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.

中文翻译：

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重复查找表。

高效的硬件实现通常使用查找表来近似数学函数，同时将近似误差保持在控制之下。对于一类常见的一维函数，即单调递增或递减函数，我们发现可以通过重复应用非常低分辨率的一维查找表来近似此类函数。级联多个相同的LUT有许多优点，包括非常简单的硬件设计和标准线性插值的使用。此外，可以避免与不等的箱尺寸有关的复杂性。我们表明，对于现实的应用，包括伽马校正，高动态范围的编码和解码曲线以及色调映射和逆色调映射应用，