A tetrahedral interpolation technique for color space conversion

Abstract

Three-dimensional interpolation is often employed to minimize calculations when approximating mathematicallydefined complex functions or producing intermediate results from sparse empirical data. Both situations occur when converting images from one device-independent color space to another, or converting information between devicedependent and device-independent color spaces; this makes three-dimensional interpolation an appropriate solution to many kinds of color space transformations. Interpolation algorithms can be analyzed by considering them as consisting of three parts: packing, in which the domain of interest of the input space is populated with sample points; extraction, which consists of selecting the sample points necessary to approximate the function for a particular input value; and calculation, which accepts the input point and the extracted points and carries out calculations to approximate the function. Those algorithms that extract four points and perform tetrahedral interpolation yield the fewest calculations. The paper presents a test for interpolation algorithm accuracy, and provides a normalization which allows various packing and extraction schemes to be compared. When subjected to the normalized accuracy test, different packing and extraction schemes yield different accuracies. The paper describes a packing and an extraction algorithm that yields accurate results for many conversions. The performance of this scheme is compared to that of several well-known packing and extraction algorithms.