD).
• Existing measures can be sensitive to outliers, limiting their application in noisy datasets.

Purpose of the Study:

• Introduce a novel divergence measure, the Total Bregman divergence (TBD), with inherent robustness to outliers.
• Derive a robust center (t-center) for positive definite matrices using the TBD.
• Apply the TBD and its t-center to diffusion tensor magnetic resonance image (DT-MRI) segmentation.

Main Methods:

• Developed the Total Bregman divergence (TBD) as a new dissimilarity measure.
• Derived the closed-form TBD center (t-center) for positive definite matrices, proving its invariance to special linear group transformations.
• Utilized the t-center for tensor interpolation and active contour segmentation of DT-MRI data.
• Formulated a piecewise smooth active contour model based on TBD for DT-MRI segmentation.

Main Results:

• The TBD is intrinsically robust to outliers.
• The derived t-center is also robust to outliers and invariant to specific matrix transformations.
• Successful application of TBD-based methods in tensor interpolation and DT-MRI segmentation.
• Demonstrated comparative advantages on real DT-MRI data.

Conclusions:

• The Total Bregman divergence offers a robust alternative to existing divergence measures, particularly in the presence of outliers.
• The TBD and its t-center provide effective tools for advanced image analysis tasks like DT-MRI segmentation.
• The proposed methods show promise for improving the accuracy and reliability of medical image segmentation.