How to get the size of a pixel cluster in R

For this kind of image analysis, you can check out EBImage:

install.packages("BiocManager")
BiocManager::install("EBImage")

Your workflow might look like this. First, load the package and read in the image. We'll also show it to show we're on the right track:

library(EBImage)
library(ggplot2)

dots <- readImage("https://i.stack.imgur.com/3RU7u.png")
display(dots, method = "raster")

Now we can use the computeFeaturesfunctions to get the centroid and maximum diameter of each cluster:

dots_bw <- getFrame(dots, 1)
labelled_dots <- bwlabel(dots_bw)
df <- as.data.frame(cbind(computeFeatures.moment(labelled_dots)[, 1:2],
                          computeFeatures.shape(labelled_dots)[, 5:6]))
df
#>        m.cx      m.cy s.radius.min s.radius.max
#> 1  65.73316  25.69588    11.095535     40.69698
#> 2 156.24181 129.77241    19.377341     33.83485
#> 3 483.60853 155.23006     9.419478     16.28808
#> 4 277.21467 409.62152    20.411710     28.77508
#> 5 397.36817 607.47749     8.424518     18.53617
#> 6 224.93790 623.28266     8.530353     15.26678

Now, we want to find out which dimension matches which blob, so let's draw a raster in ggplot and write the maximum pixel dimension above each blob.

img_df <- reshape2::melt(as.matrix(as.raster(as.array(dots))))

ggplot(img_df, aes(Var1, Var2, fill = value)) + 
  geom_raster() +
  scale_fill_identity() +
  scale_y_reverse() +
  geom_text(inherit.aes = FALSE, data = df, color = "white",
            aes(x = m.cx, y = m.cy, label = round(s.radius.max, 1))) +
  coord_equal()

If you want the total number of pixels instead of the maximum diameter (in pixels), you can also start withcomputeFeatures