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GENERAL INFORMATION

chapter 9, Three-Dimensional Lookup Table with Interpolation

from: Computational Color Technology

Author(s): Henry R. Kang

Published: 17 May 2006

Chapter DOI: http://dx.doi.org/10.1117/3.660835.ch9

Chapter Page Count: 32 pages

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Front Matter

1. Tristimulus Specification

2. Color Principles and Properties

3. Metamerism

4. Chromatic Adaptation

5. CIE Color Spaces

6. RGB Color Spaces

7. Device-Dependent Color Spaces

8. Regression

9. Three-Dimensional Lookup Table with Interpolation

10. Metameric Decomposition and Reconstruction

11. Spectrum Decomposition and Reconstruction

12. Computational Color Constancy

13. White-Point Conversion

14. Multispectral Imaging

15. Densitometry

16. Kubelka-Munk Theory

17. Light-Reflection Model

18. Halftone Printing Models

19. Issues of Digital Color Imaging

Appendices
1. Conversion Matrices

2. Conversion Matrices from RGB to ITU-R.BT.709∕RGB

3. Conversion Matrices from RGB to ROMM∕RGB

4. RGB Color-Encoding Standards

5. Matrix Inversion

6. Color Errors of Reconstructed CRI Spectra with Respect to Measured Values

7. Color Errors of Reconstructed CRI Spectra with Respect to Measured Values Using Tristimulus Inputs

8. White-Point Conversion Accuracies Using Polynomial Regression

9. Digital Implementation of the Masking Equation

Back Matter

Preview

Chapter Contents

9.1 Structure of 3D Lookup Table
9.1.1 Packing
9.1.2 Extraction
9.1.3 Interpolation
9.2 Geometric Interpolations
9.2.1 Bilinear interpolation
9.2.2 Trilinear interpolation
9.2.3 Prism interpolation
9.2.4 Pyramid interpolation
9.2.5 Tetrahedral interpolation
9.2.6 Derivatives and extensions
9.3 Cellular Regression
9.4 Nonuniform Lookup Table
9.5 Inverse Color Transform
9.6 Sequential Linear Interpolation
9.7 Results of Forward 3D Interpolation
9.8 Results of Inverse 3D Interpolation
9.9 Remarks
References

Excerpt

Color space transformation using a 3D lookup table (LUT) with interpolation is used to correlate the source and destination color values in the lattice points of a 3D table, where nonlattice points are interpolated by using the nearest lattice points. This method has been used in many applications with quite satisfactory results, and incorporated into the ICC profile standard.

In this chapter, the structure of the 3D-LUT approach is discussed and the mathematical formulations of interpolation methods are given. These methods are tested using several sets of data points. The similarities and differences of these interpolation methods are discussed.

9.1 Structure of 3D Lookup Table

The 3D lookup method consists of three parts—packing (or partition), extraction (or find), and interpolation (or computation). Packing is a process that partitions the source space and selects sample points for the purpose of building a lookup table. The extraction step is aimed at finding the location of the input pixel and extracting color values of the nearest lattice points. The last step is interpolation where the input signals and the extracted lattice points are used to calculate the destination color specifications for the input point.

9.1.1 Packing

Packing is a process that divides the domain of the source space and populates it with sample points to build the lookup table. Generally, the table is built by an equal step sampling along each axis of the source space, as shown in Fig. 9.1, of a five-level LUT. This will give (n − 1)³ cubes and n³ lattice points, where n is the number of levels. The advantage of this arrangement is that it implicitly supplies information about which cell is next to which. Thus, one needs only to store the starting point and the spacing for each axis. Generally, a matrix of n³ color patches at the lattice points of the source space is made and the destination color specifications of these patches are measured. The corresponding values from the source and destination spaces are tabulated into a lookup table.

http://dx.doi.org/10.1117/3.660835.ch9

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