Matching 3-D anatomical surfaces with non-rigid deformations using octree-splines - Szeliski, Rick; Lavallee, S. (International Journal of Computer Vision, 1994)
Presents a new method for determining the minimal nonrigid deformation between two 3D surfaces, such as those which describe anatomical structures in 3D medical images. Although the authors match surfaces, they represent the deformation as a volumetric transformation. Their method performs a least squares minimization of the distance between the two surfaces of interest. To quickly and accurately compute distances between points on the two surfaces, the authors use a precomputed distance map represented using an octree spline whose resolution increases near the surface. To quickly and robustly compute the deformation, the authors use a second octree-spline to model the deformation function. The coarsest level of the deformation encodes the global (e.g., affine) transformation between the two surfaces, while finer levels encode smooth local displacements which bring the two surfaces into closer registration. The authors present experimental results on both synthetic and real 3D surfaces. >