In this paper, Computerized Tomography cuberille grid medical data is used. The common problem of volumetric image data is that the amount of data is too much. to reduce volumetric data, wavelet transformation is already used to evaluate importance for each data. We treat a volumetric medical image data as the coefficients corresponding to a three-dimensional piecewise constant basis functions of wavelet transformation. Then, we omit the coefficients with smallest magnitude until the difference between the gray value of original data and represented data is less than the tolerance. If we select only the important data, original cuberille data becomes scattered data. In this case, Marching Cubes algorithm is no longer applicable. Even though Marching cubes is one of the most successful voxel based algorithm, the input data should be cuberille grid data instead of scattered data. In real world, many applicable data are available in a manner of scattered data rather than cuberille grid data. A tetrahedrization is the one of pre-processing steps for trivariate scattered data interpolation. The quality of a piecewise linear data points in four-dimensional space depends not only on the distribution of the data in three-dimensional space, but also on the data value. This paper discusses data dependent criteria: (1) least squares fitting, (2) gradient difference, and (3) jump in normal direction derivatives. A simulated annealing algorithm is used to achieve the global optimum for a wide class of optimization criteria. The results of trivariated scattered data interpolation is visualized through an iso-surface rendering. A Geomview package is used in Linux flatform on PC.