A myriad of design rules for what constitutes a "good" colormap can be found in the literature. Some common rules include order, uniformity, and high discriminative power. However, the meaning of many of these terms is often ambiguous or open to interpretation. At times, different authors may use the same term to describe different concepts or the same rule is described by varying nomenclature. These ambiguities stand in the way of collaborative work, the design of experiments to assess the characteristics of colormaps, and automated colormap generation. In this paper, we review current and historical guidelines for colormap design. We propose a specified taxonomy and provide unambiguous mathematical definitions for the most common design rules.

Pseudocoloring is one of the most common techniques used in scientific visualization. To apply pseudocoloring to a scalar field, the field value at each point is represented using one of a sequence of colors (called a colormap). One of the principles applied in generating colormaps is uniformity and previously the main method for determining uniformity has been the application of uniform color spaces. Here we present a new method for evaluating the feature discrimination threshold function across a colormap. The method is used in crowdsourced studies for the direct evaluation of nine colormaps for three feature sizes. The results are used to test the hypothesis that a uniform color space (CIELAB) gives too much weight to chromatic differences compared to luminance differences because of the way it was constructed. The hypothesis that feature discrimination can be predicted solely on the basis of luminance is also tested. The results reject both hypotheses and we demonstrate how reduced weights on the green-red and blue-yellow terms of the CIELAB color space creates a more accurate model when the task is the detection of smaller features in colormapped data. Both the method itself and modified CIELAB can be used in colormap design and evaluation.

Significance For over 100 y, the scientific community has adhered to a paradigm, introduced by Riemann and furthered by Helmholtz and Schrodinger, where perceptual color space is a three-dimensional Riemannian space. This implies that the distance between two colors is the length of the shortest path that connects them. We show that a Riemannian metric overestimates the perception of large color differences because large color differences are perceived as less than the sum of small differences. This effect, called diminishing returns, cannot exist in a Riemannian geometry. Consequently, we need to adapt how we model color differences, as the current standard, Δ E , recognized by the International Commission for Weights and Measures, does not account for diminishing returns in color difference perception.

Applying lossy data compression to climate model output is an attractive means of reducing the enormous volumes of data generated by climate models. However, because lossy data compression does not exactly preserve the original data, its application to scientific data must be done judiciously. To this end, a collection of measures is being developed to evaluate various aspects of lossy compression quality on climate model output. Given the importance of data visualization to climate scientists interacting with model output, any suite of measures must include a means of assessing whether images generated from the compressed model data are noticeably different from images based on the original model data. Therefore, in this work we conduct a forced‐choice visual evaluation study with climate model data that surveyed more than one hundred participants with domain relevant expertise. In addition to the images created from unaltered climate model data, study images are generated from model data that is subjected to two different types of lossy compression approaches and multiple levels (amounts) of compression. Study participants indicate whether a visual difference can be seen, with respect to the reference image, due to lossy compression effects. We assess the relationship between the perceptual scores from the user study to a number of common (full reference) image quality assessment (IQA) measures, and use statistical models to suggest appropriate measures and thresholds for evaluating lossily compressed climate data. We find the structural similarity index (SSIM) to perform the best, and our findings indicate that the threshold required for climate model data is much higher than previous findings in the literature.

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