| This dissertation demonstrates a new approach to hardware-based rendering from compressed volume formats. This method, called deferred filtering, provides efficient decompression when coupled with rendering, allowing interpolation and lighting based on gradients computed on-the-fly, all at interactive frame rates. We then address several other challenges in volumetric compression. First, we consider multidimensional coding of multivariate, time-varying volume data. We present a method that exploits correlations among related variables in order to increase the compression rate as compared to independent compression of variables. We then develop a sophisticated transform coding method that allows decompression in graphics hardware, with the result being a JPEG-like transform coding scheme that allows very large volumes to be compressed and then decompressed in real-time while rendering in graphics hardware. Finally, we describe a lossless floating-point volume compression scheme based on a switched prediction approach that is able to achieve significantly better rates as compared to existing methods with a small increase in compression time. Overall, our work addresses many of the outstanding challenges in data compression that are unique to volume data reduction.;Finally, lossy compression adds uncertainty to the volume visualization, and so in order to explore the effects of compression on volume rendering we address the issue of uncertainty in visualization. We use a self-validating computational model to compute a posteriori uncertainty bounds, based on a novel uncertainty framework that captures the various forms of uncertainty present in visualization. We then go on to show that such uncertainty-aware visualizations can produce more complete depictions of the data, thereby allowing more reliable conclusions and informed decisions. This is shown for volume rendering, where we demonstrate that fuzzy volume rendering (volume rendering based on our framework) is capable of generating a reliable volume visualization in which a range of possible renderings is produced, as opposed to a single rendering in which the degree of uncertainty is completely disregarded. Our approach, by computing and communicating the uncertainty in volume rendering, allows viewers a greater degree of confidence in assigning an interpretation to the visualization. |
