Towards Accurate and Efficient Volume Rendering

This thesis is concerned with improvements to algorithms for volume rendering; a technique that provides scientists with the means for visual exploration of three-dimensional data. Despite its numerous successes, and its increasing use within the scientific community, state-of-the-art volume rendering algorithms have many shortcomings. Difficulties include: ensuring the accuracy of the rendered images, producing images with modest computational resources, and rendering the diverse types of data that are currently being produced. The work in this thesis was motivated by the demands of an ongoing visualization project in four-dimensional cardiac visualization. We present solutions to some key problems in ensuring accuracy and in producing algorithms that can scale to handle large datasets. Although the theoretical work in this thesis applies to arbitrary data topologies, our implementations have assumed that the data is defined by sample points on a regular rectilinear grid. In the area of accuracy, we focus on the error that is introduced during volume projection. This phase of the volume rendering process involves the evaluation of the emission-absorption volume rendering line integral. This thesis presents four techniques for controlled precision volume integration. These schema depart from existing approaches in that they provide error bounds along with the solutions they generate. In each case, the error analysis leads to an algorithm for evaluating the integral to any specified tolerance. Our investigations into efficiency issues have resulted in two advances. First, an adaptive error bracketing scheme is presented that builds on the controlled precision volume integration methods. Using adaptive error bracketing, the solution for a viewing ray is continually refined until a user-specified error tolerance is met. The algorithm allows processing of the data without imposing a strict front-to-back or back-to-front evaluation order. Second, a suite of tools are presented that can be used to efficiently compute perspective projections of volume data. These include a paging strategy that is useful when a dataset is too large to fit into RAM memory and a ray splitting technique for adaptive supersampling. The latter technique ensures that all data features contribute to the final image while avoiding overcomputation in regions close to the eyepoint