The level-set method is one of the most popular techniques for capturing and tracking deformable interfaces. Although level sets have demonstrated great potential in visualization and computer graphics applications, such as surface editing and physically based modeling, their use for interactive simulations has been limited due to the high computational demands involved. In this paper, we address this computational challenge by leveraging the increased computing power of graphics processors, to achieve fast simulations based on level sets. Our efficient, sparse GPU level-set method is substantially faster than other state-of-the-art, parallel approaches on both CPU and GPU hardware. We further investigate its performance through a method for surface reconstruction, based on GPU level sets. Our novel multiresolution method for surface reconstruction from unorganized point clouds compares favorably with recent, existing techniques and other parallel implementations. Finally, we point out that both level-set computations and rendering of level-set surfaces can be performed at interactive rates, even on large volumetric grids. Therefore, many applications based on level sets can benefit from our sparse level-set method.

The Discrete Wavelet Transform (DWT) has a wide range of applications from signal processing to video and image compression. We show that this transform, by means of the lifting scheme, can be performed in a memory and computation-efficient way on modern, programmable GPUs, which can be regarded as massively parallel coprocessors through NVidia's CUDA compute paradigm. The three main hardware architectures for the 2D DWT (row-column, line-based, block-based) are shown to be unsuitable for a CUDA implementation. Our CUDA-specific design can be regarded as a hybrid method between the row-column and block-based methods. We achieve considerable speedups compared to an optimized CPU implementation and earlier non-CUDA-based GPU DWT methods, both for 2D images and 3D volume data. Additionally, memory usage can be reduced significantly compared to previous GPU DWT methods. The method is scalable and the fastest GPU implementation among the methods considered. A performance analysis shows that the results of our CUDA-specific design are in close agreement with our theoretical complexity analysis.

We present an approach for rendering the surface of a particle-based fluid that is simple to implement, has real-time performance with a configurable speed/quality trade-off, and smoothes the surface to prevent the fluid from looking "blobby" or jelly-like. The method is not based on polygonization and as such circumvents the usual grid artifacts of marching cubes. It only renders the surface where it is visible, and has inherent view-dependent level-of-detail. We use Perlin noise to add detail to the surface of the fluid. All the processing, rendering and shading steps are directly implemented on graphics hardware.

This paper is concerned with a multiresolution representation for maximum intensity projection (MIP) volume rendering based on morphological pyramids which allows progressive refinement. We consider two algorithms for progressive rendering from the morphological pyramid: one which projects detail coefficients level by level, and a second one, called streaming MIP, which resorts the detail coefficients of all levels simultaneously with respect to decreasing magnitude of a suitable error measure. The latter method outperforms the level-by-level method, both with respect to image quality with a fixed amount of detail data, and in terms of flexibility of controlling approximation error or computation time. We improve the streaming MIP algorithm, present a GPU implementation for both methods, and perform a comparison with existing CPU and GPU implementations.