A Similarity Measure for Large Color Differences

Hundreds of large color differences, of magnitude 20 E00, were generated and used in a visual sorting experiment. The process of generating these color differences and two specific experiments are described in detail. The results show that small color difference metrics, such as E00, do not consistently model the visually sorted differences for large differences. A new similarity measure, based on a cosine similarity between categorical vectors of colors, is described and used to more consistently model large color differences. This similarity metric can be used to better characterize large color errors during reproduction, for image processing operations such as segmentation or as a feature for content retrieval. The new measure can also be applied to visual phenomena, such as categorical perception, in which within category color differences are perceived as smaller than across category differences. Introduction There has been decades of research on the topic of color difference metrics.1-3 This work has primarily considered small color differences or just-noticeable differences (JND’s). These distance metrics include CIELab 1976 E*ab, E94 and E00 and are most applicable to quantifying whether or not two colors match. There has been some work in the area of large color differences but even for these publications4-8, the emphasis is on understanding how well existing color differences metrics scale up to larger color differences. Indeed unlike a threshold or JND, there is perhaps even limited consensus on what constitutes a large color difference. Likewise existing color difference metrics are based on geometric distance computations and advanced color differences metrics differ mainly in the complexity of the weighting schemes applied to underlying geometric quantities. One area where larger, non-threshold color differences have been researched, is the phenomena of categorical perception9-10. This phenomenon is the increase in perceived color differences for color pairs that cross categorical boundaries relative to perceived differences for pairs within a single category. However, this has been a separate research activity from formulation and testing of color difference metrics. One challenge for color difference research is the fact that while a given color can be perceived and described using a three dimensional representation, a color pair is six dimensional. This means that color sampling is a challenge and even simple, concise, systematic sampling results in rapid explosion in the number of color pairs. For example a 5 by 5 by 5 sampling in a given color space will result in thousands of possible different pairs of color differences. An additional challenge is the time and expense required for the collection of visual evaluations, which are typically based on the paired-comparison forced-choice technique. There are methods to sub-sample the full sampling of pairs but even with a substantially more efficient technique, this method also limits all visual evaluations to pair-wise assessments. Finally, the caveat that color difference equations, like E00, are to be used to quantify small color differences of less than 5 is widely known, but mostly ignored. How else is the maximum or 95th percentile error for a device characterization to be expressed? Experiments Given the challenges described in the introduction, we spent considerable time designing the specific experiment to investigate large color differences. The first area of effort was on the sampling of color pairs and the second area of effort was the specific experimental task. The sampling and task were used to conduct two experiments, although for this paper we focus mainly on the first of the experiments. The first experiment makes use of the World Wide Web to collect distributed data from online volunteers. A second experiment used full sampling and a single characterized display to collect data from a dozen participants in a controlled, laboratory setting. For the generation of color differences a random walk with farthest point sampling was used. This algorithm consisted of the following four steps. First, random RGB values for a known additive display were generated using a uniform random number generator. From a specific point of this set a random walk was taken away from the point in RGB space. This walk was terminated once the distance between the first point and the second point was within some error term away from a specified E00 value. For this paper, the sRGB color space was used, the error term was 0.0001 and the target E00 value was 20. Thousands of candidate pairs were generated before the next processing step. Second, given a large number of possible color pairs, farthest point sampling11 was applied to narrow down the pairs to several hundred pairs. The farthest point sampling was based on the average CIELAB coordinate of the two colors. The farthest point sampling based on the average CIELAB value effectively eliminates similar pairs of colors. Third, a nearest pair thresholding was applied to the minimum of the average color differences (between first-first/second-second points and first-second/secondfirst points of the pairs). A threshold of 15 was used and the result is a further reduction in similar pairs and elimination of mostly symmetric pairs of differences. Forth, the target number of pairs was selected, shuffled and assigned to 18 blocks of 9 color difference pairs. Additional hierarchical sampling or drawing of points from different blocks, was also applied but will not be described in this paper. The resulting set of color differences is shown in patch form on the left of Figure 1 and the corresponding a* versus b* plot on the right of Figure 1. Note that the end result of the steps described above is a collection of color difference vectors that fairly uniformly covers most of the gamut with minimal overlap of the end-points or the vectors. These vectors also lack any consistent orientation and vary randomly in their lightness, chroma and hue values. This sampling is purposely quite different from a regular, systematic sampling and can be tuned to 234 © 2014 Society for Imaging Science and Technology Figure 1. The color differences pairs used in the experiment shown as color patches, on the left, and as vectors in an a* versus b* plot on the right. All of the plotted color differences are approximately 20 E00 in magnitude. However, the differences vary from 20 to 8