Analysis of the Interpolation Error between Multiresolution Images

Many rendering or image-analysis systems require calculation of versions of an image at lesser resolutions than the original. Because the filtering required to perform such calculations accurately cannot typically be done in real time, many systems use interpolation between images at precalculated resolutions. This discrete sampling of the scale component of multiresolution image spaces is analogous to spatial sampling in discrete images. This paper quantifies and bounds the error that can be introduced during such interpolation as a function of the scale-space sampling rate used. A method is presented that uses the diffusion equation to relate spatial derivatives to scale derivatives and from there to an error bound.