D.1 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 [{( x _k, f ( x _k)}, ( x)], where { x _k} are the samples in the domain space, { f ( x _k)} are the corresponding function values in the range space, and ( 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 ( x) interpolates the output if the point x is within the convex hull of the sample set { x _k}, 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.

Multidimensional look-up tables (MLUTs) have been used for color space transformations...