Recoding Color Transfer as A Color Homography (Supplementary Material)

In this supplementary material, we show the details of solving shading with a Laplacian smoothness constraint, the complete color transfer approximation evaluation table, and its corresponding color transfer approximation visual results. Please also check our supplementary video for video color grading extraction demonstrations. 1 Laplacian shading regularization In this section, we describe how to minimize the cost function described in Equation 6 of the main paper. The Laplacian kernel K adopted in our method is defined as K = 0 1 0 1 −4 1 0 1 0  . (1) The other choices for the Laplacian kernel can also produce satisfying results. The cost function can be reformulated as: min d ∥∥Id− dmapped∥∥+ λ ‖Pd‖ (2) where d is the vector-form of the flattened 2D shading image ID, dmapped is the similar vector-form of the mapped per-pixel shadings, P is an n× n matrix that encodes the multiplicative factors for the convolution operation of each ID pixel. P is filled with the Laplacian kernel weights. For instance, to calculate the jth Laplacian shading pixel, we have: { Po,j = 1 o ∈ {j ± 1, j ± nrow} Pj,j = −4 (3) where nrow is the number of image matrix row. The other elements in P is filled with 0. The border pixels of the Laplacian shading image are also filled with the 0 (i.e. omitted for minimization). Finally, d is solved by regularized least square regression as follows: d = (I + λP P )dmapped. (4) Empirically, we find λ = 1000/( ∑ j ‖P∗,j‖ 2 /n) suitable for most of our applications. 2 Quantitative evaluation of color transfer approximation Table 1 shows the complete per-method PSNR errors corresponding to Table 1 in the main paper. 3 Color transfer approximation visual results The following 4 figures contain the color transfer approximation results based on 7 classic source and target image pairs and four popular color transfer methods [1, 3, 4, 5]. These visual results correspond to the quantitative evaluation results shown in Table 1. 1 3D Affine [2] Shading Homography Mapped Shading Homography Method [1] [3] [4] [5] [1] [3] [4] [5] [1] [3] [4] [5] Pair 1 27.80 27.42 29.83 25.42 28.54 30.27 36.26 30.48 25.98 26.69 30.83 26.85 Pair 2 25.37 24.14 24.78 31.97 30.00 29.13 33.61 32.43 27.88 27.32 29.16 30.45 Pair 3 23.22 21.74 22.64 30.45 34.16 29.59 34.09 32.95 28.82 27.15 27.18 27.79 Pair 4 27.11 26.68 25.12 30.07 38.93 35.69 36.96 43.24 30.44 30.81 30.39 32.51 Pair 5 31.68 30.49 31.54 26.10 27.93 29.34 34.83 35.32 27.14 27.97 32.47 32.65 Pair 6 26.25 26.73 28.73 28.36 24.98 28.62 36.06 30.79 23.73 27.81 34.72 30.30 Pair 7 26.54 25.05 25.76 27.09 36.05 34.79 44.07 43.17 30.37 29.36 37.13 37.74 Table 1: PSNR error between the original color transfer result and its approximation.