Hierarchical volume analysis and visualization based on morphological operators

One common problem in the practical application of volume visualization is the proper choice of transfer functions in order to color different parts of the volume meaningfully. This interactive process can be very complicated and time consuming. An alternative to the adjustment of transfer functions is the application of segmentation algorithms. These algorithms are often dedicated to a limited range of data sets and tend to be very compute intensive. We propose a morphology based hierarchical analysis to estimate the optical properties of the volume to be rendered. This approach requires fewer parameters and incorporates also spatial information, but it is far less compute intensive than most of the segmentation methods. The hierarchical analysis is constructed in analogy to the wavelet analysis, except for the fact, that nonlinear filters are used in our case. These morphological operators have a lower distortional influence on the analyzed structures than the usual linear filters. A special decomposition of the morphological operators is discussed, which leads to an efficient implementation of this approach. This technique reduces the three dimensional analysis to a one dimensional computation, as it is done in tensor product based linear filters. The resulting decomposition may also be parallelized easily. We demonstrate the usefulness of the proposed technique by applying it to medical and technical data sets.