GPU based ray casting has become a valuable tool for the visualization of medical image data. While the method produces high- quality images, its main drawback is the high computational load. We present a novel adaptive approach to speed up the rendering. In contrast to well established heuristic methods, we use the spectral decomposition of the transfer function and the dataset to derive a suitable sampling criterion. It is shown how this criterion can be e ciently incorporated into an adaptive ray casting algorithm. Two medical datasets, which each represent a typical, but di erent material distribution, are rendered using the proposed method. An analysis of the number of sample points per ray reveals that the new algorithm requires 50% to 80% less points compared to a non-adaptive method without any quality loss. We also show that the rendering speed of the GPU implementation is greatly increased with reference to the non-adaptive algorithm.