Efficient Computation of Geodesics in Color Space.

Although scientists agree that a perceptual color space is not Euclidean and color difference measures, such as CIELAB's ΔE2000, model these aspects of color perception, colormaps are still mostly evaluated through piecewise linear interpolation in a Euclidean color space. In a non-Euclidean setting, the piecewise linear interpolation of a colormap through control points translates to finding shortest paths. Alternatively, a smooth interpolation can be generalized to finding the straightest path. Both approaches are difficult to solve and are compute intensive. We compare the 11 most promising optimization algorithms for the computation of a geodesic either as the shortest or as the straightest path to find the most efficient one to use for colormap interpolation in real-world applications. For two control points, the zero curvature algorithms excelled, especially the 2D relaxation method. For multiple control points, only the mimimal curvature algorithms can produce smooth curves, amongst which the 1D relaxation method performed best.

Assessing K-12 school reopenings under different COVID-19 Spread scenarios - United States, school year 2020/21: A retrospective modeling study.

INTRODUCTION: School-age children play a key role in the spread of airborne viruses like influenza due to the prolonged and close contacts they have in school settings. As a result, school closures and other non-pharmaceutical interventions were recommended as the first line of defense in response to the novel coronavirus pandemic (COVID-19). METHODS: We used an agent-based model that simulates communities across the United States including daycares, primary, and secondary schools to quantify the relative health outcomes of reopening schools for the period of August 15, 2020 to April 11, 2021. Our simulation was carried out in early September 2020 and was based on the latest (at the time) Centers for Disease Control and Prevention (CDC)'s Pandemic Planning Scenarios released in May 2020. We explored different reopening scenarios including virtual learning, in-person school, and several hybrid options that stratify the student population into cohorts in order to reduce exposure and pathogen spread. RESULTS: Scenarios where cohorts of students return to school in non-overlapping formats, which we refer to as hybrid scenarios, resulted in significant decreases in the percentage of symptomatic individuals with COVID-19, by as much as 75%. These hybrid scenarios have only slightly more negative health impacts of COVID-19 compared to implementing a 100% virtual learning scenario. Hybrid scenarios can significantly avert the number of COVID-19 cases at the national scale-approximately between 28 M and 60 M depending on the scenario-over the simulated eight-month period. We found the results of our simulations to be highly dependent on the number of workplaces assumed to be open for in-person business, as well as the initial level of COVID-19 incidence within the simulated community. CONCLUSION: In an evolving pandemic, while a large proportion of people remain susceptible, reducing the number of students attending school leads to better health outcomes; part-time in-classroom education substantially reduces health risks.

Maximum likelihood estimation of difference scaling functions for suprathreshold judgments.

Maximum likelihood estimation (MLE) has been used to produce perceptual scales from binary judgments of triads and quadruples. This method relies on Thurstone's theory of a stochastic perceptual process where the perceived difference of two stimuli is the difference in their perceived strengths. It is possible that the perception of a suprathreshold difference is overestimated when adding smaller differences, a phenomenon referred to as diminishing returns. The current approach to construct a perceptual scale using MLE does not account for this phenomenon. We present a way to model the perception of differences using MLE and Thurstone's theory, adapted to allow the possibility of diminishing returns. This method is validated using Monte Carlo simulated responses to experimental triads and can correctly model diminishing returns, the absence of diminishing returns, and the opposite of diminishing returns both in the cases when a perceptual scale is known and when the true perceived strengths of the stimuli are unknown. Additionally, this method was applied to empirical data sets to determine its feasibility in investigations of perception. Ultimately, it was found that this analysis allows for more accurate modeling of suprathreshold difference judgments, a more complete understanding of the perceptual processes underlying comparisons, and the evaluation of Thurstone's theory of difference judgments.

The non-Riemannian nature of perceptual color space.

The scientific community generally agrees on the theory, introduced by Riemann and furthered by Helmholtz and Schrödinger, that perceived color space is not Euclidean but rather, a three-dimensional Riemannian space. We show that the principle of diminishing returns applies to human color perception. This means that large color differences cannot be derived by adding a series of small steps, and therefore, perceptual color space cannot be described by a Riemannian geometry. This finding is inconsistent with the current approaches to modeling perceptual color space. Therefore, the assumed shape of color space requires a paradigm shift. Consequences of this apply to color metrics that are currently used in image and video processing, color mapping, and the paint and textile industries. These metrics are valid only for small differences. Rethinking them outside of a Riemannian setting could provide a path to extending them to large differences. This finding further hints at the existence of a second-order Weber­Fechner law describing perceived differences.

Enabling Domain Expertise in Scientific Visualization With CinemaScience.

Scientific users present unique challenges to visualization researchers. Their high-level tasks require them to apply domain-specific expertise. We introduce a broader audience to the CinemaScience project and demonstrate how CinemaScience enables efficient visualization workflows that can bring in scientist expertise and drive scientific insight.

Measuring and Modeling the Feature Detection Threshold Functions of Colormaps.

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. In this paper we present a new method for evaluating the feature detection 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) will accurately model colormapped feature detection thresholds compared to a model where the chromaticity components have reduced weights. The hypothesis that feature detection 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.

The Good, the Bad, and the Ugly: A Theoretical Framework for the Assessment of Continuous Colormaps.

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.