A Correspondence-Free Color Chart Design for Color Calibration Hakki Can Karaimer1 Rang Nguyen 2 1School of Computer and Communication Sciences (IC), Ecole Polytechnique Fed´ erale´ de Lausanne (EPFL) 2Ho Chi Minh City University of Technology [email protected] [email protected] Abstract Colorimetric calibration computes the necessary color space transformation to map a camera’s device-specific color space to a device-independent perceptual color space. Color cal- ibration is most commonly performed by imaging a color rendi- tion chart with a fixed number of color patches with known col- orimetric values (e.g., CIE XYZ values). The color space trans- A Color errors from B Color errors from CST C Color errors from CST formation is estimated based on the correspondences between camera’s native color estimated using a estimated using our proposed the camera’s image and the chart’s colors. We present a new space transform (CST) conventional patch-based correspondence-free chart chart approach to colorimetric calibration that does not require ex- plicit color correspondences. Our approach computes a color Figure 1. (A) Color matching results based on the camera’s onboard color space transformation by aligning the color distributions of the conversion for an LG-G4 camera phone. (B) Result from calibration of the captured image to the known distribution of a calibration chart same camera using a patch-based pattern. (C) Result from calibration of containing thousands of colors. We show that a histogram-based the same camera using our proposed correspondence-free pattern. colorimetric calibration approach provides results that are on- world colors, they represents a very small sampling of the color par with the traditional patch-based method without the need to gamut. The second and most notable drawback is the the need to establish correspondences. establish correspondences by localizing the color patches in the camera image. This is generally done by having the user select Introduction and Motivation four corners in the image. This procedure however can be prone A camera’s raw sensor response is in a device-specific color to error such as the chart being upside down or partial occlusion. space related to the spectral sensitivities of the Bayer color fil- Moreover, this may not be practical for fast and accurate mobile ters found on a camera’s CMOS. One of the key procedures ap- phone imaging requirements. plied onboard a camera is to convert the camera’s color space to Contribution This paper reconsiders how color calibration a device-independent color space based on human perception – charts are designed. In particular, our goal is to design a color namely the CIE XYZ color space or one of its derivatives. The chart that does not require patch localization. To this end, we pro- color space transformation is a combination of a white balance pose a simple idea of relying on a color histogram of the imaged to first account for the scene illumination, followed by a trans- calibration chart and the known color histogram of the physical formation based on the spectral characteristics of the camera’s pattern in a perceptual color space. This histogram-based strat- sensor [10]. While cameras perform this colorimetric transfor- egy allows greater flexibility in calibration pattern design that can mation as part of the in-camera image processing procedure, it is incorporate thousands of colors. Key to this approach is a multi- often the case that the onboard colorimetric reproduction is not grid optimization strategy that is able to estimate the color space sufficiently accurate, as shown in Figure1-(A). transformation from the input image histogram and the known To improve the colorimetric mapping of a camera, espe- calibration histogram. We show that this histogram-based ap- cially for a particular scene illumination, a calibration procedure proach can produce a color space mapping with accuracy that is required in order to compute a more accurate color space map- is on-par with traditional patch-based approach but without the ping. The most common procedure is based on the color ren- need to localize patches. dition chart method introduced in 1976 for use with film cam- eras [13]. This approach relies on color patches with known CIE Preliminaries and Related Work XYZ properties distributed in fixed locations on the color chart. Preliminaries Before discussing related work, it is helpful to Using the correspondences between the imaged color chart and provide a background on how digital cameras perform their on- color patches on the chart, a mapping between the the camera and board colorimetric mapping. The goal of the color space map- CIE XYZ can be computed using linear least squares or other ping, also referred to as color space transform (CST), is to map optimization strategies. Figure1-(B) shows the improvements the camera sensor’s RGB values to a perceptual color space as if achieved by this conventional patch-based calibration procedure. the scene was observed under a reference illumination (e.g., day- This patch-based calibration has been the de facto calibra- light at a 6500K color temperature). As a result, the color space tion procedure for over 40 years. While intuitive and simplis- conversion is a combination of the white-balance correction and tic, the approach does have notable drawbacks. The first is that the color adaptation matrix (CAM) that is related to the spectral the color space mapping is computed using only a small number characteristics of the camera. Cameras first apply a 3 × 3 diag- of colors. For example, the most commonly used color chart is onal white-balance matrix (TWB) to correct for the illumination, the Macbeth ColorChecker chart (based on [13]’s original col- followed by a 3 × 3 full CAM matrix (TCAM) that transforms the ors) that has only 18 color patches with 6 neutral patches. While illumination-corrected raw values into the perceptual color space. these colors are selected to represent a wide spread of the real- We can consider this combined TWB and TCAM to correspond to the full color space transformation (CST), denoted as T. As re- Color calibration patterns cently discussed by Cheng et al. [2], for most illuminations, the diagonal TWB matrix is capable of correcting only the achromatic colors (thus the name white-balance and not color-balance), and therefore does not properly correct all colors. Because the initial white-balance correction is only an approximation, cameras generally encode two CAM matrices, B B 1 2 TCAM and TCAM, that are computed for sufficiently different il- luminations. These different CAMs compensate for the color mapping errors in the white-balance. For an arbitrary illumina- G R G R tion, the actual CST is estimated as a combination of the two Distribution of colors in Distribution of colors in our a 24-patch color chart proposed color chart CAMs that are weighted by the computed white-balance of the scene [10]. Figure 2. Example of two color charts and their corresponding histograms This reliance on only two CAMs for two illuminations is plotted in the ProPhoto [18] perceptual RGB color space. Two calibration one reason the overall color management on a camera is not suf- patterns are shown. The first is the standard 24-patch ColorChecker used ficiently accurate. Because of this, when high-quality colorimet- for conventional color calibration. The other chart is histogram-based pat- ric calibration is required – for example, for professional pho- tern used by our method. tographers or medical imaging applications where accurate color by using a simple scale and translation calculated for each color reproduction is essential – a calibration procedure is performed channel based on histogram variation among the camera images. under the specific illumination to generate an accurate CST. In Porikli [17] proposed a much more robust method that computed such cases, the CST can be computed as a single transformation, a per-channel brightness transfer function for a pair of cameras although it is still possible to do this as a combination of two sep- based on the images’ histograms. arate TWB and TCAM transformations to remain compatible with Our work is distinguished from prior work in its the standard in-camera processing workflow. goal to achieve accurate 3 × 3 color space transform in a Note that the color space transformation is not the stopping correspondence-free manner. While histogram matching has point for the final output. There are several additional steps used been used for related problems, to the best of our knowledge it to produce the final standard RGB (sRGB) output for JPEG en- has not been examined as a viable alternative for accurate colori- coding. This involves a number of color manipulation steps, such metric calibration. Moreover, the color calibration pattern design as tone-mapping and selective color rendering that substantially has not changed for over 40 years. change the image. More details of the full rendering pipeline can be found in the recent work by [9]. The focus of this paper, Correspondence-Free Color Calibration however, is on computing an accurate CST. We begin by first describing our overall approach. This is Related Work The vast majority of previous work for comput- followed by details on our optimization approach to compute the ing a color space transform is based on correspondence obtained 3 × 3 color space transformation, T using 3D color histograms. from a color chart with standardized samples (e.g., [3–5,12,19]). The main difference among these approaches is the technique Overall Framework used to obtain the mapping. For example, Finlayson and Fig.2 shows an example of two calibration chart, one Drew [3] proposed a white-point preserving least-squares solu- based on traditional 24 colors and the other representing color tion that constrained the CST such that it did not modify cor- distribution-based charts used by our proposed method.