View source for Color coding in data visualization

{{Multiple issues|
{{COI|reason=primary editor is one of the authors of the research|date=November 2020}}
{{Tone|date=July 2021}}
{{Essay|date=July 2021}}
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[[Data visualization]] involves presenting data and information using visual elements like charts, graphs, and maps. It simplifies complex data, making patterns and trends more apparent, and aiding in better understanding and decision-making.<ref>{{cite book |last1=Kirk |first1=A |title=Data Visualisation: A Handbook for Data Driven Design |date=2019 |publisher=Sage |location=Thousand Oaks, CA |edition=2nd}}</ref> And color coding in data visualization is implemented to help users of data to easily read, understand, and categorize the different facets of information that a given set data is trying to explain.

==Origins==
Origins of color coding include [[rubric]]s, the [[Four Color Theorem]] of cartography and [[Jacques Bertin]]'s 1967 book, ''[[Sémiologie Graphique]]'' (''Semiology of Graphics'').<ref>{{cite book |last1=Bertin |first1=Jacques |author-link=Jacques Bertin |title=Sémiologie Graphique. Les diagrammes, les réseaux, les cartes |date=1967 |publisher=Gauthier-Villars |location=Paris }}</ref> Contemporary color coding for [[data visualization]] is enabled by four technologies: statistics, color technology, displays and computing. Visualization of data<ref>{{cite book |last1=Wainer |first1=Howard |last2=Friendly |first2=Michael |title=Data Visualization: A History of Visual Thinking and Graphic Communication |date=2020 |publisher=Harvard University Press}}</ref> was proceduralized by statisticians [[John Tukey]] and [[Edward Tufte]] in their respective landmark books ''[[Exploratory Data Analysis]]''<ref>{{cite book |last1=Tukey |first1=John Wilder |author-link=John Tukey |title=Exploratory Data Analysis |date=1977 |publisher=Addison-Wesley |isbn=978-0-201-07616-5}}</ref> in 1977 and ''[[The Visual Display of Quantitative Information]]''<ref>{{cite book |last1=Tufte |first1=Edward |author-link=Edward Tufte |title=The Visual Display of Quantitative Information |date=2001 |publisher=Graphics Press |location=Cheshire, CT |edition=2nd}}</ref> in 1982. They did not emphasize the use of color. Others demonstrated the superiority<ref>{{cite journal |last1=Williams |first1=LG |title=The Effect of Target Specification on Objects Fixated During Visual Search |journal=Perception and Psychophysics |date=1966 |volume=1 |issue=5 |pages=315–318|doi=10.3758/BF03207398 |s2cid=143016062 |doi-access=free }}</ref> of color coding to speed visual search of displayed information,<ref>{{cite journal |last1=Christ |title=Review and Analysis of Color Coding Research for Visual Displays |journal=Human Factors |date=1975 |volume=17 |issue=6 |pages=542–570|doi=10.1177/001872087501700602 |s2cid=143323235 }}</ref> and to locate<ref>{{cite book |last1=Folk |first1=CL |editor1-last=Elliot |editor1-first=AJ |editor2-last=Fairchild |editor2-first=MD |editor3-last=Franklin |editor3-first=A |title=Handbook of Color Psychology |date=2015 |publisher=Cambridge University Press |location=Cambridge, GB |isbn=978-1-107-04323-7 |pages=481–501 |chapter=The role of color in voluntary and involuntary guidance of selective attention, Chapter 23}}</ref> and organize<ref>{{cite journal |last1=Wong |first1=B |title=Gestalt principles (Part II) |journal=Nature Methods |date=2010 |volume=7 |issue=12 |page=941|doi=10.1038/nmeth1210-941 |s2cid=35716514 |doi-access=free }}</ref> information of interest. A third prerequisite for color-coded data visualization is high-resolution, high-contrast, high-luminance color electronic displays. Honeywell Corporation<ref>{{cite book |last1=Krebs |first1=MJ |last2=Wolf |first2=JD |last3=Sandvig |first3=JH |title=Color Display Design Guide |date=1978 |publisher=Honeywell Systems and Research Center |location=Minneapolis, MN |url=https://apps.dtic.mil/sti/citations/ADA066630}}</ref> and Boeing Corporation<ref>{{cite book |last1=Silverstein |first1=LD |last2=Merrifield |first2=RM |title=The development and evaluation of color systems for airborne applications (Report No. DOT/FAA/PM-85-19) |date=1985 |publisher=US Department of Transportation |location=Washington DC |edition=Defense Technical Information Center AD-A168563 1986}}</ref> assembled technical data that are still germane to use of color displays. More recently, the US Federal Aviation Administration has published technical guidance<ref>{{cite book |title=FAA Standard Practice, Color Use in Air Traffic Control System Displays |date=24 March 2020 |publisher=US Department of Transportation|location=Washington DC}}</ref> for visualization of dynamic (air traffic) data on self-luminous color displays.

Humans have an innate ability to perform color-coded visual search. Without training or practice, the search time with color coding can be reduced by a factor of ten or more, compared to a search of the same information display without color coding. For example, Figure 1a illustrates prolonged search without color coding, while Figure 1b demonstrates color coding making data salient.

{{gallery |mode=packed
|File:Color Coding Technology Figure 2a.svg|
|File:Color Coding Technology Figure 2b.svg|
|title=Figures 1a and b. Which category has the fewest stars: 32-, 24- or 16-pointed stars?}}

==Fundamentals of color coding for data search and grouping==
===Color-coded visualization===
Color coding has diverse applications to data visualization. A general principle is to ''align salience of colors with relevance of displayed information''.<ref>{{cite journal |last1=Wong |first1=B |title=Salience to relevance |journal=Nature Methods |date=2011 |volume=8 |issue=11 |page=889|doi=10.1038/nmeth.1762 |pmid=22148153 |s2cid=8652127 |doi-access=free }}</ref> The person searching might be given the color of the item to be found, or they may know the color of the sought category based on their experience. Alternatively, their task could require looking for an item that stands out as different, signified by color, with no target color given.

