LoR-LUT: Learning Compact 3D Lookup Tables via Low-Rank Residuals

TL;DR

LoR-LUT is presented, a unified low-rank formulation for compact and interpretable 3D lookup table (LUT) generation that improves the existing perceptual quality of an image, which is primarily due to the technique's novel use of residual corrections.

Abstract

We present LoR-LUT, a unified low-rank formulation for compact and interpretable 3D lookup table (LUT) generation. Unlike conventional 3D-LUT-based techniques that rely on fusion of basis LUTs, which are usually dense tensors, our unified approach extends the current framework by jointly using residual corrections, which are in fact low-rank tensors, together with a set of basis LUTs. The approach described here improves the existing perceptual quality of an image, which is primarily due to the technique's novel use of residual corrections. At the same time, we achieve the same level of trilinear interpolation complexity, using a significantly smaller number of network, residual corrections, and LUT parameters. The experimental results obtained from LoR-LUT, which is trained on the MIT-Adobe FiveK dataset, reproduce expert-level retouching characteristics with high perceptual fidelity and a sub-megabyte model size. Furthermore, we introduce an interactive visualization tool, termed LoR-LUT Viewer, which transforms an input image into the LUT-adjusted output image, via a number of slidebars that control different parameters. The tool provides an effective way to enhance interpretability and user confidence in the visual results. Overall, our proposed formulation offers a compact, interpretable, and efficient direction for future LUT-based image enhancement and style transfer.

Figures (8)

• Figure 1: Comparison between conventional adaptive 3D-LUTs and our LoR-LUT. (a) conventional adaptive 3D-LUTs rely on fusing several dense basis LUTs. (b) LoR-LUT replaces dense fusion with a compact low-rank residual, achieving similar flexibility with fewer parameters and identical interpolation complexity.
• Figure 2: Trilinear interpolation in a 3D LUT. Each input color $(r,g,b)$ lies within a cube defined by eight lattice vertices $\mathbf{L}[x_i,y_j,z_k]$. The output color $\mathbf{y}$ is a weighted sum of eight vertices of the cube, where $w_{ijk}$ is a trilinear interpolation weight that decreases with distance from $(r,g,b)$ along each axis.
• Figure 3: Low-rank residual representation. Each rank-1 component factorizes the correction tensor into three axis-specific vectors and a color coefficient. Summing $R$ such components yields a compact yet expressive residual tensor $\Delta\mathbf{L}$.
• Figure 4: Overall architecture of LoR-LUT. Two lightweight networks predict the fusion weights and low-rank residual factors from the input image. The reconstructed LUT is then applied using the standard trilinear interpolation operator. The entire pipeline is differentiable and end-to-end trainable.
• Figure 5: Visualization of low-rank residual correction in LoR-LUT. (a) Base LUT (identity, $K{=}0$); (b) residual output; and (c) combined base+residual result. The bottom row shows the corresponding 3D LUT cubes. The low-rank residual introduces subtle yet structured color shifts.