Image histograms tell a story

The simplest data about an image it that contained within its histogram, or rather the distribution of pixel intensities. In an 8-bit grayscale image, this results in a 256-bin histogram which tells a story about how the pixels are distributed within the image. Most digital cameras also have some form of colour histogram which can be used to determine distribution of colours in an image.  This lets the photographer determine whether the photograph is over- under- or correctly exposed.  A correctly exposed photograph will have a fairly uniform histogram, whereas an under-exposed one has a bias towards darker tones, and an over-exposed one will have a bias towards brighter  tones.

This by no means means that a histogram that has two distinct modes does not represent a good image. As long as the histogram is well distributed between the lower and upper limits of the colour space. Consider the image below:

From an aesthetic perspective, this does not seem like a bad looking image. Its histogram somewhat collaborates this:

In fact there is limited scope for enhancement here. Application of  contrast-stretching or histogram equalization will increase its aesthetic appeal marginally. One of the properties of an image that a histogram helps identify is contrast, or dynamic range. On the other end of the spectrum, consider this image which has a narrow dynamic range.

The histogram clearly shows the lack of range in the image.

Stretching the histogram to either end of the spectrum increases the contrast of the image. The result is shown below.

It has a broader dynamic range, and a greater contrast of features within the image.

Colour versus grayscale pixels

Colour pixels are different from grayscale pixels. Colour pixels are RGB, meaning they have three pieces of information associated with them, namely the Red, Green and Blue components. Grayscale pixels have one component, a gray tone derived from a graduate scale from black to white. A colour pixel is generally 24-bit (3 × 8-bit), and a gray pixel is just 8-bit. This basically means that a colour pixel has a triplet value comprised of 0..255 for each of red, green and blue components, whereas a grayscale pixel has a single values 0..255. The figure below compares a colour and grayscale pixel. The colour pixel has the R-G-B value 61-80-136.The grayscale pixel has the value 92.

It is easy to convert a pixel from colour to grayscale (like applying a monochrome filter in a digital camera). The easiest method is simply averaging the three values of R, G, and B. In the sample above, the grayscale pixel is actually the converted RGB: (61+80+136)/3 = 92.

Now colour images also contain regions that are gray in colour – these are 24-bit “gray” pixels, as opposed to 8-bit grayscale pixels. The example below shows a pixel in a grayscale image, and the corresponding “gray” pixel in the colour image. Grayscale pixels are pure shades of gray. Pure shades of gray in colour images are often represented with RGB all having the same value, e.g. R=137, G=137, B=137.

Pure gray versus RGB gray

More on Mach bands

Consider the following photograph, taken on a drizzly day in Norway with a cloudy sky, and the mountains somewhat obscured by mist and clouds.

Now let’s look at the intensity image (the colour image has been converted to 8-bit monochrome):

If we look at a region near the top of the mountain, and extract a circular region, there are three distinct regions along a line. To the human eye, these appear as quite uniform regions, which transition along a crisp border. In the profile of a line through these regions though, there are two “cliffs” (Aand B) that marks the shift from one region to the next. Human eyes don’t perceive these “cliffs”.

The Mach bands is an illusion that suggests edges in an image where in fact the intensity is changing in a smooth manner.

The downside to Mach bands is that they are an artificial phenomena produced by the human visual system. As such, it might actually interfere with visual inspection to determine the sharpness contained in an image.