Conjoint Analysis of Parametrized Gamut Mapping Algorithms

We show that conjoint analysis, a popular multi-attribute preference assessment technique used in market research, is a well suited tool to simultaneously evaluate a multitude of gamut mapping algorithms with a psycho-visual testing load not much higher than in conventional psycho-visual tests of gamut mapping algorithms. The gamut mapping algorithms that we test using conjoint analysis are derived from a master algorithm by choosing different parameter settings. Simultaneously we can also test the influence of additional parameters like gamut size on the perceived quality of a mapping. Conjoint analysis allows us to quantify the contribution of every single parameter value to the perceived quality. Introduction Rendering of a color image in the presence of device limitations, also called gamut mapping, is a fundamental problem in digital color reproduction. Despite being a classical topic, for an overview see Morovic [1], gamut mapping is still an active area of research. Lately, research on gamut mapping algorithms (GMAs) has focused on image dependence [2, 3] and spatial mapping algorithms [4, 5, 6]. A very important part in the development of GMAs is their evaluation. Here human perception is the ultimate judge that determines which of the different competing algorithms is the most effective. Psycho-metrical scaling is a common method to measure image quality and image differences [7]. The quality of GMAs is typically measured with psycho-visual tests that involve paired comparisons. In a paired comparison a test person is shown an original image and two images obtained from different mapping algorithms. The test person has to identify the mapped image perceived to better represent the original. In order to improve the quality and comparability among studies, the technical committee of CIE published guidelines [8] on how to conduct psycho-visual tests assessing the quality of GMAs. Here we use psycho-visual tests not only to compare a few final GMAs but already in the development stage of mapping algorithms. Our approach builds on the insight that gamut mapping can be seen as a highly parametrized problem. There are many, sometimes competing parameters relevant for gamut mapping: first of all the preservation of hue, lightness and saturation. Important parameters for image dependent algorithms are spatial image information and parameters like local contrast and smoothness gradients. Also, when realizing a GMA we have a choice of working color space, mapping direction, compression type. We use psycho-visual tests—paired comparison—to determine an optimal parameter setting. The data elicitation phase of our test is the same as in traditional psycho-visual tests used to compare different GMAs. In particular, the number of paired comparisons per test person is not larger, neither is the number of test persons significantly larger, whereas the potential number of mapping algorithms that can be compared is much larger. The difference to traditional psycho-visual tests used to compare GMAs is in the way how we analyze the elicited data. We are using conjoint analysis that essentially fits a linear model [9] to the data by assigning a part-worth value to every parameter level. The value of a parameter setting—besides the algorithm’s parameters this can include additional parameters like gamut size—is then the sum of the part-worth values of the parameter levels used. The number of potential parameter settings that can be compared using conjoint analysis is determined by the number of levels tested for each parameter, i.e., it is the product of these numbers which can be quite large and easily exceed 1000. We should point out that we are not the first who systematically include observer experiments in the development of GMAs, see for example the work done by Kang et al. [10]. Multivariate analysis techniques also have been used in image processing to gauge the importance of parameters [11]. This paper is organized as follows. In the next section, “Mapping Algorithms”, we describe the parameters that we have studied and evaluated for gamut mapping. Section “Conjoint Analysis” reviews a conjoint analysis technique which was developed in [9] by extending Thurstone’s law of comparative judgment to the multi-attribute case. In Section “Results” we present and discuss two user studies that we conducted to evaluate the parametrized GMA. We conclude the paper with a discussion of our results. Mapping Algorithms We consider finding a good GMA as a parameter optimization problem, i.e., we consider one master algorithm with free parameters for which we want to determine optimal values from psycho-visual tests. The master algorithm is quite simple, it maps any color point in the source gamut along a line segment connecting the color point and a focal point into the destination gamut. We consider also additional parameters that are not parameters of our master algorithm, but whose variation may affect the perceived quality of the mapping. We are especially interested in how the shape of the destination gamut affects the quality of the mapping. Hence we considered the following additional parameters: the size of the destination gamut as well as small shifts and rotations of the destination gamut. Shifts and rotations of destination gamuts turned out to be not so important parameters. Thus in a second user study we replaced them by two other parameters, namely shift of the focal point (Color/Density shifts) and hue rotations. In the following we summarize all the parameters that we have studied. Note that we always used sRGB as source gamut, i.e., we did not consider the source gamut as a parameter. 38 ©2008 Society for Imaging Science and Technology Compression. The compression parameter describes how the mapping along the line segment is done. We studied four different strategies: linear compression (lin), clipping (clip) and two sigmoidal compression algorithms (sig1 and sig2). The sigmoidal compression strategy maps a color point towards the focal point by a scale factor 0 β 1 calculated as follows