Repeated Look-up Tables

Efficient hardware implementations routinely approximate mathematical functions with look-up tables, while keeping the error of the approximation under control. For a certain class of commonly occurring 1D functions, namely monotonically increasing or decreasing functions, we found that it is possible to approximate such functions by repeated application of a very low resolution 1D look-up table. There are many advantages to cascading multiple identical LUTs, including the promise of a very simple hardware design and the use of standard linear interpolation. Further, the complexity associated with unequal bin sizes can be avoided. We show that for realistic applications, including gamma correction, high dynamic range encoding and decoding curves, as well as tone mapping and inverse tone mapping applications, multiple cascaded look-up tables can reduce the approximation error by more than 50% compared to a single look-up table with the same total memory footprint.