Time- and space-efficient error calculation for multiresolution direct volume rendering

Abstract

Multiresolution data representations are crucial for viewing large volumetric datasets interactively. When data is too large to fit into texture memory, or into main memory, a “cut” must be made through the multiresolution data hierarchy to attain a subset of the data that satisfies the memory requirements. Ideally, a subset is chosen such that the error made when visualizing the subset (compared to a visualization of the full data set) is smaller than that of any other subset of the same size. For real-time applications it is computationally too expensive to calculate the exact error during runtime. Further, computing error in a preprocessing step is usually not practical due to a large number of possible different configurations each requiring its own error computation. For example, when coupling a multiresolution representation with a direct volume rendering technique, screen-space error depends on the transfer function and viewing direction, making impossible its precomputation. We present an algorithm that stores an intermediate form of the error, which allows us to approximate screen-space error efficiently. The input for our algorithm is any spatially subdivided multiresolution representation of grid-aligned scalar or multivariate volume data. We focus on octree- and wavelet-based multiresolution techniques. For each level in the multiresolution hierarchy, the algorithm estimates screen-space error “on the fly,” with respect to the current transfer function and viewing direction. The error is approximated by means of a two-dimensional histogram of error pairs. We have extended previous methods by presenting an approach that balances computational and memory costs with approximation quality of the error estimate.