Digital Color Management: Encoding Solutions, 2nd Edition

I

Mathematical Transforms

The color transformations described throughout this book can be implemented using a number of different mathematical techniques. The best method for a given application will depend on the hardware, software, and computational resources available. Nevertheless, different types of mathematical operations generally are appropriate for particular types of transformations, and the comments in this appendix regarding each are applicable in most circumstances.

One-dimensional lookup tables

A one-dimensional lookup table (1-D LUT) essentially is a list relating each individual input value to a corresponding output value. Such tables are an obvious choice for transforming a set of channel-independent image values to a different set of channel-independent values. Typical applications include reshaping grayscales for rendering or re-rendering, applying color-balance and exposure shifts, applying or removing camera nonlinearities in digital video and digital still images, and implementing calibration corrections for input and output devices. Table I.1 tabulates sample input/output pairs for an example 1-D LUT that might be used to prevent highlight clipping when extended luminance dynamic range input values are transformed to output 8-bit digital code values. The complete LUT is depicted graphically in Figure I.1.

In systems with limited resources, 1-D LUTs can be particularly useful. Consider, for example, a 24-bit color system (8 bits per color channel) employing ...