Abstract: Many volume data possess symmetric features that can be clearly observed, for example, those existed in diffusion tensor image data sets. The exploitations of symmetries for volume data sets, however, are relatively limited due to the prohibitive computational cost of detecting the symmetries. In this paper we present an efficient parallel algorithm for symmetry computation in volume data represented by regular grids. Optimization is achieved by converting the raw data into a hierarchical tree-like structure.We design a novel algorithm to partition the tree and distribute the data among processors to minimize the data dependency at run time. The computed symmetries are useful for several volume data applications, including POF minimal opacity selection, transfer function generation and slice position selection.