Topological volume skeletonization is a novel approach for automating transfer function design in visualization by extracting the topological structure of a volume dataset. The skeletonization process yields a graph called a volume skeleton tree, which consists of volumetric critical points and their connectivity. The resultant graph provides critical field values whose color and opacity are accentuated in the design of transfer functions for direct volume rendering. Visually pleasing results of volume visualization demonstrate the feasibility of the present approach.