Recent improvements in tensor scale computation and new applications to medical image registration and interpolation

Recommended Citation Xu, Ziyue. "Recent improvements in tensor scale computation and new applications to medical image registration and interpolation." other faculties, staffs and students at the Iowa Institute for Biomedical Imaging for their help and lectures. iii ABSTRACT 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. Table 1 Mean absolute errors (gray value range 0~255) and standard deviation of the absolute errors between 20 pairs of successive image slices before and after applying different registration methods.. Figure 16 Performance of different methods for data at different noise level measured by (a) MAD and (b) square root of MSD.. Figure 17 Performance of different methods for data at different level of intensity non-uniformity measured by (a) MAD and (b) square root of MSD.. Figure 18 Performance of different methods on 12 images measured by (a) MAD and (b) square root of MSD. .