Recoding Color Transfer as A Color Homography

Abstract

The recently discovered color homography theorem proves that colors across a change in photometric viewing condition are related by a homography [2]. In this paper, we propose a color-homography-based color transfer decomposition which encodes color transfer as a combination of chromaticity shift and shading adjustment. Our experiments show that the proposed color transfer decomposition provides a very close approximation to many popular color transfer methods. We believe that our color transfer model is useful and fundamental for developing simple and efficient color transfer algorithms. Our model also enables users to amend the imperfections of a color transfer result or extract a concise form of the original desired effect (which allows a more efficient re-application of the original color transfer). In Figure 1, we start with the outputs of the prior-art algorithms. Assuming we relate source image I s to target image I t with a pixel-wise correspondence, we represent the RGBs of I s and I t as two n × 3 matrices A and B respectively where n is the number of pixels. These n × 3 matrices can be reconstituted into the original image grids. The chromaticity mapping is modeled as a 3 × 3 linear transform but because of the relative positions of light and surfaces there might also be per-pixel shading perturbations. Assume the Lambertian image formation is an accurate physical model,where D is an n × n diagonal matrix of shading factors and H is a 3 × 3 chromaticity mapping matrix. A color transfer can be decomposed into a diagonal shading matrix D and a homography matrix H. The homography matrix H is a global chromaticity mapping. The matrix D can be seen as a change of surface reflectance or position of illuminant. Equation 1 can be solved by Alternating Least Squares [2]. To apply the extracted color transfer effect to a different scene, the shading adjustment D is further modeled as a smooth brightness-to-shading function f as follows:which is denoted by Mapped Shading Homography. We show some visual results of color transfer approximations in Figure 2. Global 3D affine mapping [3] does not well reproduce the shading adjustments of color transfer. In Figure 3, the original shading homography approximation retains the artifacts of noise and over-saturation of the

3D color homography model for photo-realistic color transfer re-coding

“…Similarly, this method also does not address the tonal difference between the input and output images. Gong et al [11] proposed a planar color homography model which re-codes a color transfer effect as a combination of 2D perspective transform of chromaticity and shading adjustments. Compared with [18], it requires less parameters to represent a non-tonal color change.…”

“…However, the assumption of a 2D chromaticity distortion limits the range of color transfer it can represent. Their [11] tonal adjustment (mean intensity-to-shading mapping) also does not preserve image gradients and the original color rank. Another important work is probabilistic moving least squares [12] which calculates a largely parameterized transform of color space.…”

“…In addition, the complexity of a color transfer method usually leads to longer processing time. To address these issues, previous methods [11,13,18] were proposed to approximate the color change produced by a color transfer, such that an original complicated color transfer can be re-formulated as a simpler and faster algorithm with an acceptable level of accuracy and some introduced artifacts.…”

“…Our model is extended from a recent planar color homography color transfer model [11] to the 3D domain, as opposed to the original 2D planar domain. In our improved model, we decompose an unknown color transfer into 3D color perspective transform and mean intensity mapping components.…”

“…In our improved model, we decompose an unknown color transfer into 3D color perspective transform and mean intensity mapping components. Based on [11], we make two new contributions: (1) a 3D color mapping model that better re-codes color change by relating two homogeneous color spaces and (2) a monotonic mean intensity mapping method that prevents artifacts without adding unwanted blur. Our experiments show significant improvements in color transfer re-coding accuracy.…”