Salient colors might be used, for example, to highlight patterns or to enable rapid search:
{|
|width=400px valign=top|
* for a particular information-item or items on a geographic plot
**among friendly, hostile and neutral forces on a military situation display<ref>{{cite report |first=Susan F. |last=Chipman |date=June 2007 |chapter=Annex B – Visualisation Research and Development in the United States |title=Multimedia Visualisation of Massive Military Datasets |publisher=Research and Technology Organisation of NATO |id=RTO-TR-IST-021 |isbn=978-92-837-0067-8 |chapter-url=https://www.sto.nato.int/publications/STO%20Technical%20Reports/RTO-TR-IST-021/$$TR-IST-021-ALL.pdf}}</ref>
**on a weather map<ref name="Fortyeight"/>
**among geographically-displayed geologic, topographic, health, political, economic, demographic, technical or aeronautical data<ref name="Schontz">{{cite journal |last1=Schontz |first1=WD |last2=Trumm |first2=GA |last3=Williams |first3=LG |title=Color coding for information location |journal=Human Factors |date=1971 |volume=13 |issue=3 |pages=237–246 |doi=10.1177/001872087101300304|pmid=5558217 |s2cid=28424671 }}</ref>
**for cartography<ref>{{cite book |last1=Brewer |first1=CA |editor1-last=MacEachren |editor1-first=AM |editor2-last=Taylor |editor2-first=DRF |title=Visualization in Modern Cartography |date=1994 |publisher=Elsevier Science |location=Tarrytown NY |pages=123–147 |chapter=Color Use Guidelines for Mapping and Visualization, Chapter 7}}</ref><ref>{{cite book |last1=Brewer |first1=CA |editor1-last=Bares |editor1-first=J |title=Color Hard Copy and Graphic Arts III. Proceedings of the International Society for Optical Engineering (SPIE) |date=1994 |publisher=SPIE |location=San Jose CA |pages=54–63 |edition=Vol 2171 |chapter=Guidelines for Use of the Perceptual Dimensions of Color for Mapping and Visualization}}</ref>
|width=200px valign=top|
* in scientific visualization of
**medical images
**[[Fractal art|mathematical images]]
**[[Hyperspectral imaging|hyperspectral images]]
|width=400px valign=top|
* along flow charts including 
**input flows, output flows, reservoirs, mixing chambers and condensation towers etc. in an industrial-process flow
**project flow charts
**process flow charts
**sales flow charts
**organization charts
**financial flows, to follow the money
**cause-and-effect diagrams
|width=250px valign=top|
* within statistical visualizations like
**scatter plots
**pie diagrams
**bar graphs
**function plots
**[[Exploratory data analysis|exploratory data analyses]]<ref>{{cite journal |last1=Wong |first1=B |last2=Shoresh |first2=N |title=Data exploration |journal=Nature Methods |date=2012 |volume=9 |issue=1 |page=5|doi=10.1038/nmeth.1829 |pmid=22312636 |s2cid=20997239 |doi-access=free }}</ref>
|}

Another application of color coding is to show symmetries in visualized data.<ref>{{cite journal |last1=Chipman |first1=SF |title=Towards a synthetic eye: Psychological issues in data visualization |journal=ResearchGate |date=2020 |doi=10.13140/RG.2.2.31920.99841}}</ref> Color coding can connect and untangle, e.g., trends on a plot, or the [[Brainbow|continuity of axons in the neural connectome]]. New applications of the innate skill to search, or group, based on color are still being invented, e.g., for networks,<ref>{{cite journal |last1=Gehlenborg |first1=N |last2=Wong |first2=B |title=Networks |journal=Nature Methods |date=2012 |volume=9 |issue=2 |page=115|doi=10.1038/nmeth.1862 |pmid=22396963 |s2cid=29741258 |doi-access=free }}</ref> the [[Road coloring theorem|Road Coloring Theorem]], [[Heat map|heat maps]],<ref>{{cite journal |last1=Gehlenborg |first1=N |last2=Wong |first2=B |title=Heat Maps |journal=Nature Methods |date=2012 |volume=9 |issue=3 |page=213|doi=10.1038/nmeth.1902 |pmid=27974286 |s2cid=28870914 |doi-access=free }}</ref> the genome,<ref>{{cite journal |last1=Nielsen |first1=C |last2=Wong |first2=B |title=Representing the genome |journal=Nature Methods |date=2012 |volume=9 |issue=5 |page=423|doi=10.1038/nmeth.1992 |pmid=22803197 |s2cid=6207156 |doi-access=free }}</ref> genomic structural variation,<ref>{{cite journal |last1=Nielsen |first1=C |last2=Wong |first2=B |title=Representing genomic structural variation |journal=Nature Methods |date=2012 |volume=9 |issue=7 |page=631|doi=10.1038/nmeth.2018 |pmid=22930825 |s2cid=1878491 |doi-access=free }}</ref> genome browsers,<ref>{{cite journal |last1=Nielsen |first1=C |last2=Wong |first2=B |title=Managing deep data in genome browsers |journal=Nature Methods |date=2012 |volume=9 |issue=6 |page=521|doi=10.1038/nmeth.2049 |pmid=22874978 |s2cid=5785111 |doi-access=free }}</ref> and spatial data like molecules.<ref>{{cite journal |last1=Gehlenborg |first1=N |last2=Wong |first2=B |title=Into the third dimension |journal=Nature Methods |date=2012 |volume=9 |issue=9 |page=851|doi=10.1038/nmeth.2151 |pmid=23097778 |s2cid=6417810 |doi-access=free }}</ref> Color coding has utility to visualize outliers and errors in unfamiliar data.

Color coding is used also for [[Color code|purposes]] other than visualization of displayed data. Data visualization complements, and does not substitute for or contradict, those other uses. Where conflict is possible, for example ''when there are established meanings of colors in other contexts such as signal lights, then those meanings should be given deference when choosing colors for a data-visualization color code.''

===Time required to find visualized information===
[[Visual search]] is accomplished<ref>{{cite journal |last1=Kotowicz |first1=Andreas |last2=Rutishauser |first2=Ueli |last3=Koch |first3=Christof |title=Time course of target recognition in visual search |journal=Frontiers in Human Neuroscience |date=2010 |volume=4 |issue=Article 31 |page=31 |doi=10.3389/fnhum.2010.00031 |pmid=20428512 |pmc=2859879 |doi-access=free }}</ref> through rapid involuntary and subconscious eye movements called [[saccades]]. The eye makes about three saccades per second during visual search. Such eye movements constrain human cognitive performance.<ref>{{Citation|title=A summary of the EPIC Cognitive Architecture.|last=Kieras|first=DE|pages=27–48|year=2017|chapter=Chapter 2|place=The Oxford Handbook of Cognitive Science|publication-place=New York|publisher=Oxford University Press|editor-last=Chipman|editor-first=SEF}}</ref> Search involves a neural network in the brain for processing motion and location, and controlling saccades.<ref name="Furman">{{Citation|title=Neuronal Networks in Brain Function, CNS Disorders, and Therapeutics; Chapter 19|last=Furman|first=M|pages=247–260|date=2014|work=Visual Network|location=New York|publisher=Elsevier|editor-last=Faingold|editor-first=CL|editor2-last=Blumenthal|editor2-first=H}}</ref> This neural network is sensitive to color and to change; ''color and flash-coding (temporally-varying brightness) can complement each other to enhance search speed, without mutual interference.''<ref>{{cite journal |last1=Van Orden |first1=Karl |last2=DiVita |first2=J |last3=Shim |first3=MJ |title=Redundant use of luminance and flashing with shape and color as highlighting codes in symbolic displays |journal=Human Factors |date=1993 |volume=35 |issue=2 |pages=195–204|doi=10.1177/001872089303500201 |pmid=8349285 |s2cid=15879572 }}</ref>

