Hierarchical volume analysis and visualization based on morphological operators

One common problem in the practical application of volume visu- alization 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. In this paper we propose a morphology based hierarchical anal- ysis to estimate the optical properties of the volume to be rendered. This approach requires fewer parameters and incorporates also spa- tial 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 non-linear 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 will be discussed, that leads to an efficient implementation of this ap- proach. 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. uncertainty associated with the proposed transformation is also re- flected in the final visualization of the data set. The method we propose is a multi-scale method, which is based on morphological operations. This approach requires fewer parameters to be adjusted by the user and incorporates spatial information. In the final re- sult, regions of the volume, where a defined frequency is present, are labeled with a certain color. This multi-scale method has been constructed in analogy to the wavelet transformation. The application of scale-space theory has become very popu- lar in the computer graphics and pattern analysis community along with the increasing application of the wavelet transformation. The wavelet transformation has not only been used for image compres- sion as described by Stollnitz et. al. (16), but also to detect edges and to characterize signal properties as explained in the articles of