Rectangular ranges

If we wanted to define ranges for magenta pixels, we would look for pixels near the RGB value of [1, 0, 1]. To expand this range a little, we could define the following conditions:

• Red: 0.7 to 1.0
• Green: 0 to 0.3
• Blue: 0.7 to 1.0

Then we search for pixels whose colors satisfy all three conditions. In countcolors, you do this by specifying a lower and an upper set of RGB triplets:

This is why it’s referred to as a ‘rectangular’ range – it draws a box around a region of color space.

Spherical ranges

Sometimes, rather than boundaries, you want to specify a particular color and a search radius around that color. countcolors uses this to draw a sphere in color space centered around a single color, whose size depends on the radius. Say we’re looking at a mossy green color, with an RGB triplet of [0.4, 0.7, 0.4]. If we set the radius very small – say, 5% of maximum color distance – we only get a few pixels back:

But if we increase that radius to 25%, we get a much bigger search space and many more pixels back:

All countcolors does is search for pixels within a color range specified by the user, count them, and tell you how many there are and where they are in the image. It also comes with a couple of diagnostics to check that you’re picking the right color range.

1: Of course, there are many color spaces besides RGB, such as HSV (probably familiar), CMYK (maybe familiar), and CIELab (probably only familiar if you’ve worked with color spaces before, in which case you definitely don’t need my explanation). RGB is actually considered quite a poor representation of how human beings perceive color, but it works just fine for quantifying color proportions. A full discussion of color spaces is well beyond the scope of this introduction, but if you want to know more, I recommend Bruce Lindbloom’s website.

Finding the right color range

The success of any of the functions in countcolors relies on providing them with the right color range(s).To find the color range, there are a few things you can try, including:

1. Open the image in ImageJ, Preview, Photoshop, or another image viewer and finding the exact RGB triplets of a few pixels in the area of interest using a color picker.

2. Plot the pixels in color space to look for approximate natural boundaries, like above.

3. Use k-means clustering to find natural groupings of colors, together with exact centers².

That last one is obviously a little more complicated, but we can actually use colordistance to do it in one line:

# Find K-means clusters
kmeans.clusters <- colordistance::getKMeanColors("norway.jpg", n = 3, plotting = FALSE)
colordistance::extractClusters(kmeans.clusters)

To plot the clusters in an interactive plot, you can use colordistance::plotClusters, but for now we’ll just look at the clusters themselves. The green one is the third row: [0.34, 0.45, 0.24]. We’ll use that as our guideline and try a couple of different radii (for spherical ranges) and boundaries (for rectangular ranges). In countcolors, ranges are specified using RGB triplets, which are just vectors of length 3 assumed to be in R-G-B order.

center.spherical <- c(0.24, 0.45, 0.24) # Center color for spherical range

lower.rectangular <- c(0.2, 0.35, 0.2) # Lower limit for each of the three color channels
upper.rectangular <- c(0.3, 0.55, 0.3) # Upper limit for each of the three color channels

2: It’s tempting to just use the output of the k-means clustering, but this usually doesn’t work as well as you might think. Because of the way the algorithm works, it tends to either group colors together or artificially break them up into a large number of clusters. In this case, it works because the green, blue, and white are sufficiently far apart that pixels from one don’t get assigned to the other color’s cluster, but in more complicated images this is very common. K-means is better as a guideline.

Counting the pixels

Now that we have color ranges to try out, we can actually use the functions. The main function of countcolors is, unsurprisingly, countColors, which calls on the other functions of the package to do three things:

1. Find the locations of pixels within a target range or ranges;
2. Find the proportion of the image (optionally ignoring the background) covered by those pixels;
3. Provide a version of the image with those pixels masked out in order to check whether the function worked.

First, we’ll walk through what the function does step-by-step, using the functions that countColors actually calls on. Then we’ll see how use countColors to do all of that under the roof of one function.

# Read the image into the R environment
norway <- jpeg::readJPEG("norway.jpg")

# Find all the pixels within a 10% radius
norway.spherical <- countcolors::sphericalRange(norway, center = center.spherical, radius = 0.1, color.pixels = FALSE, plotting = FALSE); names(norway.spherical)

## [1] "pixel.idx"    "pixel.count"  "img.fraction" "original.img"

norway.spherical$img.fraction

## [1] 0.1372811

sphericalRange accepts a color center and a radius to define a color search space, and returns a list including row and column indices of the pixels within the range (pixel.idx), the number of pixels within that range (pixel.count), the fraction of the image covered by that amount (img.fraction), and the original RGB array.