If there are N items to be searched in a display, N/2 saccades tend to be needed to locate a particular item.<ref name="Three"/> Given three saccades per second, N/(2*3) = N/6 seconds is an estimate of search time to find one item among N. The estimate is improved by adding reaction time, perhaps a second; ''expected search time equals 1 + N/6 seconds to find a target item among N displayed items''.<ref name="Three">{{cite journal |last1=Williams |first1=LG |title=Target conspicuity and visual search |journal=Human Factors |date=1966 |volume=8 |issue=1 |pages=80–92 |doi=10.1177/001872086600800109 |pmid=5966605 |s2cid=26712216 }}</ref> This estimate accords with empirical search times.<ref>{{cite journal |last1=Cahill |first1=MC |last2=Carter |first2=RC |title=Color code size for searching displays of different density |journal=Human Factors |date=1976 |volume=18 |issue=3 |pages=273–280|doi=10.1177/001872087601800308 |s2cid=111132459 }}</ref><ref name="JEPHPP">{{cite journal |last1=Carter |first1=RC |title=Visual search with color |journal=Journal of Experimental Psychology: Human Perception and Performance |date=1982 |volume=8 |issue=1 |pages=127–36 |doi=10.1037/0096-1523.8.1.127 |pmid=6460078 }}</ref> In such a situation, ''color-coded search time increases linearly with the number of information items on a display that share the distinct target color''.<ref>{{cite journal |last1=Carter |first1=RC |last2=Cahill |first2=MC |title=Regression models of search time for color-coded information displays |journal=Human Factors |date=1978 |volume=20 |issue=3 |pages=293–302 |doi=10.1177/001872087902100304 |pmid=511182 |s2cid=12964263 }}</ref> Furthermore, ''search is faster when the target-colored items are spatially organized'', for instance in sinuous paths<ref name="JEPHPP"/> or presentation layout<ref>{{cite journal |last1=Wong |first1=B |title=Layout |journal=Nature Methods |date=2011 |volume=8 |issue=10 |page=783|doi=10.1038/nmeth.1711 |pmid=22053339 |s2cid=5463317 |doi-access=free }}</ref> or design of data figures.<ref>{{cite journal |last1=Wong |first1=B |title=Design of data figures |journal=Nature Methods |date=2010 |volume=7 |issue=9 |page=665|doi=10.1038/nmeth0910-665 |s2cid=22865156 |doi-access=free }}</ref>
 
Search time has an exponential statistical distribution.<ref>{{cite journal |last1=Carter |first1=RC |title=Search time with a color display: Analysis of distribution functions |journal=Human Factors |date=1982 |volume=24 |issue=2 |pages=203–12 |doi=10.1177/001872088202400206 |pmid=7095808 |s2cid=38762867 }}</ref> In an [[exponential distribution]], the variability (standard deviation) equals the expected value or average. As expected search time increases, so does the variability of search time. Longer expected search time implies a few very-long searches. For example, with 30 different search items (N=30) randomly distributed on the display, the expected search time is 6 seconds, but 5% of searches will last longer than 18 seconds. See Table 1 for similar results.
{| class="wikitable"
|+ Table 1. Calculated effects of the exponential distribution on variability of search times, illustrating that longer average search time is associated with some unacceptably long searches.
|-
! Number of search items !! 5 !! 6 !! 7 !! 8 !! 9 !! 10 !! 15 !! 20 !! 30
|-
| Expected time to find target (sec) || 1.8 || 2.0 || 2.2 || 2.3 || 2.5 || 2.7 || 3.5 || 4.3 || 6.0
|-
| 5% of searches longer than (sec)|| 5.5 || 6.0 || 6.5 || 7.0 || 7.5 || 8.0 || 10.5 || 13 || 18
|}

''Short expected search time prevents unacceptably long searches associated with longer average search time.'' 
Based on the linear increase of search time with the number of potential targets, and the exponential distribution of search times (see Table 1), ''limiting displayed items sharing the target’s color to fewer than about 11 would keep search times to less than 10 seconds almost all of the time.<ref name="Schontz"/> More items could share the target color if the objective were to group subsets (different colors) of dispersed items for some purpose other than search.''<ref>{{cite journal |last1=Wong |first1=B |title=Gestalt principles (Part I) |journal=Nature Methods |date=2010 |volume=7 |issue=11 |page=863|doi=10.1038/nmeth1110-863 |pmid=21049588 |s2cid=13604942 |doi-access=free }}</ref>

===Choosing salient colors for color coding===
Color coding can make information salient<ref>{{cite journal |last1=Wong |first1=B |title=Salience |journal=Nature Methods |date=2010 |volume=7 |issue=10 |page=773|doi=10.1038/nmeth1010-773 |pmid=20936751 |s2cid=34837264 |doi-access=free }}</ref> (see Figure 1b). Discriminable color codes reduce or eliminate interference with search by all items not sharing the salient target color.<ref name="Eleven">{{cite journal |last1=Carter |first1=EC |last2=Carter |first2=RC |title=Color and Conspicuousness |journal=Journal of the Optical Society of America |date=1981 |volume=71 |issue=6 |pages=723–9 |doi=10.1364/JOSA.71.000723 |pmid=7252614 |bibcode=1981JOSA...71..723C }}</ref> Qualitative, subjective methods to choose distinct colors for coding are limited to a few colors.<ref name="Fifteen">{{cite journal |last1=Wong |first1=B |title=Color Coding |journal=Nature Methods |date=2010 |volume=7 |issue=8 |page=573|doi=10.1038/nmeth0810-573 |pmid=20704014 |s2cid=33475794 |doi-access=free }}</ref> Color engineering achieved 22 paint colors of maximum contrast,<ref>{{cite journal |last1=Kelly |first1=KL |title=Twenty-two Colors of Maximum Contrast |journal=Color Engineering |date=1965 |volume=3 |pages=26–27}}</ref> before the advent of self-luminous color displays. Self-luminous devices, such as computer screens, are capable of higher luminances (wider color [[gamut]]), higher resolution (smaller symbols and image segments) and higher contrasts (more-salient distinctions from background) than are usually achievable with reflective materials like paint. These characteristics of self-luminous displays create color-coding opportunities and problems as discussed below.

