Comparisons of three-dimensional interpolation techniques by simulations

Henry R. Kang

doi:10.1117/12.206538

10 April 1995 Comparisons of three-dimensional interpolation techniques by simulations

Henry R. Kang

Proceedings Volume 2414, Device-Independent Color Imaging II; (1995) https://doi.org/10.1117/12.206538
Event: IS&T/SPIE's Symposium on Electronic Imaging: Science and Technology, 1995, San Jose, CA, United States

Abstract

Several 3D interpolation techniques for the color space transformation are compared via software simulations. Comparisons are made among four geometric interpolations, trilinear, prism, pyramid, and tetrahedral, with respect to the look-up table (LUT) size and packing. Three different LUT sizes and two ways of packing, uniform and nonuniform, are applied to the forward and inverse transformations of the XeroxRGB and CIELAB. Each simulation is tested by a set of 3072 points that are sampled around the entire RGB color space. Results indicate: (1) Interpolation errors of various 3D geometric interpolations are about the same and the errors with respect to the true values decrease as the LUT size increases. (2) The interpolation error peaks at the center of the cell and diminishes at nodes (lattice points). (3) The highest error occurs at the darkest region. For equally spaced LUTs, the error drops quickly as the level increases. (4) Nonuniform LUTs have a much lower fundamental error peak but the errors are rippled to the higher levels; this gives a more even error distribution and a better average value. From this study, it is conceivable that the colorimetric reproduction can be achieved to a very high degree of precision. With proper packing, the 3D interpolation provides the capability to closely approximate the true values in all regions of the color space. From the considerations of the implementation cost and computation speed, the tetrahedral interpolation is particularly attractive.

Citation Download Citation

Henry R. Kang "Comparisons of three-dimensional interpolation techniques by simulations", Proc. SPIE 2414, Device-Independent Color Imaging II, (10 April 1995); https://doi.org/10.1117/12.206538

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