Above, we started with a fairly conservative 10% radius around the color, which apparently covers about 13.7% of the image. It’s hard to tell if that’s the right proportion without seeing it, so the next step is to mask out the pixels within that range using changePixelColor to see if we missed anything:

countcolors::changePixelColor(norway, norway.spherical$pixel.idx, target.color="magenta")

We got most of the visible green, but we’re clearly missing an awful lot here. One option is to nudge the center color around, but first we’ll try increasing the radius. We’ll also set plotting = TRUE in the sphericalRange function, which calls on changePixelColor to generate the masked image:

# Find all the pixels within a 17% radius
norway.spherical <- countcolors::sphericalRange(norway, 
                    center = center.spherical, radius = 0.15, 
                    color.pixels = FALSE, plotting = TRUE, 
                    target.color = "magenta"); norway.spherical$img.fraction

## [1] 0.260676

That’s more like it! It looks like the green is masked out by magenta, but not the ocean, the clouds, or the mountaintops. Of course, the 15% radius was arrived at cooking-show style after I tested a few different radii that were too high or too low, and most images will require some experimentation.

Using a rectangular range is a very similar procedure:

# Trying with our original color ranges
norway.rectangular <- countcolors::rectangularRange(norway, 
                      upper = upper.rectangular, lower = lower.rectangular, 
                      target.color = "yellow")

# Trying with our cooking show values
norway.rectangular <- countcolors::rectangularRange(norway, 
                      upper = c(0.55, 0.75, 0.4), lower = c(0.1, 0.25, 0), 
                      target.color = "yellow"); norway.rectangular$img.fraction

## [1] 0.259773

The rectangular range gave us an area of 25.9%, while the spherical one was 26%; the values are very close, but understandably not identical, since we were looking at differently shaped regions of color space.

Using countColors

countColors calls on the above functions, but it also allows you to:

• Save the masked images instead of printing them to the plot window (faster),
• Ignore certain colors, such as if you masked out the background;
• Screen out multiple different colors

For example, if we also wanted to count the amount of white in the image, we could include both the green center and white center, specifying a radius for each:

# Using multiple colors
green.center <- c(0.24, 0.45, 0.24)
white.center <- c(1, 1, 1)

two.colors <- countcolors::countColors("norway.jpg", color.range="spherical", 
                                       center = c(green.center, white.center), radius = c(0.15, 0.1),
                                       bg.lower=NULL, bg.upper=NULL, plotting = TRUE,
                                       target.color=c("magenta", "cyan"))

## Using spherical range(s):

## Center: 0.24, 0.45, 0.24 +/- 15%

## Center: 1, 1, 1 +/- 10%

# Note that the fraction of all colors COMBINED is provided - to get them
# separately, call the function multiple times
two.colors$pixel.fraction

## [1] 0.2826229

Or let’s say we wanted to ignore the ocean, and just find the percentage of green on the land. This would require specifying a color (dark blue) to ignore when finding the image fraction. (Try masking out the ocean using these background parameters as upper and lower ranges to see convince yourself these are good values.)

# Using multiple colors
green.center <- c(0.24, 0.45, 0.24)
bg.upper <- c(0.2, 0.2, 0.45)
bg.lower <- c(0, 0, 0)

bg.ignore <- countcolors::countColors("norway.jpg", color.range="spherical", 
                                       center = green.center, radius = 0.15,
                                       bg.lower=bg.lower, bg.upper=bg.upper, plotting = TRUE)

## Using spherical range(s):

## Center: 0.24, 0.45, 0.24 +/- 15%

# Nearly 60%, as opposed to 26%, because we're no longer counting the water
bg.ignore$pixel.fraction

## [1] 0.5872671

Multiple images

If you have many images to analyze, the countColorsInDirectory function may be useful. It’s a wrapper for countColors that first searches for any JPEG or PNG images in a provided directory, and then applies the same parameters to each one. It returns a list of countColors lists.

Questions or feedback?

Email me: hannahiweller@gmail.com