Total Bregman divergence and its applications to DTI analysis.
Divergence measures provide a means to measure the pairwise dissimilarity between "objects," e.g., vectors and probability density functions (pdfs). Kullback-Leibler (KL) divergence and the square loss (SL) function are two examples of commonly used dissimilarity measures which along with others belong to the family of Bregman divergences (BD). In this paper, we present a novel divergence dubbed the Total Bregman divergence (TBD), which is intrinsically robust to outliers, a very desirable property in many applications. Further, we derive the TBD center, called the t-center (using the l(1)-norm), for a population of positive definite matrices in closed form and show that it is invariant to transformation from the special linear group. This t-center, which is also robust to outliers, is then used in tensor interpolation as well as in an active contour based piecewise constant segmentation of a diffusion tensor magnetic resonance image (DT-MRI). Additionally, we derive the piecewise smooth active contour model for segmentation of DT-MRI using the TBD and present several comparative results on real data.
Department of Computer and Information Science and Engineering (CISE), The University of Florida, Gainesville, FL 32611, USA. vemuri@cise.ufl.edu
Baba C
BC
Vemuri
Meizhu
M
Liu
Shun-Ichi
S
Amari
Frank
F
Nielsen
D000465:Algorithms; D000818:Animals; D001921:Brain / Q000033:anatomy & histology; D056324:Diffusion Tensor Imaging / Q000379:methods*; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D016018:Least-Squares Analysis; D051381:Rats; D012815:Signal Processing, Computer-Assisted; D013116:Spinal Cord / Q000033:anatomy & histology