**IEEE Transactions on Visualization and Computer Graphics (Proceedings of InfoVis 2021)**

Min Lu^{1} Joel Lanir^{2} Chufeng Wang^{1} Yucong Yao^{1} Wen Zhang^{1} Oliver Deussen^{3} Hui Huang^{1*}

^{1}Shenzhen University ^{2}The University of Haifa ^{3}University of Konstanz

Fig. 1. Four charts of the same dataset, but with different pairs below the Just Noticeable Difference (JND) threshold. From left to right: a bar chart with no pairs below JND, the difference between all pairs of bars in the graph is noticeable; with a different order, there is a pair of bars below JND (A-B); two pairs of indistinguishable fans are detected in the pie chart (A-B and C-F); three pairs of circles are detected as not distinguishable in the bubble chart (A-B, C-F and D-E).

**Abstract**

One of the fundamental tasks in visualization is to compare two or more visual elements. However, it is often difficult to visually differentiate graphical elements encoding a small difference in value, such as the heights of similar bars in bar chart or angles of similar sections in pie chart. Perceptual laws can be used in order to model when and how we perceive this difference. In this work, we model the perception of Just Noticeable Differences (JNDs), the minimum difference in visual attributes that allow faithfully comparing similar elements, in charts. Specifically, we explore the relation between JNDs and two major visual variables: the intensity of visual elements and the distance between them, and study it in three charts: bar chart, pie chart and bubble chart. Through an empirical study, we identify main effects on JND for distance in bar charts, intensity in pie charts, and both distance and intensity in bubble charts. By fitting a linear mixed effects model, we model JND and find that JND grows as the exponential function of variables. We highlight several usage scenarios that make use of the JND modeling in which elements below the fitted JND are detected and enhanced with secondary visual cues for better discrimination.

Fig. 4. Distribution of JND according to the two independent variables: (left) in bar chart, a strong positive correlation can be observed between JND and the distance between bars, while a weak to non-existent correlation between JND and the height of bars; (middle) both distance and radius of circles show positive correlation with JND in bubble chart; (right) in pie chart, JND shows a strong correlation to the angles of fans to be compared, while weak correlation with angular distance.

Fig. 6. The coefficients and regression diagnostics of the linear models and log-linear models.

**Data & Code**

**Note that the DATA and CODE are free for Research and Education Use ONLY. **

**Please cite our paper (add the bibtex below) if you use any part of our ALGORITHM, CODE, DATA or RESULTS in any publication.**

**Link:** https://github.com/deardeer/JND-in-Charts

**Acknowledgements**

We sincerely thank Prof. Daniel Cohen-Or for his exceptional enthusiasm and knowledge that inspired this work, Prof. Ye Fei from Capital University of Economics and Business for his help in JND modeling. We also would like to celebrate the first year of Minâ€™s baby Rixin with this work. This work is supported in parts by NSFC (61802265, U2001206), GD Talent Program (2019JC05X328), DEGP Key Project (2018KZDXM058), Shenzhen Science and Technology Program (RCJC20200714114435012), Shenzhen Support Program (20200812122821001), DFG (422037984), National Engineering Laboratory for Big Data System Computing Technology, and Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ).

**Bibtex**

@article{JND21,

title={Modeling Just Noticeable Differences in Charts},

author={Min Lu and Joel Lanir and Chufeng Wang and Yucong Yao and Wen Zhang and Oliver Deussen and Hui Huang},

journal={IEEE Transactions on Visualization and Computer Graphics (Proceedings of InfoVis)},

volume={},

number={},

pages={},

year={2021},

}