An analytic approach to tensor scale with efficient computational solution and applications to medical imaging

Abstract

Scale is a widely used notion in medical image analysis that evolved in the form of scale-space theory where the key idea is to represent and analyze an image at various resolutions. Recently, a notion of local morphometric scale referred to as “tensor scale” was introduced using an ellipsoidal model that yields a unified representation of structure size, orientation and anisotropy. In the previous work, tensor scale was described using a 2-D algorithmic approach and a precise analytic definition was missing. Also, with previous framework, 3-D application is not practical due to computational complexity. The overall aim of the Ph.D. research is to establish an analytic definition of tensor scale in n-dimensional (n-D) images, to develop an efficient computational solution for 2and 3-D images and to investigate its role in various medical imaging applications including image interpolation, filtering, and segmentation. Firstly, an analytic definition of tensor scale for n-D images consisting of objects formed by pseudo-Riemannian partitioning manifolds has been formulated. Tensor scale captures contextual structural information which is useful in local structure-adaptive anisotropic parameter control and local structure description for object/image matching. Therefore, it is helpful in a wide range of medical imaging algorithms and applications. Secondly, an efficient computational solution of tensor scale for 2and 3-D images has been developed. The algorithm has combined Euclidean distance transform and several novel differential geometric approaches. The accuracy of the algorithm has been verified on both geometric phantoms and real images compared to the theoretical results generated using brute-force method. Also, a matrix representation has been derived facilitating several operations including tensor field smoothing to capture larger contextual knowledge. Thirdly, an inter-slice interpolation algorithm using 2-D tensor scale information of adjacent slices has been developed to determine the interpolation line at each image