High-resolution splatting

Abstract

Volume rendering is a research area within scientific visualisation, where images are computed from volumetric data sets for visual exploration. Such data sets are typically generated by Computer aided Tomography, Magnetic Resonance Imaging, Positron Emission Tomography or gained from simulations. The data sets are usually interpreted using optical models that assign optical properties to the volume and define the illumination and shading behaviour. Volume rendering techniques may be divided into three classes: object-order, image-order or hybrid methods. Image-order or ray casting methods shoot rays from the view plane into the volume and simulate the variation of light intensities along those rays. Object-order techniques traverse the volume data set and project each volume element onto the view plane. Hybrid volume rendering techniques combine these two approaches. A very popular object-order rendering method is called splatting. This technique traverses the volume data set and projects the optical properties of each volume element onto the view plane.

This thesis consists of two parts. The first part introduces two new splatting methods, collectively called high-resolution splatting, which are based on standard splatting. Both high-resolution splatting methods correct errors of splatting by applying major modifications. We propose the first method, called fast high-resolution splatting, as an alternative to standard splatting. It may be used for quick previewing, since it is faster than standard splatting and the resulting images are significantly sharper. Our second method, called complete high-resolution splatting, improves the volume reconstruction, which results in images that are very close to those produced by ray casting methods.

The second part of the thesis incorporates wavelet analysis into high-resolution splatting. Wavelet analysis is a mathematical theory that decomposes volumes into multi-resolution hierarchies, which may be used to find coherence within volumes. The combination of wavelets with the high-resolution splatting method has the two advantages. Firstly the extended splatting method, called high-resolution wavelet splatting, can be directly applied to wavelet transformed volume data sets without performing an inverse transform. Secondly when visualising wavelet compressed volumes, only a small fraction of the wavelet coefficients need to be projected.

For all three versions of the new high-resolution splatting method, complexity analyses, comprehensive error and performance analyses as well as implementation details are discussed.