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In this work a visualization pipeline for surface extraction from unstructured point-based volume data is proposed. The pipeline includes all necessary steps to produce high-quality visualizations by extracting surfaces with different properties. An isosurface extraction step directly extracts isosurfaces in point-cloud representation. No global or local polyhedrization or reconstruction over a regular grid is applied. Instead, isopoints are computed by linearly interpolating between neighboring pairs of sample points. The neighbor information is retrieved by approximating natural neighbors as defined by Voronoi diagrams. The authors achieved surface extractions of high quality with significantly faster computation times than comparable approaches. For noisy data or highly varying point densities, a level-set-based preprocessing step was introduced. This step generalizes the well-known technique of level sets, formerly only applicable to gridded data, such that it can be directly applied to unstructured point-based data without any reconstructions in data domain. By utilizing hyperbolic advection combined with mean curvature flow, the introduced level-set function is deformed such that its gradients stay normalized and the zero level set approximates the sought isosurface. By executing this step before isosurface extraction, the authors were able to extract smooth isosurfaces also from noisy or highly varying data. The achieved results are comparable in terms of quality with other approaches, that tackle similar problems. However, the level-set method is the only one able to be directly applied to unstructured point-based data. As the surfaces are extracted in point-cloud representation, it is favorable to use point-cloud rendering techniques to visualize them. For this purpose, two different approaches have been presented. The first computes a set of circular splats with associated normal fields. Afterwards the set of splats is ray traced to generate a visualization of the surface which allows for photorealistic effects like global illumination, reflection, and refraction. In contrast, the second approach generates an interactive yet smooth visualization of the surface without any precomputations. The lit points are projected to screen space and possible holes are filled using image-space operations. Optionally the processing of an associated normal field allows the application of illustrative rendering techniques to enhance the depth perception of the interactive visualization. For both point-cloud rendering approaches the authors achieved results of comparable visual quality and faster computation times, when compared to related state-of-the-art rendering techniques. The presented visualization pipeline has been tested with the help of several data sets with different types of origin. The individual steps have been compared to competitive methods and assets and drawbacks have been discussed. The practicability of the pipeline is not only demonstrated on real-world data sets, but also directly in cooperation with data set providers.