Improved tensor scale computation with application to medical image interpolation

Tensor scale (t-scale) is a parametric representation of local structure morphology that simultaneously describes its orientation, shape and isotropic scale. At any image location, t-scale represents the largest ellipse (an ellipsoid in three dimensions) centered at that location and contained in the same homogeneous region. Here, we present an improved algorithm for t-scale computation and study its application to image interpolation. Specifically, the t-scale computation algorithm is improved by: (1) enhancing the accuracy of identifying local structure boundary and (2) combining both algebraic and geometric approaches in ellipse fitting. In the context of interpolation, a closed form solution is presented to determine the interpolation line at each image location in a gray level image using t-scale information of adjacent slices. At each location on an image slice, the method derives normal vector from its t-scale that yields trans-orientation of the local structure and points to the closest edge point. Normal vectors at the matching two-dimensional locations on two adjacent slices are used to compute the interpolation line using a closed form equation. The method has been applied to BrainWeb data sets and to several other images from clinical applications and its accuracy and response to noise and other image-degrading factors have been examined and compared with those of current state-of-the-art interpolation methods. Experimental results have established the superiority of the new t-scale based interpolation method as compared to existing interpolation algorithms. Also, a quantitative analysis based on the paired t-test of residual errors has ascertained that the improvements observed using the t-scale based interpolation are statistically significant.