An objective method of choosing distinctive colors for color-coded visualization of electronically-displayed data is to consider the color coordinates<ref name="Seventeen">{{cite book |last1=Berns |first1=RS |title=Billmeyer and Saltzman's Principles of Color Technology |date=2019 |publisher=Wiley |location=New York |edition=4th}}</ref> of the colors available within the display's [[gamut]]. Typically, a color is represented by three coordinates [[RGB color model|(R, G, B)]], each in the range 0 to 255 in the case of 8-bit representation. The most widely used color representation is a variant of RGB known as [[sRGB]], while device-dependent RGB color representations are also used. An advantage of a device-dependent RGB representation is that if the device uses RGB light emitters, it can specify every color that can be produced by that particular device. Most displays use RGB light emitters, although [[multi-primary color display]] alternatives do exist, such as the [[Quattron]] displays produced by [[Sharp Corporation]].

[[File:Your_display's_gamut;_salient_colors_from_the_edges_and_vertices.svg|thumb|center|500px|
Figure 2. Some salient colors suitable for color coding are located on the outer boundary of the display's color gamut. The (R,G,B) coordinates of each color are shown in the corresponding colored hexagon.]]

[[File:Schematic_of_the_relation_between_calculated_color_difference_and_apparent_color_similarity_during_search._This_version_of_the_figure_has_bigger_font_size.svg|thumb|right|Figure 3. Schematic summary of the relation between apparent color similarity and calculated color difference. The red line is most relevant here. Other lines in Figure 3 will be discussed below.]]
Optical measurements can be used to calculate the [[color difference]] between each pair of colors in the color code. This involves spectro-radiometrically measuring<ref name="Seventeen" /> the tristimulus values of colors available from the display. [[CIE 1931 color space|Tristimulus values]] (X, Y, Z) are device-independent color coordinates used to calculate color difference. [[Luminance]], a correlate of grayscale, is the Y tristimulus value, for instance.<ref>{{cite book |last1=Wyszecki |first1=Gunter |last2=Stiles |first2=W.S. |title=Color Science: Concepts and Methods, Quantitative Data and Formulae |date=1982 |publisher=John Wiley and Sons |location=New York |page=157 |edition=2nd}}</ref> ''The CIEDE2000, or CIECAM02 color difference formulas are statistically superior as metrics of large-color-difference discriminability.''<ref name="Twelve" /> Generally, color difference calculations give more weight to red-green differences, and less to blue-yellow differences and [[luminance]] (i.e., gray scale) differences, in that order of efficacy.<ref name="Seventeen"/>

Code colors having small color differences from the target color make distractor items look similar to the target color, as measured in terms of search time<ref name="JEPHPP" /> or in terms of eye movements.<ref name="Twelve">{{cite journal |last1=Carter |first1=RC |last2=Huertas |first2=R |title=Ultra-Large Color Difference and Small Subtense |journal=Color Research and Application |date=2010 |volume=35 |pages=4–17|doi=10.1002/col.20557 }}</ref> Displayed items with large color differences from the target do not interfere with target salience.<ref name="JEPHPP" /> Figure 3 summarizes this relationship between color similarity or salience during visualization and calculated color difference.<ref name="Twelve" /> ''The discipline of identifying (and separating, in color difference) the most similar colors in the color code will be useful, whatever method is used to choose code colors.''

In a code with n colors, there are n(n-1)/2 pairs of colors (see Figure 4), each pair having a color difference.<ref>{{cite journal |last1=Carter |first1=RC |title=CIE L*u*v* equations for self-luminous displays |journal=Color Research and Application |date=1983 |volume=8 |pages=252–253|doi=10.1002/col.5080080414 }}</ref> The proliferation of color differences, as the number of colors increases, necessitates a systematic, algorithmic and automated method of color selection. For instance, aeronautical charts<ref name="Schontz"/> might be color coded with 28 colors, implying 378 pairwise color differences.
[[File:This_file_is_a_graph_of_the_number_of_pairwise_connections_among_n_objects.svg|thumb|center|500px|Figure 4. The number of color pairs, and hence color differences, in a color code increases rapidly as the number of colors increases.]]

Salience of many colors, seen in the context of each other, can be optimized. Because the smallest color differences interfere with search while large-enough color differences do not interfere (see Figure 3), the optimization objective<ref>{{cite journal |last1=Carter |first1=RC |last2=Carter |first2=EC |title=High-contrast sets of colors |journal=Applied Optics |date=1982 |volume=21 |issue=16 |pages=2936–9 |doi=10.1364/AO.21.002936 |pmid=20396153 |bibcode=1982ApOpt..21.2936C }}</ref> is to ''maximize the minimum calculated color-difference, among the n(n-1)/2 color differences in an n-color code, in order to derive a large number (n) of distinct colors for a color code custom-fit to a particular display’s gamut.'' This basic method was elaborated for industrial use.<ref>{{cite journal |last1=Silverstein |first1=LD |last2=Lepkowski |first2=JS |last3=Carter |first3=RC |last4=Carter |first4=EC |editor1-first=Elliott |editor1-last=Schlam |title=Modeling of display color parameters and algorithmic color selection |journal=Proceedings of SPIE – the International Society for Optical Engineering, Advances in Display Technology VI |series=Advances in Display Technology VI |date=1986 |volume=624 |pages=26–34|doi=10.1117/12.961221 |bibcode=1986SPIE..624...26S |s2cid=57237683 }}</ref> The method has been applied to account for ambient illumination reflected from a display.<ref>{{cite journal |last1=DeCorte |first1=W |title=High contrast sets of colours for colour CRTs under various conditions of illumination. |journal=Displays |date=1985 |volume=6 |issue=2 |pages=95–100|doi=10.1016/0141-9382(85)90034-4 |bibcode=1985Displ...6...95D }}</ref> The optimization method has been extended to alternative objective functions.<ref>{{cite journal |last1=DeCorte |first1=W |title=Finding appropriate colors for color displays |journal=Color Research and Application |date=1986 |volume=11 |pages=56–61|doi=10.1002/col.5080110111 }}</ref> It has been applied to complex display situations<ref>{{cite journal |last1=DeCorte |first1=W |title=Optimum colors, phosphors, and illuminant characteristics for CRT displays: the algorithmic approach |journal=Human Factors |date=1986 |volume=28 |issue=1 |pages=39–47 |doi=10.1177/001872088602800105 |pmid=3710484 |s2cid=110327602 }}</ref><ref>{{cite journal |last1=DeCorte |first1=W |title=Ergonomically optimal CRT colours for nonfixed ambient illumination conditions |journal=Color Research and Application |date=1988 |volume=13 |issue=5 |pages=327–331|doi=10.1002/col.5080130510 }}</ref> and to small symbols.<ref name="Fourteen"/> Technical color measurement<ref name="Seventeen"/> and optimized color difference can generate several alternative equally-effective codes that exploit the full gamut of the display and human color discrimination capability. This availability of alternative coding choices enables use of apropos colors with pre-established meanings or avoidance of inappropriate colors.

