Scattered data interpolation methods for electronic imaging systems: a survey

Numerous problems in electronic imaging systems involve the need to interpolate from irregularly spaced data. One example is the calibration of color input/output devices with respect to a common intermediate objective color space, such as XYZ or Lab*. In the present report we survey some of the most important methods of scattered data interpolation in two-dimensional and in three-dimensional spaces. We review both single-valued cases, where the underlying function has the form f:R2→R or f:R3→R, and multivalued cases, where the underlying function is f:R2→R2 or f:R3→R3. The main methods we review include linear triangular (or tetrahedral) interpolation, cubic triangular (Clough-Tocher) interpolation, triangle based blending interpolation, inverse distance weighted methods, radial basis function methods, and natural neighbor interpolation methods. We also review one method of scattered data fitting, as an illustration to the basic differences between scattered data interpolation and scattered data fitting