Abstract
This thesis presents a new volume rendering model, which uses a different representation of the voxels from previous volume rendering methods: that is, it represents voxels as small volumes rather than as ideal sample points of a continuous 3D scalar function, considering the fact from the medical imaging scanning process that the original value assigned to each voxel represents the average value within a small volume. Further, the new model uses a weighted compositing equation to integrate the visual information of voxels to obtain the 2D image. Using the weighted compositing equation is a more accurate simulation of the interaction between the light and the volume. It respects the fact that the longer the light travels through a material, the more the energy is absorbed. Furthermore, the new model reduces the interpolation process to a minimal level. In addition, the new model casts viewing beams instead of ideal viewing rays. Furthermore, the new model renders the shadow information, which is an important enhancement in revealing the 3D relationship. The brute-force algorithms implementing the new model are presented in pseudo-code format in this thesis. Acceleration techniques, such as early ray termination and hierarchical volume data representation, have been used to improve the rendering speed and reduce the computational cost. The new volume rendering model has been implemented and applied to MRI and CT volume data of living patients. Results from rendering clinical volume data show images of high quality. Compared with Levoy's rendering model, the new model eliminates the process of selecting a proper sampling rate along each viewing ray, and renders images of improved image quality in most of our experiments.In this thesis, we also propose mathematical model design techniques for image quality testing. The image quality testing is important because the rendering accuracy is of the highest concern in 3D medical imaging volume visualization applications. The image quality testing is to demonstrate if a visualization model accurately reveals the 3D relationship in the generated 2D images, Mathematical models can serve the purpose of image quality testing because we have full knowledge of the 3D relationship of the objects in these computer generated scenes. Different from previous methods, we employ 3D scalar functions to mathematically describe the value distribution of typical 3D geometric primitives in 3D space and propose a method adapted from the constructive solid geometry (CSG) to construct complex scenes from the 3D primitives by the use of geometric transformations and integration operations. We present the algorithm of converting the mathematically represented 3D scenes to discrete volume data. Using these techniques, we construct several mathematical models and apply our rendering model and previous rendering model to these computer generated volume data. The results show that the new volume rendering model is able to reveal 3D relationship in an accurate and reliable way. In most of our experiments, the quality of images generated by our model is better than that of previous models.