==Practical problems of color coding for information salience==
===Symbol size affects color salience===
''Apparent color difference between objects depends upon the visual angle of the objects that are viewed. Smaller symbols cause reduced color differences.''<ref name="Fourteen">{{cite journal |last1=Carter |first1=RC |last2=Silverstein |first2=LD |title=Perceiving Color Across Scale: Great and Small, Discrete and Continuous |journal=Journal of the Optical Society of America A |date=2012 |volume=29 |issue=7 |pages=1346–55 |doi=10.1364/JOSAA.29.001346 |pmid=22751398 |bibcode=2012JOSAA..29.1346C }}</ref> Calculated color difference assumes a 2-degree visual subtense. The thumb-nail joint (from thumb-tip to joint-by-the-nail) appears about two degrees of visual subtense at arm’s length for example. Typical display symbols might subtend only 7 minutes, or less than 1/16 of two degrees.<ref name="Six">{{cite journal |last1=Carter |first1=RC |last2=Carter |first2=EC |title=Color coding for rapid location of small symbols |journal=Color Research and Application |date=1988 |volume=13 |issue=4 |pages=226–234|doi=10.1002/col.5080130407 }}</ref> Consider this in the context of these facts<ref name="Fortytwo">{{cite book |last1=Shevell |first1=SK |title=The Science of Color |date=2003 |publisher=Elsevier |location=Cambridge}}</ref>
# there are virtually no short-wavelength (blue) sensing cells on the retina within a 20-minute-diameter disk around the line of sight (LOS), 
# they comprise only about 7% of all daylight receptors and 
# the blue-sensing cells are about 4 minutes apart at their closest (within a degree of the LOS), increasing to about 8 minutes apart with greater eccentricity.
For these reasons, blue distinctions (involving colors on any tritan line,<ref name="Fortytwo"/>) are lost for small symbols. This is called small-field tritanopia, which is a color deficiency for blueness-differences among small visual fields, to which everyone is subject. Hence, ''blueness differences should be discounted (or even eliminated from consideration) when selecting coding colors for small symbols, less than about 30 minutes of (i.e., the sun’s and moon’s) angular subtense''.<ref>{{cite journal |last1=Albrecht |first1=M |title=Color blindness |journal=Nature Methods |date=2010 |volume=7 |issue=10 |page=775|doi=10.1038/nmeth1010-775a |pmid=20885436 |s2cid=205417940 |doi-access=free }}</ref> Even color-differences not involving blueness appear to fade (however less than blue fades) when symbols diminish in size. For example, objects appear darker (less light) as they trend to a smaller visual subtense; larger areas with the same luminance appear lighter than smaller areas.<ref name="Fourteen"/> ''It is possible to estimate the effect of visual subtense on apparent color difference, including grayscale difference.<ref name="Thirteen">{{cite journal |last1=Carter |first1=RC |last2=Silverstein |first2=LD |title=Size Matters: Improved Color-Difference Estimation for Small Visual Targets |journal=Journal of the Society for Information Display |date=2010 |volume=18 |pages=17–28|doi=10.1889/JSID18.1.17 |s2cid=56769750 }}</ref> Smaller visual subtense of symbols implies fewer salient, or even discriminable, colors in the same display gamut.<ref name="Fourteen"/> Code colors will be salient if their color differences are at least 14 CIEDE2000 units for symbols having a two-degree visual subtense, or the equivalent color difference as estimated for smaller subtense.''<ref name="Thirteen"/> For instance, salience of the 1.5-degree-by-0.75-degree visual-search targets used by Williams<ref name="Three"/> improved for increases of their color differences to at least 21 CIEDE2000 units; beyond about 21 their salience did not improve further.<ref name="Twelve"/> (The minimum color-difference values of salient colors given here correspond to the lower bound of the 95% [[confidence interval]] in the cited scientific literature.) The blue line and arrow in Figure 3 summarize the effect of small visual subtense (< 2 degrees of visual angle) on apparent color similarity, as a function of calculated color difference.<ref name="Six"/> The [[visual angle]] subtended by a displayed symbol or other image segment can be precisely measured or calculated.

===Deficiency of color vision can affect symbol salience===
The most common forms of [[Color blindness|inherited color deficiency]] involve red-green confusions.<ref>{{cite journal |last1=Wong |first1=B |title=Color blindness |journal=Nature Methods |date=2011 |volume=8 |issue=6 |page=441|doi=10.1038/nmeth.1618 |pmid=21774112 |s2cid=36690778 }}</ref> These color-perception confusions are due to a deficiency in retinal cells to sense long (e.g., red) or medium (e.g., green) wavelengths.<ref name="Fortytwo"/> Red or green would look darker for people deficient in the corresponding cells. Small visual subtense of symbols, or a rarer form of color deficiency (tritanopia), deplete blueness differences (due to sparse sampling by short-wavelength-sensing cells in the retina). ''A color code for general use, where neither color deficiency nor small visual subtense (e.g., distant viewing) can be avoided, is white, black, orange, and grays discriminable in luminance from the other code colors and from the background luminance.''<ref name="Fifteen"/> This assumes distant viewing by a person who retains the ability to sense either long or medium-wavelengths. Blue (but discriminably lighter than black) could be added, due to the rarity of deficient short-wavelength sensing cells, if viewing distances ensure visual subtense of color-coded symbols greater than 30 minutes. (See Figure 1b.)

Even grayscale perception can be affected by color deficiencies.<ref name ="Fortysix">{{cite book |last1=Kvitle |first1=AK |last2=Oddløkken |first2=H |last3=Green |first3=PJ |last4=Nussbaum |first4=P |title=2018 Colour and Visual Computing Symposium (CVCS) |chapter=Methods for psychophysical assessment of colour difference by observers with a colour vision deficiency |date=2018 |volume=Gjøvik Norway|pages=1–6 |doi=10.1109/CVCS.2018.8496594 |isbn=978-1-5386-5645-7 |s2cid=53014475 }}</ref> Red-green-color-deficient observers who retain long-wavelength-sensing cells (deuteranopes) are accurate judges of color differences near red.<ref name="Fortysix" /> Hence, ''the best color code for color-deficient observers would depend upon the type of color deficiency''.

