Analysis of Palette Colors

library(peRsian)
library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union

While there is always a qualitative aspect to choosing colors for data visualizations, it’s also possible to quantitatively assess how distinguishable the colors within a palette are.

We can use the colorblindcheck package to evaluate how distinguishable the colors in each palette are, both under normal vision and various forms of colorblindness, which is particularly important for ensuring accessibility in visualizations.

`peRsian` Palettes

Let’s start by listing all available palettes in the peRsian package.

names(persian_palettes)
#>  [1] "fery"     "tehran"   "hamburg"  "isfahan"  "munich"   "leyli"   
#>  [7] "tabriz"   "abbas"    "reyhaneh" "berlin"   "pooran"   "hooshang"
#> [13] "floral"

Next, we can have a look at an evaluation of each palette using colorblindcheck.

# Generate a subjeading and evaluation for each palette
for(palette_name in names(persian_palettes)) {
  cat("\n\n### ", palette_name, "\n\n")
  
  colors <- persian_palette(palette_name)
  check_results <- colorblindcheck::palette_check(colors, plot = TRUE)
  
  check_results |>
    knitr::kable(digits = 2) |>
    print()
}

fery

name	n	tolerance	ncp	ndcp	min_dist	mean_dist	max_dist
normal	8	15.32	28	28	15.32	44.03	81.71
deuteranopia	8	15.32	28	26	6.20	43.21	82.91
protanopia	8	15.32	28	26	11.93	41.82	78.92
tritanopia	8	15.32	28	25	11.68	44.40	77.83

tehran

name	n	tolerance	ncp	ndcp	min_dist	mean_dist	max_dist
normal	8	14.66	28	28	14.66	37.53	71.85
deuteranopia	8	14.66	28	22	2.36	28.37	60.75
protanopia	8	14.66	28	21	1.59	27.80	69.35
tritanopia	8	14.66	28	28	15.56	38.95	71.06

hamburg

name	n	tolerance	ncp	ndcp	min_dist	mean_dist	max_dist
normal	8	10.07	28	28	10.07	45.91	81.62
deuteranopia	8	10.07	28	25	3.48	38.97	82.43
protanopia	8	10.07	28	26	5.30	38.37	78.94
tritanopia	8	10.07	28	27	8.17	38.28	74.83

isfahan

name	n	tolerance	ncp	ndcp	min_dist	mean_dist	max_dist
normal	6	17.68	15	15	17.68	35.81	59.96
deuteranopia	6	17.68	15	12	6.26	31.66	53.51
protanopia	6	17.68	15	12	8.04	31.54	54.06
tritanopia	6	17.68	15	13	8.42	35.05	60.43

munich

name	n	tolerance	ncp	ndcp	min_dist	mean_dist	max_dist
normal	7	16.62	21	21	16.62	40.90	93.83
deuteranopia	7	16.62	21	18	12.14	36.13	94.46
protanopia	7	16.62	21	20	9.80	36.08	92.87
tritanopia	7	16.62	21	21	17.31	40.04	91.23

leyli

name	n	tolerance	ncp	ndcp	min_dist	mean_dist	max_dist
normal	9	13.12	36	36	13.12	28.14	49.33
deuteranopia	9	13.12	36	29	3.68	23.71	51.18
protanopia	9	13.12	36	29	5.58	22.47	48.22
tritanopia	9	13.12	36	29	5.71	26.88	55.62

tabriz

name	n	tolerance	ncp	ndcp	min_dist	mean_dist	max_dist
normal	6	11.76	15	15	11.76	27.51	42.58
deuteranopia	6	11.76	15	14	6.20	24.18	40.79
protanopia	6	11.76	15	14	3.92	23.26	41.99
tritanopia	6	11.76	15	14	7.73	27.65	43.73

