We present a new hierarchical graph representation for volume data as well as its associated operations to enable interactive feature segmentation for high-resolution volume data. Our method constructs a low-resolution graph which represents a coarser resolution of the data. This graph enables the user to interactively sample and edit a feature of interest by drawing strokes on data slices. A subgraph representing the feature is derived with a growing process, and is used to extract the high-resolution version of the feature from the original volume data by performing an automatic mapping and refinement procedure. Our three-level, graph-based approach overcomes partial volume effects that are introduced by downsampling the volume data, and enables interactive segmentation of fine features. We demonstrate the effectiveness of this approach with several challenging 3D segmentation applications.