Images can be enhanced for viewing by color-deficient observers.<ref name=":45">{{cite book |title=Enhancement of Images for Colour-Deficient Observers |year=2020 |publisher=CIE |location=Vienna |isbn=978-3-902842-80-0 |doi= 10.25039/TR.240.2020 |s2cid=242786806 }}</ref> The recommended methods are edge enhancement, recoloring and pattern superposition to complement color. Three kinds of images are envisioned: natural scene, scientific visualization or an office document. No technique satisfies the requirements of all applications.[[File:Demonstration_of_effect_of_luminance_contrast_on_legibility.svg|thumb|right|500px|Figure 5. A demonstration of how the luminance difference between a symbol and its background affects symbol legibility. The horizontal stripes and the vertical message-columns are each a constant color.]]

===Legibility in the context of color coding===
[[Legibility]] is different from salience, discussed above. Legibility is related to clearly and distinctly seeing edges, shapes and spatial details, and therefore to reading. ''Legibility of a symbol depends upon luminance difference (not color difference) between the symbol and the background upon which the symbol is presented.'' Figure 5, the concept of which was presented by Australian architect Paul Green-Armytage,<ref>{{cite book |last1=Green-Armytage |first1=Paul |title=Colour as Trademarks – Clarification and limitations |date=2017 |publisher=AIC, International Colour Association |location=Seogwipo, Jeju Korea |chapter=Oral Presentation, with visual slides; AIC Conference, OS05-5 Design & Communication II, Monday 16th October 3-5PM}}</ref> demonstrates this effect of luminance difference upon legibility. For this reason, yellow (a high-luminance color) is less legible on a bright white background, and conversely so are white symbols less legible on a yellow background. Dark blue (a low-luminance color) symbols are less legible on a black background, and conversely black letters are less legible on a dark blue background. This is despite yellow being salient on a white background and blue being conspicuous on a black background. ''Having adequate color difference among visualized items is complementary to, and compatible with, enabling legibility with adequate luminance difference between the items and their background.'' There are resources for quantifying the required luminance difference to enable legibility.

==Grayscale, an important tool for visualization of data==
In addition to its effect of on legibility, [[luminance]] also affects grayscale. Lightness and brightness differences are grayscale attributes of color difference, so they can affect conspicuousness of symbols. Grayscale is accessible to people with color-vision deficiencies,<ref name ="Fortysix"/> and it is less susceptible (than chromatic differences) to fading due to small visual subtense.<ref name="Thirteen"/> ''Grayscale (rather than chromatic color difference) has been shown to be particularly apt for coding ordinal data such as temperature on a weather map.''<ref name="Fortyeight">{{cite journal |last1=Breslow |first1=LA |last2=Trafton |first2=JG |last3=McCurry |first3=JM |last4=Ratwani |first4=RM |title=An algorithm for generating color scales for both categorical and ordinal coding |journal=Color Research and Application |date=2010 |volume=35 |pages=18–28|doi=10.1002/col.20559 }}</ref><ref>{{cite journal |last1=Gehlenborg |first1=N |last2=Wong |first2=B |title=Mapping quantitative data to color |journal=Nature Methods |date=2012 |volume=9 |issue=8 |page=769|doi=10.1038/nmeth.2134 |pmid=23019685 |s2cid=5645863 |doi-access=free }}</ref>
 
''Changing the background luminance makes salient the difference between the (possibly color-coded) symbols having luminances just greater than, and just less than, each background luminance selected.'' The dotted gray line in Figure 3 summarizes this effect. Leon Williams,<ref>{{cite book |last1=Williams |first1=Leon G |title=A study of visual search using eye movement recordings, Honeywell Document 12009-1R2, Contract NONR 4774(00) |date=1967 |publisher=Honeywell Corporation |location=Saint Paul MN |ref=Contract NONR 4774(00)}}</ref> observed this and suggested a data-visualization technique he called data slicing, as exemplified in Figure 6.
{{Gallery
|File:Four_Figures_have_the_same_dot_data,_this_one_had_a_high-luminance_background.svg|
|File:Four_files_have_the_same_dot_data,_this_one_has_a_high-intermediate_background_luminance.svg|
|File:Four_files_have_the_same_dot_data,_this_file_has_a_low-intermediate_background_luminance.svg|
|File:Last_of_four_dot_luminance_data_displays,_this_one_has_a_black_(unilluminated)_background.svg|
|title=Figures 6a-d. Data slicing, or changing the background luminance of an image, can render different data more salient. There are four copies of the same data, each copy with a different background luminance.|mode=packed}}

''The Whittle logarithmic grayscale calculation<ref name="Fifty"/> for self-luminous devices quantifies visual effects of luminance differences among displayed symbols.'' It enables calculation of any number of equal perceptible differences<ref name="Fiftyfive"/> (nEPD) as small as the threshold of visibility, or of any suprathreshold magnitude. The unit size of nEPD is three or four times the absolute threshold of visibility for luminance change. This nEPD unit is “just noticeable at a glance” with free viewing of an electronic display.<ref name="Fifty">{{cite journal |last1=Whittle |first1=P |title=Brightness, discriminability and the 'Crispening Effect' |journal=Vision Research |date=1992 |volume=32 |issue=8 |pages=1493–1507|doi=10.1016/0042-6989(92)90205-W |pmid=1455722 |s2cid=38768696 }}</ref>

The Whittle calculation is unusual (among grayscale formulae) in four ways.
#It includes the background luminance.<ref name="Fifty"/> 
#It applies to all [[Photopic vision|photopic]] (i.e., daylight) luminances, based on data for thresholds<ref name="Fiftyfive"/> and matching.<ref name="Fiftythree" /> 
#Its [[derivative]]s are meaningful.<ref name="Fiftysix"/> 
#It can account for the spatial scale of the contrast.<ref name="Fifty"/>

The derivative (slope) of nEPD with respect to background luminance implies an optimum background luminance.<ref>{{cite journal |last1=Carter |first1=RC |title=Gray-scale perceptions calculated: Optimum display background luminance |journal=Applied Optics |date=1997 |volume=36 |issue=8 |pages=1705–1717|doi=10.1364/AO.36.001705 |pmid=18250856 |bibcode=1997ApOpt..36.1705C }}</ref> White backgrounds are used for historical reasons related to legibility of small symbols. However, ''there is no symbol size or symbol-luminance range for which a white background is optimum, in the sense of maximizing the number of visibly-different gray shades that symbols can have in this luminance range. The optimum background can double the number of gray shades visible among larger symbols. The optimum background luminance is always less than 46% of the maximum of the symbol luminance range, for ranges including zero.''<ref name="Sixtyone">{{cite journal |last1=Yoon |first1=G |last2=Carter |first2=RC |title=Intraocular scattering effects on color appearance |journal=Unpublished |date=2020}}</ref>