abbas

name	n	tolerance	ncp	ndcp	min_dist	mean_dist	max_dist
normal	5	13.89	10	10	13.89	30.28	66.85
deuteranopia	5	13.89	10	9	12.26	30.30	67.68
protanopia	5	13.89	10	9	12.69	29.44	65.37
tritanopia	5	13.89	10	10	15.66	30.42	67.36

reyhaneh

name	n	tolerance	ncp	ndcp	min_dist	mean_dist	max_dist
normal	4	10.92	6	6	10.92	22.66	33.38
deuteranopia	4	10.92	6	4	2.83	19.44	30.52
protanopia	4	10.92	6	5	5.63	17.50	30.00
tritanopia	4	10.92	6	4	6.85	18.31	26.09

berlin

name	n	tolerance	ncp	ndcp	min_dist	mean_dist	max_dist
normal	8	10.24	28	28	10.24	32.75	51.84
deuteranopia	8	10.24	28	26	6.27	26.29	54.16
protanopia	8	10.24	28	26	8.72	25.71	48.48
tritanopia	8	10.24	28	25	8.07	33.11	56.35

pooran

name	n	tolerance	ncp	ndcp	min_dist	mean_dist	max_dist
normal	6	14.38	15	15	14.38	35.29	54.31
deuteranopia	6	14.38	15	14	12.71	30.26	57.05
protanopia	6	14.38	15	13	11.63	28.50	51.68
tritanopia	6	14.38	15	14	11.93	36.11	66.67

hooshang

name	n	tolerance	ncp	ndcp	min_dist	mean_dist	max_dist
normal	4	17.24	6	6	17.24	33.19	48.85
deuteranopia	4	17.24	6	5	12.70	31.95	52.02
protanopia	4	17.24	6	5	15.49	30.77	48.10
tritanopia	4	17.24	6	5	10.31	35.05	50.88

floral

name	n	tolerance	ncp	ndcp	min_dist	mean_dist	max_dist
normal	5	10.7	10	10	10.70	22.99	31.90
deuteranopia	5	10.7	10	9	3.81	18.65	32.22
protanopia	5	10.7	10	8	5.28	16.21	29.82
tritanopia	5	10.7	10	9	8.60	25.33	38.66

Quantitative Comparison

With the scores produced by colorblindcheck, we can now perform a proper quantitative analysis to check which palettes meet certain thresholds and which might need adjustments.

Colorblind-Safety

Let’s compare peRsian with the popular viridis palette, which has specifically been designed to handle colorblindness well, to put its the color difference scores into perspective.

# Helper function to conveniently calculate scores and assign a palette name
calculate_palette_scores <- function(colors, palette_name, ...) {
  check_results <- colorblindcheck::palette_check(colors, ...)
  cbind(
    data.frame(palette = palette_name),
    check_results
  )
}

First, we calculate the scores for viridis.

viridis_scores_df <- calculate_palette_scores(
  viridisLite::viridis(8),
  "viridis",
  plot = TRUE
)

viridis_scores_df |>
  knitr::kable(digits = 2)

palette	name	n	tolerance	ncp	ndcp	min_dist	mean_dist	max_dist
viridis	normal	8	12.45	28	28	12.45	46.62	100.32
viridis	deuteranopia	8	12.45	28	24	8.43	39.97	90.16
viridis	protanopia	8	12.45	28	25	5.34	41.44	93.43
viridis	tritanopia	8	12.45	28	25	8.01	38.42	76.80

Let’s use the smallest difference in viridis as the threshold to identify which palettes in peRsian we deem “colorblind-safe”.

viridis_min_score <- min(viridis_scores_df$min_dist)
viridis_min_score
#> [1] 5.339964

# Create a dataframe with scores for all palettes in the package
persian_scores_df <- do.call(rbind, lapply(names(persian_palettes), function(palette_name) {
  calculate_palette_scores(
    persian_palette(palette_name),
    palette_name,
    tolerance = viridis_min_score
  )
}))

Now we can use this information to only mark palettes as colorblind-safe, where the smallest difference is above the threshold across ALL different forms of visual perception.

