Title:  An Affine Invariant Tensor Dissimilarity Measure and its 
        Applications to Tensor-valued Image Segmentation


			Baba C. Vemuri
		  UFRF Professor & Director
	  Center for Computer Vision & Visualization
	             Dept. of CISE, E324
		       Univ. of Florida
		 Gainesville, Fl. 32611-6120
		       FAX:352-392-1239
		http://www.cis.ufl.edu/~vemuri


Abstract:
Tensor fields specifically, matrix valued data sets, have recently
attracted increased attention in the fields of image processing,
computer vision, visualization and medical imaging. In this paper, we
present a novel definition of tensor "distance" grounded in concepts
from information theory and incorporate it in the segmentation of
tensor-valued images.  In some applications, a symmetric positive
definite (SPD) tensor at each point of a tensor valued image can be
interpreted as the covariance matrix of a local Gaussian
distribution. Thus, a natural measure of dissimilarity between SPD
tensors would be the KL divergence or its relative. We propose the
square root of the J-divergence (symmetrized KL) between two Gaussian
distributions corresponding to the tensors being compared and derive a
novel closed form expression. Unlike the traditional Frobenius
norm-based tensor distance, our "distance" is affine invariant, a
desirable property in many applications.  We then incorporate this new
tensor ``distance'' in a region based active contour model for bimodal
tensor field segmentation and show its application to the segmentation
of diffusion tensor magnetic resonance images (DT-MRI) as well as for
the texture segmentation problem in computer vision.  Synthetic and
real data experiments are shown to depict the performance of the
proposed model.