Abstract
Abstract The reconstruction of a 3-D surface is important in many medical applications. These 3-D surface data can be used to reconstruct the object for visualization, surgery, radiation treatment planning and diagnosis. To register images for different modalities, such as MR and positron emission tomography (PET), these data must be re-digitized. The image interpolation is a useful tool to help solve these problems. Gray-level and shape-based image interpolation methods have been discussed and used extensively. However, these methods bring some drawbacks into existence. In this dissertation, we propose a novel image interpolation method that uses polygon approximation to improving those mentioning methods. Aim for polygon approximation is to capture the essence of the object shape with the fewest possible polygonal segments. Image interpolation or contour construction is then performed based on the polygon vertexes or edges. In Chapter 2, we assume that approximates the object shape. If the polygon vertexes are defined, then the contour can be approximated from these vertexes using a cubic spline interpolation. In Chapters 3 and 4, we use a polygon to approximate the object shape and perform the interpolation. For each pixel inside the target polygon, we determine its relative location in the source slices using the vertices or edges of a polygon as the references, respectively. The target slice gray-level is then interpolated from the corresponding source image pixels. For contour interpolation, our method yields a better contour and is computationally more efficient than shape-based interpolation. In addition, the image quality of this interpolation method is better and the mean squared difference is smaller compared with traditional gray-level image interpolation.