Contrasts (e.g., displayed symbols) have a luminance difference from their background.<ref name="Fifty"/> The contrast luminance would be less than the background luminance for negative contrasts and the contrast luminance exceeds the background luminance for positive contrasts. The derivative of nEPD with respect to contrast luminance predicts the threshold of contrast visibility (e.g., to prevent banding in a digital image) for any daylight combination of symbol and background luminance.<ref name="Fiftyfive">{{cite journal |last1=Carter |first1=RC |title=Suprathreshold gray scale is implied by thresholds |journal=Applied Optics |date=2018 |volume=57 |issue=29 |pages=8751–8756|doi=10.1364/AO.57.008751 |pmid=30461954 |bibcode=2018ApOpt..57.8751C |s2cid=53747363 }}</ref><ref>{{cite journal |last1=Carter |first1=RC |title=Suprathreshold gray scale is implied by thresholds: erratum |journal=Applied Optics |date=2019 |volume=58 |issue=12 |page=3133 |doi=10.1364/AO.58.003133 |pmid=31044787 |bibcode=2019ApOpt..58.3133C |s2cid=143424176 }}</ref> The Whittle calculation’s derivative with respect to contrast luminance also quantifies human suprathreshold sensitivity to luminance differences, or changes, for all combinations of daylight target and background luminance.<ref name="Fiftysix">{{cite journal |last1=Carter |first1=RC |title=CIE self-luminous gray-scale calculation: inflections, parameters, and high-contrast limiting behavior |journal=Journal of the Optical Society of America A |date=2020 |volume=37 |issue=1 |pages=115–122|doi=10.1364/JOSAA.37.000115 |pmid=32118888 |bibcode=2020JOSAA..37..115C |s2cid=211727514 }}</ref> This derivative is germane to digital image processing, and particularly histogram specification,<ref>{{cite journal |last1=Carter |first1=RC |title=Biological Gray Scale for Digital Imagery |journal=Journal of Electronic Imaging |date=2005 |volume=14 |issue=2 |pages=023004-1–023004-10 |doi=10.1117/1.1900135 |bibcode=2005JEI....14b3004C |issn=1017-9909}}</ref> suggesting applicability to medical-image windowing. The Whittle calculation shows the magnitude of positive contrast beyond which contrast brightness increases (with increasing contrast luminance) as fast against any background as against an unilluminated (black) background.<ref name="Fiftysix"/> At lesser positive contrasts, and for negative contrasts, symbol lightness depends upon the background luminance of the symbol (in ways described by the Whittle calculation, and known as lightness constancy). ''Display luminance-contrast calibration<ref>{{cite journal |last1=Woods |first1=RL |last2=Goldstein |first2=RB |last3=Peli |first3=E |title=Psychophysical contrast calibration |journal=Vision Research |date=2013 |volume=90 |pages=15–24|doi=10.1016/j.visres.2013.04.011 |pmid=23643843 |pmc=3744609 }}</ref> would be necessary in mission-critical applications.''
 
[[File:Plot_of_CIE_gray-scale_calculation_for_self-luminous_devices,_for_optotype_E_subtending_10_arc_minutes.svg|thumb|right|Figure 7. Plot of the Whittle grayscale calculation (adopted by CIE<ref>{{cite book |title=Grey-scale calculation for self-luminous devices, TR 228-2018 |date=2018 |publisher=International Commission on Illumination |location=Vienna |isbn=978-3-901906-97-8}}</ref>) for self-luminous devices, as applied to an optotype E subtending 10 arc minutes (1/3 the diameter of the sun or full moon). See text for details about this plot.]]
In Figure 7, there is a different nEPD curve for each background luminance. The steepest part of each curve (most change of grayscale per unit change of symbol luminance) is for symbol luminances almost equal to their background luminance. Another relatively steep part of each curve is at the extreme left, where symbol luminance is near zero.<ref name="Fiftysix"/> Negative nEPD corresponds to negative contrasts and positive nEPD corresponds to positive contrasts. Symbols with equal nEPD from their respective backgrounds will appear the same shade of gray,<ref>{{cite journal |last1=Carter |first1=RC |title=Gray scale and achromatic color difference |journal=Journal of the Optical Society of America A |date=1993 |volume=10 |issue=6 |pages=1380–1391|doi=10.1364/JOSAA.10.001380 |bibcode=1993JOSAA..10.1380C }}</ref> despite being on different backgrounds. (See Figure 8, which illustrates this matching of grays seen on different backgrounds.) The logarithmic curvature of the Whittle calculation has a rational basis.<ref>{{cite journal |last1=Brill |first1=MH |last2=Carter |first2=RC |title=Does Lightness Obey a Log or Power Law? Or Is That The Right Question? |journal=Color Research and Application |date=2014 |volume=39 |pages=99–101|doi=10.1002/col.21777 }}</ref> An intermediate background luminance for Figure 7 itself increases the number of grayscale steps visible among the curves, making plausible an optimum background luminance.

The Whittle calculation for self-luminous devices has a parameter, k, relating to the spatial scale of the symbol.<ref name="Fiftysix"/> It (k) is the proportion (between 0 and 100%) of image contrast (target luminance minus background luminance) lost to intraocular scattering on the way to becoming a retinal image.<ref name="Fifty"/> ''Reducing the angular subtense of a symbol always reduces the physical luminance difference between the symbol and its background (due to intraocular scattering), hence reducing legibility and conspicuousness'' and increasing k.<ref name="Fifty"/> This parameter, k, can be calculated from optical principles,<ref name="Sixtyone"/> as it was for the gray scale of the 10-arc-minute (k=0.2) optotype E represented in Figure 7. When symbol angular subtense (represented by k) is reduced, the optimum background luminance also is reduced.<ref name="Sixtyone"/> The Whittle calculation is unaffected by highlights remote from the contrast, as verified experimentally.<ref>{{cite journal |last1=Carter |first1=RC |last2=Sibert |first2=L |last3=Templeman |first3=J |last4=Ballas |first4=J |title=Luminous backgrounds and frames affect gray-scale lightness, thresholds and suprathreshold discriminations |journal=Journal of Experimental Psychology: Applied |date=1999 |volume=5|issue=2 |pages=190–204 |doi=10.1037/1076-898X.5.2.190 }}</ref> The effect of remote highlights on grayscale appearance is due to intraocular scattering.<ref name="Fiftysix"/>

[[File:This_Figure_illustrates_how_a_more-luminous_background_darkens_the_appearance_of_an_image-segment_grayscale_grayscale.svg|thumb|right|Figure 9. Identical wreaths of six grayscale hexagons having different background luminances. A more-luminous background darkens the grayscale.]][[File:This_image_illustrates_matching_grays_seen_against_different_background_luminances.svg|thumb|left|Figure 8. This figure illustrates the concept of matching grays with different background luminances. Each hexagon has a different luminance.]]

