To categorize jet colormap by pixels of some color

Data

I want to categorize it by counting the following pixels through HSV (Hue-Saturation-Lightness)

dark blue
blue
green
yellow
red

To show RGB channels (source) without HSV

x = linspace(0,1, size(Map)(1));
  figure(Fignr) 
  lw = 4; 
  plot( x, Map(:,1),'color',[1,0,0],'linewidth',lw,
        x, Map(:,2),'color',[0,1,0],'linewidth',lw, 
        x, Map(:,3),'color',[0,0,1],'linewidth',lw,
        x, mean(Map,2),'color',[0.7,0.7,0.7],'o') 
  xlabel 'fraction' 
  ylabel 'intensity' 
end

where example showRGBchannels(1,summer(500)) gives

This is just an example about one mapping where you can see fractions of different colors Red, Green and Blue about one figure. However, the color map must be extended to colors yellow, green and dark blue too.

You can assume that

dark blue has value [0, 0.2)
blue [0.2, 0.4)
green [0.4, 0.6)
yellow [0.6, 0.8)
red [0.8, 1.0)

However, I think this is not way to go, since HSV can a good choice here. I was also recommended to use other colors than Rainbow for the visualization (continuous red-blue, publication here).

There are many implementations to separate colors and argumentation about which color seem to use. Let's focus here on RGB colors and their separation. Possibly, through HSV or any other appropriate method not mentioned.

How can you categorize and count the appropriate pixels i.e. colours of the first picture through HSV? Any classes and/or papers for it?

Note Before reading. You seem to be confusing the choice of colormap with colour segmentation. It is important to note:

Colormap: used for user-friendly visualization. You don't use the colours of a colormap as data, you use the original data. However human eyes see more friendly a colour picture than a grayscale picture for example. Therefore there are different ways to visualize data with different choice of visualization colours. If your data is single valued (e.g. the figure you described represents z=f(x,y), then use the z for your data analysis, not the colour representation of the z).
Colour representation: In case you have some data that represents colours (i.e. a picture of a potato), then you can describe this data in different colour spaces, such as RGB, HSB, Cie Lab, ... This are ways of describing the same data, some useful for certain mathematicla calculations, some for other (i.e. HSV is good to segment colours while CIElab is designed to find colours that are similar for the human eye)

EDIT: ADDITIONAL DISCUSSION ABOUT USING COLORMAPS

As a student working in medical imaging, I can tell that for sure colours are NOT used for segmentation, but the numerical values of data (usually single channel) itself. The use of different colourmaps its only for visualization pourposes.

There are a wide range of opinions in here, but generally centred in: The jet colormap is not clear enough (and its the most widely used!). The Moreland colormaps for example, rely in having a clear midpoint in the visualization, so it is clear for the user to see which values are above the average and which below.

Even Matlab is starting to agree with the idea of stop using the jet colormap, as the default colormap of matlab is not any-more jet (R2014b). Read more here.

Another opinion is that the jet colormap does not translate good to gryscale. Read more here.

However, note that all this discussion has ABSOLUTELY nothing to do with how the colour is described. You can describe any of the colormaps discussed about in RGB, HSV, CIE Lab* or any other colour representation you'd want.

Original answer

So, rather than giving you code (that you can fin in SO also) I will just put an small example of how the HSV space work. As you have seen, in RGB, separating colours by their numerical values seems to be not possible. Therefore some other colour space is needed.

One of the most common approaches is to use the HSV space.

As you can see in the picture, this space has 3 values. Hue (the angle), Saturation and Value. Among the three of them, they create a cylindrical coordinate system, that points you to an specific color. From the figure, you can notice that while S and V change the "brightness" and "amount of colour" -like parameters, HUE is the only one that actually changes the chroma of the colour. So all Reds are in the same range of H, inddependently of the values of S and V.

See in the next figure a slice of this cylinder: