Scattered data interpolation methods for electronic imaging systems: a survey

Numerous problems in electronic imaging systems in- volve the need to interpolate from irregularly spaced data. One ex- ample is the calibration of color input/output devices with respect to a common intermediate objective color space, such as XYZ or L*a*b*. In the present report we survey some of the most impor- tant 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:R 2 !R or f:R 3 !R, and multivalued cases, where the underlying function is f:R 2 !R 2 or f:R 3 !R 3 . The main methods we review include linear triangular (or tetrahedral) interpolation, cubic triangular (Clough-Tocher) interpo- lation, triangle based blending interpolation, inverse distance weighted methods, radial basis function methods, and natural neigh- bor interpolation methods. We also review one method of scattered data fitting, as an illustration to the basic differences between scat- tered data interpolation and scattered data fitting. © 2002 SPIE and

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