Geometric shapes embedded in 2D or 3D images often have boundaries with both high and low curvature regions. These
boundaries of varying curvature can be efficiently captured by adaptive grids such as quadtrees and octrees. Using these
trees, we propose to store sample values at the centers of the tree cells in order to simplify the tree data structure, and to take
advantage of the image pyramid. The difficulty with using a cell-centered tree approach is the interpolation of the values
sampled at the cell centers. To solve this problem, we first restrict the tree refinement and coarsening rules so that only a
small number of local connectivity types are produced. For these connectivity types, we can precompute the weights for
a continuous interpolation. Using this interpolation, we show that region-based image segmentation of 2D and 3D images
can be performed efficiently.