AI 中文总结
本文提出用低分辨率三维查找表结合四面体插值高效逼近光滑三维函数，用于RGB到CMYK转换，仅需38 KiB且整数运算，平均误差0.08%，适合低功耗实时应用。
AI 中文摘要
光滑的三维函数可以通过分辨率显著降低的三维查找表结合四面体插值来高效且准确地逼近。在预处理步骤中，函数在粗网格上被采样一次。对于每个输入，定位包含该输入的网格立方体，选择该立方体中的6个四面体之一，并将其4个角的值通过加权和进行组合。对于RGB到CMYK的颜色转换（这是该方法的特别频繁应用），每轴$n = 16$个单元的表格（$17^3$个节点，16位值）需要38 KiB。而完整的8位表格需要64 MiB。实验评估表明，$n = 16$表格的平均误差为每通道0.08%的墨量。对于8位输入，查找仅使用整数运算（第~\ ef{sec:integer}节），不需要浮点运算和除法，所有中间值均适合32位。浮点运算仅在离线构建表格时需要一次。整数结果与使用精确分数的四面体插值最多相差16位输出的1个单位，且白色和黑色被精确重现。这使得该方法适用于计算资源受限的低功耗设备和实时应用。
英文摘要
A smooth 3D function can be efficiently and accurately approximated by a 3D lookup table of significantly lower resolution combined with tetrahedral interpolation. The function is sampled once on a coarse grid in a preprocessing step. For each input, the enclosing grid cube is located, one of the 6 tetrahedra in this cube is selected, and the values at its 4 corners are combined by a weighted sum. For RGB to CMYK color conversion, a particularly frequent application of this, a table with $n = 16$ cells per axis ($17^3$ nodes, 16-bit values) requires 38\,KiB. A full 8-bit table requires 64\,MiB. As shown in an experimental evaluation, the mean error of the $n = 16$ table is 0.08\,\% ink per channel. For 8-bit input, the lookup uses integer arithmetic only (Section~\ref{sec:integer}). It requires no floating point and no division, and all intermediate values fit in 32 bits. Floating point is needed only to build the table, once and offline. The integer result differs from tetrahedral interpolation with exact fractions by at most 1 unit of the 16-bit output, and white and black are reproduced exactly. This makes the approach suitable for low-power devices and real-time applications where computational resources are limited.
