Colormap optimization with data equality


Colormap is a visualization tool to realize the mapping from data to colors. The data patterns can be revealed by color distribution, and the data details can be explored by the mapping. Most colormaps use a linear mapping between data and colors. When the data are unevenly distributed, most data samples are encoded in very few colors, so that the patterns hidden in these huge amount of data samples encoded by very small range of colors cannot be explored. Every data sample is equally important, it should map to the exclusive color in the colormap. Inspired by force-directed model-based node layout in network visualization, we propose a novel colormap optimization algorithm with data equality, called spring model-based colormap. It formulates the proposed proportionality rule and data ink rule by a dynamically balanced spring system. The proportionality rule is that the color perception difference is proportional to the values of data samples for better identification of data values. The data ink rule lets the spring system make colors associated with data samples as separate as possible in the color space for better data distribution reveal. To accelerate the colormap generation, a fast solution for the colormap optimization algorithm is proposed. The effectiveness of our method is evaluated by eye tracking experiments. The results show that the fixations on both our colormap and the encoded visualization are more dispersed, which indicates that our method is better at both data distribution reveal and identification of data values.

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  1. Bernard J, Steiger M, Mittelstadt S, Thum S, Keim D, Kohlhammer J (2015) A survey and task-based quality assessment of static 2D colormaps. Vis Data Anal 9397:247–262

    Google Scholar 

  2. Borland D, Taylor M (2007) Rainbow color map (still) considered harmful. IEEE Comput Graph Appl 27(2):14–17

    Article  Google Scholar 

  3. Burch M, Chuang L, Fisher B, Schmidt A, Weiskopf D (2017) Eye tracking and visualization: foundations, techniques, and applications. Springer, Berlin

    Google Scholar 

  4. Chuang J, Weiskopf D, Möller T (2009) Energy aware color sets. Comput Graph Forum 28:203–211

    Article  Google Scholar 

  5. Cleveland WS (2012) Graphical methods for data presentation: full scale breaks, dot charts, and multibased logging. IEEE Trans Vis Comput Graph 38(4):270–280

    Google Scholar 

  6. Duchowski AT, Price MM, Meyer M, Orero P (2012) Aggregate gaze visualization with real-time heatmaps. In: Proceedings of the Symposium on Eye Tracking Research and Applications, pp 13–20

  7. Eades P (1984) A heuristic for graph drawing. Congr Numer 42:149–160

    MathSciNet  Google Scholar 

  8. Eisemann M, Albuquerque G, Magnor M (2011) Data driven color mapping. In: International Workshop on Visual Analytics

  9. Gramazio CC, Laidlaw DH, Schloss KB (2017) Colorgorical: creating discriminable and preferable color palettes for information visualization. IEEE Trans Vis Comput Graph 23(1):521–530

    Article  Google Scholar 

  10. Harrower M, Brewer CA (2003) an online tool for selecting colour schemes for maps. Cartogr J 40(1):27–37

    Article  Google Scholar 

  11. Kamada T, Kawai S (1989) An algorithm for drawing general undirected graphs. Inf Process Lett 31(1):7–15

    MathSciNet  Article  Google Scholar 

  12. Khosravan N, Celik H, Turkbey B, Jones EC, Wood B, Bagci U (2018) A collaborative computer aided diagnosis (c-cad) system with eye-tracking, sparse attentional model, and deep learning. Med Image Anal 51:101–115

    Article  Google Scholar 

  13. Kindlmann G, Durkin JW (1998) Semi-automatic generation of transfer functions for direct volume rendering. In: IEEE Symposium on Volume Visualization, pp 79–86

  14. Kovesi P (2015) Good colour maps: How to design them. arXiv:150903700

  15. Lee S, Sips M, Seidel HP (2013) Perceptually-driven visibility optimization for categorical data visualization. IEEE Trans Vis comput Graph 10(10):1746–1757

    Article  Google Scholar 

  16. Lin S, Fortuna J, Kulkarni C, Stone M, Heer J (2013) Selecting semantically-resonant colors for data visualization. Comput Graph Forum 32(3):401–410

