Image-Difference Measure Optimized Gamut Mapping

Even though there is still room for improvement, recent perceptual image-difference measures show a prediction performance that makes them interesting to be used as objective functions for optimizing image processing algorithms. In this paper, we use a color enhanced modification of the Structural Similarity (SSIM) index for optimizing gamut mapping. An iterative algorithm is proposed that minimizes this measure for a given reference image subject to in-gamut images. Since distortions within remote image regions contribute independently to the measure a descent direction can be specified locally. The step-length is chosen to be a fraction of the just-noticeable-distance ensuring a decrease of the measure. Results show that the proposed approach preserves contrast and structural information of reference images. Some artifacts suggest modifications of the employed image-difference measure. Introduction Every color-reproduction workflow incorporates a color gamut mapping transformation to account for the limited ability of output devices to reproduce colors. A common objective of a gamut mapping transformation is to minimize the perceived difference between the original image and the reproduction. To avoid artifacts, such as color banding, usually more than the non-reproducible colors have to be modified. In the early stage of gamut mapping research pixel-wise transformations have been investigated. A good overview of such gamut mapping methods is given by Morovic et al. [1]. In order to preserve local image contrasts, spatial gamut mapping has become of increasing interest in recent years [2, 3, 4, 5, 6]. An independent comparison of selected spatial gamut mapping methods can be found in [7]. Nearly all of these methods work within perceptual color spaces (e.g., hue linearized CIELAB or IPT color space [8]) but are based on heuristics (e.g., preserving hue is more important than preserving chroma). Calculating the gamut mapping operator by minimizing the perceptual difference to the original is rarely addressed in literature. Nakauchi et al. [9] proposed a method that minimizes a color image-difference measure which is very similar to the S-CIELAB-based image difference. Kimmel et al. [10] used a related measure but added gradients to the objective function in order to account for perceptual feature differences (e.g., color banding). Minimizing this objective function is similar to solving an Euler-Lagrange differential equation and finally (after a reformulation) a quadratic programming problem. Kimmel’s approach is more of theoretical interest, since it requires devices with convex gamuts – a property that most real devices do not possess. Furthermore, Nakauchi and Kimmel et al. construct their objective function in a way that ∆L∗, ∆a∗ and ∆b∗ image-difference plains are treated separately and without considering the direction of difference. Optimizing such objective functions might lead, for instance, to adverse hue shifts. In a recent publication Zolliker et al. [11] used a hueenhanced modification of the SSIM index [12] to fuse images resulting from different gamut mapping algorithms. Visual experiments show that the resulting images are judged to be more similar to the originals than the results of the gamut mapping methods employed for the fusion process. Further enhancements considering chromatic deviations were able to significantly improve the prediction performance of the SSIM index for gamut mapping distortions [13, 14]. Even though there is still much room for improvement, such imagedifference measures could be directly used as objective functions for gamut mapping. In this paper, we propose an algorithm that incorporates a slightly modified version of an image-difference measure described in [14] as an objective function for gamut mapping. Our aim is not only to present this method but also to learn more about the underlying image-difference measure. The Image-Difference Measure An image-difference measure maps two images and a set of parameters specifying the viewing conditions into a single number that is a prediction of the perceived image difference. The measure employed in this paper is called color image-difference (CID) measure. It is based upon an extension of the SSIM index [12] to color images [14]. For computing the CID measure between two images X ,Y of the same size, they need to be normalized in a preceding step to reference viewing conditions by an image appearance model (e.g., to the viewing distance, luminance level, etc.) and then transformed into a working color space. We used the nearly perceptually uniform LAB2000HL opponent color space [15], which is moreover hue linear with respect to the Hung-Berns data [16], i.e. lines of constant perceived hue agree well with lines of predicted hue. The color space has a lightness axis ”L”, a redgreen axis ”a” and a blue-yellow axis ”b” similar to the CIELAB color space that has some shortcomings with respect to hue linearity and perceptual uniformity. The CID measure incorporates five terms to predict local lightness (lL), chroma (lC), and hue (lH ) differences as well as local lightness-contrast (cL) and lightness-structure (sL) differences. The terms are defined on rectangular windows covering the same regions within the images X and Y :