Converting 3D vector to scalar output

We're recording RGB values from ImageJ, and each RGB value corresponds to a scalar pH. The ultimate goal is to input an RGB vector, and output the corresponding pH value based on the standardized data. How can we take a 3D vector and convert it to a scalar output? I assume I have to do some sort of PCA or regression model, but I'm not sure how to do that. I have uploaded the file with the RGB values that all correspond to specific pHs (Multiple RGB values can correspond to the same pH).

Answer 1

[Samson]

Do you know which pH value each RGB value corresponds to? If you do a lookup table should prove usefull.

Im reducing the total amount of colors to keep it short here... This is by no means the best way of implementing a lookup table, but it can get you started in thinking.

Say the RGB triplet [1,1,0] represents a pH of 8;

We create an array of all rgb triplets

RGB = [ 0 0 0 
        1 0 0 
        0 1 0 
        0 0 1
        1 1 0
        1 0 1
        0 1 1
        1 1 1];

We then define a vector of corresponding ph Values

pH = [1
      2 
      4
      7
      8
      9
      12];

We find the index in RGB that matches the RGB data from imageJ

imageJ = [1,1,0];

for i = 1:size(RGB,1)
    if imageJ == RGB(i,:);
        ind = i;
        break
    end
end

ResultingpH = pH(i)

ResultingpH = 8

Answer 2

[Benjamin Thompson]

You can export your data to CSV and import into MATLAB as a table. Then use this script to review it and get some insight. It is not following any nice pattern in the RGB coordinate space. But if all you want is a pH assignment to the nearest 0.5 value, then you could try calculating the centroid for each color group using the "mean" function. Then assign a pH value from the choices of {4.5, 5.0, ..., 7.5, 8.0} based on which centroid the RGB triplet is closest to.

The centroid is also where I plot the "text" value for each pH group in the attached script. Some are very close together but it might work.