Accurate high-speed spatial normalization using an octree method

The goal of regional spatial normalization is to remove anatomical differences between individual three-dimensional (3-D) brain images by warping them to match features of a standard brain atlas. Full-resolution volumetric spatial normalization methods use a high-degree-of-freedom coordinate transform, called a deformation field, for this task. Processing to fit features at the limiting resolution of a 3-D MR image volume is computationally intensive, limiting broad use of full-resolution regional spatial normalization. A highly efficient method, designed using an octree decomposition and analysis scheme, is presented to resolve the speed problem while targeting accuracy comparable to current volumetric methods. Translation and scaling capabilities of octree spatial normalization (OSN) were tested using computer models of solid objects (cubes and spheres). Boundary mismatch between transformed and target objects was zero for cubes and less than 1% for spheres. Regional independence of warping was tested using brain models consisting of a homogenous brain volume with one internal homogenous region (lateral ventricle). Boundary mismatch improved with successively smaller octant-level processing and approached levels of less than 1% for the brain and 5% for the lateral ventricle. Five 3-D MR brain images were transformed to a target 3-D brain image to assess boundary matching. Residual boundary mismatch was approximately 4% for the brain and 8% for the lateral ventricle, not as good as with homogeneous brain models, but similar to other results. Total processing time for OSN with a 256(3) brain image (1-mm voxel spacing) was less than 10 min.