The Mechanics of Look-Up Table Inversion
A standard Look-Up Table (LUT) maps three-dimensional RGB coordinates from a source color space to a target color space, commonly compressing range for Rec.709 displays. Inverting this process requires mapping the output coordinates back to the source input points. Mathematically, this involves taking the inverse transfer function of the mapping grid. In a 3D LUT, tri-linear interpolation is applied to traverse the 3D grid and compute coordinates for intermediate points. When building a Reverse LUT, we re-calculate these grid locations, effectively turning the output display value back into a scene-referred log value, restoring grading flexibility.