Histogram equalization using a selective filter.

Many popular modern image processing software packages implement a naïve form of histogram equalization. This implementation is known to produce histograms that are not truly uniform. While exact histogram equalization techniques exist, these may produce undesirable artifacts in some scenarios. In this paper we consider the link between the established continuous theory for global histogram equalization and its discrete implementation, and we formulate a novel histogram equalization technique that builds upon and considerably improves the naïve approach. We show that we can linearly interpolate the cumulative distribution of a low-bit image by approximately dequantizing its intensities using a selective box filter. This helps to distribute the intensities more evenly. The proposed algorithm is subsequently evaluated and compared with existing works in the literature. We find that the method is capable of producing an equalized histogram that has a high entropy, while distances between similar intensities are preserved. The described approach has implications on several related image processing problems, e.g., edge detection.

Interactive rendering of dynamic geometry.

Fluid simulations typically produce complex three-dimensional (3D) isosurfaces whose geometry and topology change over time. The standard way of representing such "dynamic geometry" is by a set of isosurfaces that are extracted individually at certain time steps. An alternative strategy is to represent the whole sequence as a four-dimensional (4D) tetrahedral mesh. The iso-surface at a specific time step can then be computed by intersecting the tetrahedral mesh with a 3D hyperplane. This not only allows the animation of the surface continuously over time without having to worry about the topological changes, but also enables simplification algorithms to exploit temporal coherence. We show how to interactively render such 4D tetrahedral meshes by improving previous GPU-accelerated techniques and building an out-of-core multi-resolution structure based on quadric error simplification. As a second application, we apply our framework to time-varying surfaces that result from morphing one triangle mesh into another.