Efficient error calculation for multiresolution texture-based volume visualization

Multiresolution texture-based volume visualization is an excellent technique to enable interactive rendering of massive data sets. Interactive manipulation of a transfer function is necessary for proper exploration of a data set. However, multiresolution techniques require assessing the accuracy of the resulting images, and re-computing the error after each change in a transfer function is very expensive. We extend our existing multiresolution volume visualization method by introducing a method for accelerating error calculations for multiresolution volume approximations. Computing the error for an approximation requires adding individual error terms. One error value must be computed once for each original voxel and its corresponding approximating voxel. For byte data, i.e., data sets where integer function values between 0 and 255 are given, we observe that the set of "error pairs" can be quite large, yet the set of unique error pairs is small. Instead of evaluating the error function for each original voxel, we construct a table of the unique combinations and the number of their occurrences. To evaluate the error, we add the products of the error function for each unique error pair and the frequency of each error pair. This approach dramatically reduces the amount of computation time involved and allows us to re-compute the error associated with a new transfer function quickly.