# the image histogram (ii) – grayscale vs colour

In terms of image processing there are two basic types of histogram: (i) colour, and (ii) intensity (or luminance/grayscale) histograms. Figure 1 shows a colour image (an aerial shot of Montreal), and its associated RGB and intensity histograms. Colour histograms are essentially RGB histograms, typically represented by three separate histograms, one for each of the components – Red, Green, and Blue. The three R,G,B histograms are sometimes shown in one mixed histogram with all three R,G,B, components overlaid with one another (sometimes including an intensity histogram).

Both RGB and intensity histograms contain the same basic information – the distribution of values. The difference lies in what the values represent. In an intensity histogram, the values represent the intensity values in a grayscale image (typically 0 to 255). In an RGB histogram, divided into individual R, G, B histograms, each colour channel is just a graph of the frequencies of each of the RGB component values of each pixel.

An example is shown in Figure 2. Here a single pixel is extracted from an image. The RGB triplet for the pixel is (230,154,182) i.e. it has a red value of 230, a green value of 154, and a blue value of 182. Each value is counted in its respective bin in the associated component histogram. So red value 230 is counted in the bin marked as “230” in the red histogram. The three R,G, B histograms are visually no different than an intensity histogram. The individual R, G, and B histograms do not represent distributions of colours, but merely distributions of components – for that you need a 3D histogram (see bottom).

Applications portray colour histograms in many different forms. Figure 3 shows the RGB histograms from three differing applications: Apple Photos, ImageJ, and ImageMagick. Apple Photos provides the user with the option of showing the luminance histogram, the mixed RGB, or the individual R, G, B histograms. The combined histogram shows all the overlaid R, G, B histograms, and a gray region showing where all three overlap. ImageJ shows the three components in separate histograms, and ImageMagick provides an option for their combined or separate. Note that some histograms (ImageMagick) seem a little “compressed”, because of the chosen x-scale.

One thing you may notice when comparing intensity and RGB histograms is that the intensity histogram is very similar to the green channel or the RGB image (see Figure 4). The human eye is more sensitive to green light than red or blue light. Typically the green intensity levels within an image are most representative of the brightness distribution of the colour image.

An intensity image is normally created from an RGB image by converting each pixel so that it represents a value based on a weighted average of the three colours at that pixel. This weighting assumes that green represents 59% of the perceived intensity, while the red and blue channels account for just 30% and 11%, respectively. Here is the actual formula used:

`gray = 0.299R + 0.587G + 0.114B`

Once you have a grayscale image, it can be used to derive an intensity histogram. Figure 5 illustrates how a grayscale image is created from an RGB image using this formula.

Honestly there isn’t really that much useful data in RGB histograms, although they seem to be very common in image manipulation applications, and digital cameras. The problem lies with the notion of the RGB colour space. It is a space in which chrominance and luminance are coupled together, and as such it is difficult to manipulate any one of the channels without causing shifts in colour. Typically, applications that allow manipulation of the histogram do so by first converting the image to a decoupled colour space such as HSB (Hue-Saturation-Brightness), where the brightness can be manipulated independently of the colour information.

A Note on 3D RGB: Although it would be somewhat useful, there are very few applications that provide a 3D histogram, constructed from the R, G, and B information. One reason is that these 3D matrices could be very sparse. Instead of three 2D histograms, each with 256 pieces of information, there is now a 3D histogram with 2563 or 16,777,216 pieces of information. The other reason is that 3D histograms are hard to visualize.