Interpolação tridimensional de imagens de tomografia computadorizada utilizando equações diferenciais parciais

Abstract

The visualization of a 3D image obtained from computerized tomography examinations has shown itself to be an important factor for increasing the quality of medical diagnoses and, consequently, treatment efficacy. There already exist on the market, several visualization softwares, which use different techniques to show the 3D tomography image. However, to show a high quality 3D image, sophisticated devices must be used to obtain slices, close to one another, thus increasing the incidence of X-ray given to the patient. An interpolation slice method which resulted from the TC examination produces good results, and is able to reduce the X-ray incidence upon the patient. This method must reconstruct the curvature from the patient s internal structures without using slices in close proximity. This work proposes a method of 3D image interpolation, composed of a juxtaposition of the slices from CT examination results. The goal of this method is to increase the quality of 3D visualization through the production of sharp and precise structure contours. This thesis proposes the division of the interpolation method into two steps. In the first step, the goal is to obtain an initial representation of the image in 3D, which is composed of real slices as well as virtual slices which are referred to in this work as initial virtual slices. In the second step, the empty spaces of the structure are recovered by the 3D image inpainting process. This work also proposes a method to obtain the initial virtual slice and two different methods for inpainting the 3D image. These inpainting methods are the transversal slice line prolongation method and the transportation and diffusion of information. Both methods use the differential equation theory. The transportation and diffusion of information method shows better results than other methods proposed in this work, besides this, this method presents better results than the linear interpolation and Goshtasby et al. [1] methods also implemented in this work. Visual and numerical comparisons are used to obtain this conclusion. The numerical measures used are statistical correlation, the PSNR and the Hausdorff distance [2]. The transportation and diffusion of information method shows itself able to produce better results than all the other tested methods. Besides this principal contribution, this work also developed a KIT to implement 2D and 3D CT visualize applications.