Document Type


Date of Degree

Spring 2009

Degree Name

MS (Master of Science)

Degree In

Electrical and Computer Engineering

First Advisor

Punam K. Saha

First Committee Member

Milan Sonka

Second Committee Member

Mona K. Garvin


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 is the parametric representation of the largest ellipse (an ellipsoid in 3D) centered at that location and contained in the same homogeneous region.

Recently, we have improved the t-scale computation algorithm by: (1) optimizing digital representations for LoG and DoG kernels for edge detection and (2) ellipse fitting by using minimization of both algebraic and geometric distance errors. Also, t-scale has been applied to computing the deformation vector field with applications to medical image registration. Currently, the method is implemented in two-dimension (2D) and the deformation vector field is directly computed from t-scale-derived normal vectors at matching locations in two images to be registered. Also, the method has been used to develop a simple algorithm for computing 2D warping from one shape onto another. Meanwhile, t-scale has been applied to generating interpolation lines with applications to medical image interpolation using normal vector. Normal vector yields local structure orientation pointing to the closest edge. However, this information is less reliable along the medial axis of a shape as it may be associated with either of the two opposite edges of the local shape. This problem is overcome using a shape-linearity measure estimating relative changes in scale along the orthogonal direction. Preliminary results demonstrate the method's potential in estimating deformation between two images and interpolating between neighboring slices in a grey scale image.


interpolation, registration, tensor scale


vii, 48 pages


Includes bibliographical references (pages 45-48).


Copyright 2009 Ziyue Xu