    Article  Google Scholar 

  17. Liu Y, Heer J (2018) Somewhere over the rainbow: An empirical assessment of quantitative colormaps. In: CHI Conference on Human Factors in Computing Systems

  18. Machado GM, Oliveira MM, Fernandes LAF (2009) A physiologically-based model for simulation of color vision deficiency. IEEE Trans Vis Comput Graph 15(6):1291–1298

    Article  Google Scholar 

  19. Mandy Ryan NK, Hermens F (2018) The eyes have it: using eye tracking to inform information processing strategies in multi-attributes choices. Health Econ 27:709–721

    Article  Google Scholar 

  20. Mittelstadt S, Jackle D, Stoffel F, Keim DA (2015) ColorCAT: Guided Design of Colormaps for Combined Analysis Tasks. In: Eurographics Conference on Visualization, pp 115–119

  21. NASA (2020) Nasa giss.

  22. NOAA (2020) All gridded datasets: Noaa phisical sciences laboratory.

  23. Obaidellah U, Al Haek M, Cheng CH (2018) A survey on the usage of eye-tracking in computer programming. Acm Comput Surv 51(1):1–58

    Article  Google Scholar 

  24. Pizer SM, Zimmerman JB (1983) Color display in ultrasonography. Ultrasound Med Biol 9(4):331–345

    Article  Google Scholar 

  25. Rayner K (1998) Eye movements in reading and information processing: 20 years of research. Psychol Bull 124:372–422

    Article  Google Scholar 

  26. Rowe LA, Davis M, Messinger E, Meyer C, Spirakis C, Tuan A (1986) A browser for directed graphs. Tech. rep., EECS Department, University of California, Berkeley,

  27. Schulze-Wollgast P, Tominski C, Schumann H (2005) Enhancing visual exploration by appropriate color coding. pp 203–210

  28. Tominski C, Fuchs G, Schumann H (2008) Task-driven color coding. In: International Conference Information Visualisation, pp 373–380

  29. Treinish L (1995) A rule-based tool for assisting colormap selection. In: IEEE Conference on Visualization

  30. Trumbo BE (1981) A theory for coloring bivariate statistical maps. Am Stat 35(4):220–226

    Google Scholar 

  31. Tufte ER (2001) The visual display of quantitative information. Graphics Press, Cheshire

    Google Scholar 

  32. Wang L, Mueller K (2008) Harmonic colormaps for volume visualization. In: Volume Graphics, pp 33–39

  33. Ware C, Turton TL, Bujack R, Samsel F, Shrivastava P, Rogers DH (2019) Measuring and modeling the feature detection threshold functions of colormaps. IEEE Trans Vis Comput Graph 25(9):2777–2790

    Article  Google Scholar 

  34. Zeng Q, Wang Y, Zhang J, Zhang W, Tu C, Viola I, Wang Y (2019) Data-driven colormap optimization for 2d scalar field visualization. In: IEEE Visualization Conference, pp 266–270

  35. Zhou L, Hansen CD (2016) A survey of colormaps in visualization. IEEE Trans Vis Comput Graph 22(8):2051–2069

    Article  Google Scholar 

  36. Zhou L, Rivinius M, Johnson CR, Weiskopf D (2020) hotographic high-dynamic-range scalar visualization. IEEE Trans Vis Comput Graph 26(6):2156–2167

    Article  Google Scholar 

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This work was supported by National Key R&D Program of China (2018YFB0704301), Fundamental Research Funds for the Central Universities (FRF-TP-18-007A3, FRF-BR-19-001B), Interdisciplinary Research Project for Young Teachers of USTB (Fundamental Research Funds for the Central Universities) (FRF-IDRY-19-030).

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Correspondence to Jingyan Qin.

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Wang, X., Yin, J., Cheng, B. et al. Colormap optimization with data equality. J Vis (2020).

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  • Colormap
  • Spring model
  • Data equality
  • Data distribution