# Keep only palettes where all entries are above threshold
palettes_above_threshold <- persian_scores_df |>
  group_by(palette) |> 
  # Number of comparisons == Number of comparisons above threshold
  filter(all(ncp == ndcp))

colorblind_safe_palettes <- palettes_above_threshold$palette |>
  unique()

colorblind_safe_palettes
#> [1] "fery"     "isfahan"  "munich"   "abbas"    "berlin"   "pooran"   "hooshang"

Let’s also collect the names of all palettes that didn’t make it (use these with caution!).

non_colorblind_safe_palettes <- names(persian_palettes)[!names(persian_palettes) %in% palettes_above_threshold$palette]

non_colorblind_safe_palettes
#> [1] "tehran"   "hamburg"  "leyli"    "tabriz"   "reyhaneh" "floral"

Ordering Palettes

Finally, we can order all palettes by their minimum color difference (under full vision) to get a better overview of which ones are most distinguishable and which ones may need more work.

persian_scores_df |>
  filter(name == "normal") |>
  arrange(desc(min_dist))
#>     palette   name n tolerance ncp ndcp min_dist mean_dist max_dist
#> 1   isfahan normal 6  5.339964  15   15 17.68255  35.80945 59.96357
#> 2  hooshang normal 4  5.339964   6    6 17.24044  33.19147 48.85390
#> 3    munich normal 7  5.339964  21   21 16.62231  40.89513 93.82743
#> 4      fery normal 8  5.339964  28   28 15.31689  44.03096 81.71196
#> 5    tehran normal 8  5.339964  28   28 14.66018  37.52704 71.85012
#> 6    pooran normal 6  5.339964  15   15 14.38322  35.29478 54.31265
#> 7     abbas normal 5  5.339964  10   10 13.88681  30.27786 66.84959
#> 8     leyli normal 9  5.339964  36   36 13.12127  28.13639 49.32902
#> 9    tabriz normal 6  5.339964  15   15 11.75663  27.51236 42.57928
#> 10 reyhaneh normal 4  5.339964   6    6 10.92315  22.65976 33.38325
#> 11   floral normal 5  5.339964  10   10 10.69823  22.98735 31.90445
#> 12   berlin normal 8  5.339964  28   28 10.24284  32.74987 51.84005
#> 13  hamburg normal 8  5.339964  28   28 10.06714  45.90776 81.61558

Palettes which may need adjustments:

persian_scores_df |>
  filter(name == "normal") |>
  arrange(min_dist)
#>     palette   name n tolerance ncp ndcp min_dist mean_dist max_dist
#> 1   hamburg normal 8  5.339964  28   28 10.06714  45.90776 81.61558
#> 2    berlin normal 8  5.339964  28   28 10.24284  32.74987 51.84005
#> 3    floral normal 5  5.339964  10   10 10.69823  22.98735 31.90445
#> 4  reyhaneh normal 4  5.339964   6    6 10.92315  22.65976 33.38325
#> 5    tabriz normal 6  5.339964  15   15 11.75663  27.51236 42.57928
#> 6     leyli normal 9  5.339964  36   36 13.12127  28.13639 49.32902
#> 7     abbas normal 5  5.339964  10   10 13.88681  30.27786 66.84959
#> 8    pooran normal 6  5.339964  15   15 14.38322  35.29478 54.31265
#> 9    tehran normal 8  5.339964  28   28 14.66018  37.52704 71.85012
#> 10     fery normal 8  5.339964  28   28 15.31689  44.03096 81.71196
#> 11   munich normal 7  5.339964  21   21 16.62231  40.89513 93.82743
#> 12 hooshang normal 4  5.339964   6    6 17.24044  33.19147 48.85390
#> 13  isfahan normal 6  5.339964  15   15 17.68255  35.80945 59.96357

- peRsian Palettes
- Quantitative Comparison