Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Mathematical representation
- 3 Elementary display of images
- 4 Quantization
- 5 Frequency domain representation
- 6 Spatial sampling
- 7 Image characteristics
- 8 Photometry and colorimetry
- 9 Color sampling
- 10 Image input devices
- 11 Image output devices and methods
- 12 Characterization of devices
- 13 Estimation of image model parameters
- 14 Image restoration
- A Generalized functions and sampling representation
- B Digital image manipulation and matrix representation
- C Stochastic images
- D Multidimensional look-up tables
- E Psychovisual properties
- References
- Index
D - Multidimensional look-up tables
Published online by Cambridge University Press: 06 July 2010
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Mathematical representation
- 3 Elementary display of images
- 4 Quantization
- 5 Frequency domain representation
- 6 Spatial sampling
- 7 Image characteristics
- 8 Photometry and colorimetry
- 9 Color sampling
- 10 Image input devices
- 11 Image output devices and methods
- 12 Characterization of devices
- 13 Estimation of image model parameters
- 14 Image restoration
- A Generalized functions and sampling representation
- B Digital image manipulation and matrix representation
- C Stochastic images
- D Multidimensional look-up tables
- E Psychovisual properties
- References
- Index
Summary
Introduction
A look-up table (LUT) is basically a function from one space to another that is defined in terms of a few samples, their corresponding function values, and a method to calculate any particular mapping from those samples. Mathematically, the LUT is defined as L[{(xk, f (xk)}, I(x)], where {xk} are the samples in the domain space, {f (xk)} are the corresponding function values in the range space, and I(x) is the function, or algorithm, that is used to compute the value in the range space for an arbitrary point in the domain space, x. The function I(x) interpolates the output if the point x is within the convex hull of the sample set {xk }, and extrapolates the output if it is not.
Look-up tables are a simple and computationally efficient way to generate nonlinear and nonparametric functions. Because of their efficiency and ease of implementation, look-up tables are often used to compute standard functions, such as sinusoids and exponentials. The accuracy of the tabularized function depends upon the resolution of the table. The key to the efficiency is that the interpolation between elements in the table is simple and fast. This means that accuracy depends on the resolution of the table, rather than the approximation of the interpolation to an ideal functional form.
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- Chapter
- Information
- Fundamentals of Digital Imaging , pp. 486 - 498Publisher: Cambridge University PressPrint publication year: 2008