A grayscale phenomenon calculable with the Whittle calculation for self-luminous devices is matching grays having different background luminances.<ref name="Fiftythree">{{cite journal |last1=Carter |first1=RC |last2=Brill |first2=MH |title=Calculation of Self-luminous Neutral Scale: How Many Neutral Steps Can You See on That Display? |journal=Journal of the Society for Information Display |date=2014 |volume=22 |issue=4 |pages=177–186|doi=10.1002/jsid.234 |s2cid=61000862 }}</ref> Conversely, the calculation can be used to find the background luminances that will make specified contrast luminances match. According to the calculation (as can be seen in Figure 7), ''it is impossible to match negative contrasts with positive contrasts; negative contrasts always look darker than positive contrasts.'' Three positive-contrast clouds in Figure 8 have greater luminance than their respective background hexagons; the three negative-contrast clouds have less luminance than their background.

According to the Whittle calculation, ''darker grays are achievable with a more-luminous background.''<ref name="Fifty"/> The effect is more pronounced for larger subtenses, but can be seen in the lower left of Figure 7 where more-negative nEPD is achieved when the background luminance is greater. Figure 9 exemplifies the effect; the same hexagonal visual target is seen as a darker gray (including black) when its background is more luminous, according to the Whittle calculation.

==Ongoing research and development==
Research and development continues on data visualization technologies. For instance, there is ongoing research and development to improve color difference calculations.<ref name="CAM16"/> The primary motivation for this R&D is determination of minimum detectable thresholds of color difference, for quality control over industrial color processes (e.g., food, paint, textiles, plastics, print and self-luminous displays). As color difference calculations have been improved for threshold determination, they fortuitously have become better for the suprathreshold applications related to data visualization.<ref name="Twelve" /> Ever since the relationship in Figure 3 was first shown,<ref name="Eleven"/> there has been practical interest in more-precise determination of the (calculated color-difference) location of the knee of the curve for two-degree visual subtense and for smaller subtenses.<ref name="Thirteen"/> A general societal concern for inclusiveness, and particularly for accommodating disabilities, has stimulated research on color applications for people with color deficient vision.<ref name=":45"/> A vibrant area of research (for instance by [[Brian Wandell]] and David Brainard,<ref>{{cite journal |last1=Cottaris |first1=NP |last2=Jiang |first2=H |last3=Ding |first3=X |last4=Wandell |first4=BA |last5=Brainard |first5=DH |display-authors=3|title=A computational observer model of spatial contrast sensitivity: Effects of wave-front based optics, cone mosaic structure and inference engine |journal=Journal of Vision |date=2019 |volume=19 |issue=4 |pages=8|doi=10.1167/19.4.8 |pmid=30943530 |doi-access=free }}</ref> and CIE<ref name="CAM16">{{cite journal |last1=Li |first1=Changjun |last2=Li |first2=Zhiqiang |last3=Wang |first3=Zhifeng |last4=Yang |first4=Xu |last5=Luo |first5=Ming Ronnier |last6=Cui |first6=Guihua |last7=Melgosa |first7=Manuel |last8=Brill |first8=Michael H |last9=Pointer |first9=Michael |display-authors=3|title=Comprehensive color solutions: CAM16, CAT16, and CAM16‐UCS |journal=Color Research and Application |date=2017 |volume=42 |issue=6 |pages=703–718 |doi=10.1002/col.22131}}</ref>) is computational modelling to predict (e.g., color) appearance, including all factors such as intraocular optics, retinal cone-cell responses, effects of visual subtense, eccentricity from the line of sight,<ref>{{cite book |title=Colour Appearance in Peripheral Vision, CIE 211:2014 |date=2014 |publisher=International Commission on Illumination |location=Vienna |isbn=978-3-902842-47-3}}</ref> atmospheric optics, the illuminating light spectrum, context and color adaptation. There is research of methods to calibrate displays,<ref>{{cite journal |last1=Karatzas |first1=D |last2=Wuerger |first2=S |title=A hardware-independent color calibration technique |journal=Annals of the BMVA |date=2007 |volume=2007 |issue=3 |pages=1–11 |url=https://www.academia.edu/2736877}}</ref> for example to make colors salient on a display located remote from the person programming the data visualization, and to more-accurately render color on displays.<ref>{{cite journal |last1=Hao |first1=Xie |last2=Farnand |first2=SP |last3=Murdoch |first3=MJ |title=Observer metamerism in commercial displays |journal=Journal of the Optical Society of America A |date=2020 |volume=37 |issue=4 |pages=A61–A69|doi=10.1364/JOSAA.382228 |pmid=32400517 |bibcode=2020JOSAA..37A..61X |s2cid=212763244 }}</ref> High dynamic range (HDR) displays enable the most-salient colors for visualization; HDR is an active area of research.<ref>{{cite journal |last1=Hexley |first1=Allie C |last2=Ozgur Yontem |first2=Ali |last3=Spitschan |first3=Manuel |last4=Smithson |first4=Hannah E |last5=Mantiuk |first5=Rafal |display-authors=3|title=Demonstrating a multi-primary high dynamic range display system for vision experiments |journal=JOSA A |date=2020 |volume=37 |issue=4 |pages=A271–A284 |doi=10.1364/JOSAA.384022|pmid=32273669 |pmc=7145446 |bibcode=2020JOSAA..37A.271H |s2cid=215719955 }}</ref> Research continues on visual pathways and circuits in the brain;<ref name="Furman"/> some of this is relevant to data visualization and comprehension. Proprietary developments of color-display technology, computers and software improve data visualization, too. There is research to apply artistic color-coding techniques to visualization "to enable nonscientists to work with actual data to communicate issues that are critical to humanity."<ref>{{cite journal |last1=Frederick |first1=Robert |title=A More Universal Language |journal=American Scientist |date=2020 |volume=108 |issue=5 |page=272|doi=10.1511/2020.108.5.272 |s2cid=226741374 }}</ref>

==See also==
*[[False color]]
*[[Impossible color]]
*[[Map coloring]]

==References==
{{reflist}}

[[Category:Color codes]]
[[Category:Electrical components]]
[[Category:Electrical engineering]]