Finding Height Using Color Spectrum

I have an image, where the colors correspond to height. Please refer to below image. On the colormap spectrum: Blue is -500 meters Red is +500 meters

1) I want to Make plot for the height along Line 1

2) Make plot for the height along Line 2

3). Create a 2D array for the height values for the image. Basically, for every pixel position, give a corresponding height value. For simplicity, you can assume the grey pixels have a value of -1000 m.

Your help will be much appreciated.

Thanks in advance.

[Walter Roberson]

That is homework and you have not shown any effort.

There is not enough information to solve the problem. Giving two color endpoints does not tell you how height varies with color.

[Walter Roberson]

Are we to assume that depth is linear with difference in hue? https://www.researchgate.net/figure/a-RGB-b-HSV-color-space_fig2_335470954

[Adnan Khan]

I have tried things but it didn't work. I segmented the foreground and background, and tried to measure the end points, I also tried to use color thresholder app of matlab. But I don't have clear direction on how to apply my efforts to tackle this problem.

[Adnan Khan]

If there is not enugh information, then what assumptions do we need to solve it? What information/parameters do we need in addition to the ones specified in probelm statement?

[Walter Roberson]

If we were permitted to assume that depth is linear in angle of difference of hue, then convert to hsv, and find the hue channel difference compared to pure blue and do linear interpolation.

[Adnan Khan]

Thank you, I will try this.

[Adnan Khan]

In the third step, after finding the hue channel, you want me to subtract it from pure blue?

[Walter Roberson]

Hue is an angle. Pure red is 0. If you head one direction around the circle then blue is 120 degrees away. If you head the other direction around the circle then 120 degrees is green and blue is 240 degrees. You need to study the diagram I linked to and experiment with rgb2hsv to figure out which direction you need to travel and what values rgb2hsv uses to represent the angles.

[Adnan Khan]

Sir I studied that. What I observed is that after going to hsv scheme we have values in the range 0 to 1. I am not quite sure if I am correct but 0 corresponds to angle 0 and 140 degrees in the blue direction corresponds to a fraction 140/360 = 0.3888. You may like to see what I have tried up until now.

Original Image

Converted to HSV

Now since the problem statement says that color corresponds to height, here in hsv the whole circle is of same color 'Cyan'. In hsv its angle is 180 degrees between the green and blue. In response to your comment, I would say I need to travel 180 degrees to reach this color (Not sure I may be wrong). But how do I find height out of it Sir?

[Walter Roberson]

timg = permute([1 0 0; 0 0 1], [3 1 2])

timg = 
timg(:,:,1) =

     1     0


timg(:,:,2) =

     0     0


timg(:,:,3) =

     0     1

image(timg)

thsv = rgb2hsv(timg)

thsv = 
thsv(:,:,1) =

         0    0.6667


thsv(:,:,2) =

     1     1


thsv(:,:,3) =

     1     1

thue = thsv(:,:,1)

thue = 1×2

0 0.6667

Pure red has a hue of 0. Pure blue has a hue of 2/3.

Pure red corresponds to a height of +500 meters. Pure blue corresponds to a height of -500 meters.

A*0 + B = 500

A*2/3 + B = -500

Subtract. 2*A/3 + (B-B) = -500 - 500 --> 2*A/3 = -1000 --> 2*A = -3000 -> A = -3000/2 --> A = -1500.

You should be able to work out B easily from this, and from that you should easily be able to calculate the formula that maps hue to height in your system.

Remember, Hue is the first pane of an HSV image, not all of the panes.

[Adnan Khan]

Thanks sir for your kind help.

[Adnan Khan]

Accept answer tab is not appearing here. I want to accept the procedure you told because it worked. Thanks once again.

Answer 1

[Walter Roberson]

(Moving down from comments)

timg = permute([1 0 0; 0 0 1], [3 1 2])

timg = 
timg(:,:,1) =

     1     0


timg(:,:,2) =

     0     0


timg(:,:,3) =

     0     1

image(timg)

thsv = rgb2hsv(timg)

thsv = 
thsv(:,:,1) =

         0    0.6667


thsv(:,:,2) =

     1     1


thsv(:,:,3) =

     1     1

thue = thsv(:,:,1)

thue = 1×2

0 0.6667

Pure red has a hue of 0. Pure blue has a hue of 2/3.

Pure red corresponds to a height of +500 meters. Pure blue corresponds to a height of -500 meters.

A*0 + B = 500

A*2/3 + B = -500

Subtract. 2*A/3 + (B-B) = -500 - 500 --> 2*A/3 = -1000 --> 2*A = -3000 -> A = -3000/2 --> A = -1500.

You should be able to work out B easily from this, and from that you should easily be able to calculate the formula that maps hue to height in your system.

Remember, Hue is the first pane of an HSV image, not all of the panes.