A novel interpolation problem: surface based matching

Classical interpolation theory, proposes to find a function f(x) which satisfies a set of interpolative constraints, f(x_i)=y _i. This approach has been used in the alignment of images and volumetric data sets. However, in many applications, it is difficult if not impossible to find corresponding fiducial points. In these applications however, it is possible to identify homologous geometrical structures, such as surfaces. We have explored algorithms for using these sorts of data for image alignment, which requires a novel formulation of the interpolation problem. This paper describes the principle of surface-based alignment, and examines its performance and accuracy