Progressive Direct Volume-to-Volume Transformation

We present a novel technique to generate transformations between arbitrary volumes, providing both expressive distances and smooth interpolates. In contrast to conventional morphing or warping approaches, our technique requires no user guidance, intermediate representations (like extracted features), or blending, and imposes no restrictions regarding shape or structure. Our technique operates directly on the volumetric data representation, and while linear programming approaches could solve the underlying problem optimally, their polynomial complexity makes them infeasible for high-resolution volumes. We therefore propose a progressive refinement approach designed for parallel execution that is able to quickly deliver approximate results that are iteratively improved toward the optimum. On this basis, we further present a new approach for the streaming selection of time steps in temporal data that allows for the reconstruction of the full sequence with a user-specified error bound. We finally demonstrate the utility of our technique for different applications, compare our approach against alternatives, and evaluate its characteristics with a variety of different data sets.