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This thesis focuses on the utilization of modern graphics hardware (GPU) for visualization and computation purposes, especially of volumetric data from medical imaging. The considerable increase in raw computing power in recent years has turned commodity systems into high-performance workstations. In combination with the direct rendering capabilities of graphics hardware, "visual computing" and "computational steering" approaches on large data sets have become feasible. In this regard several example applications and concepts such as the "ray textures" have been developed and are discussed in detail. As the amount of data to be processed and visualized is steadily increasing, memory and bandwidth limitations require compact representations of the data. While the compression of image data has been investigated extensively in the past, the thesis addresses possibilities of performing computations directly on the compressed data. Therefore, different categories of algorithms are identified and represented in the wavelet domain. By using special variants of the compressed format, efficient implementations of essential image processing algorithms are possible and demonstrate the potential of the approach. From the technical perspective, the GPU-based framework "Cascada" has been developed in the course of this thesis. The introduction of object-oriented concepts to shader programming, as well as a hierarchical representation of computation and/or visualization procedures led to a simplified utilization of graphics hardware while maintaining competitive performance. This is shown with different implementations throughout the contributions, as well as two clinical projects in the field of diagnosis assistance. On the one hand the semi-automatic segmentation of low-resolution MRI data sets of the human liver is evaluated. On the other hand different possibilities in assessing abdominal aortic aneurysms are discussed; both projects make use of graphics hardware. In addition, "Cascada" provides extensions towards recent general-purpose programming architectures and a modular design for future developments.