quantaize data and build an histogram

Hello,

I have a 3D data (X,Y,Z). Where X is between 0 to 360, Y is between 0 to 180 and Z is between -100 to + 100.

I'd like to quantize the data to NxM scale values on X and Y axes respectively and to have some mean value for Z.

This data shall be displayed on 2D plot where the Z values shall be represented by colors (if value is close to 100, then green, if the value is close to -100 then red).

How this could be done?

Answer 1

[Ganesh]

Hi @michael,

You can use the following code to achieve what you are trying to do:

X = randi([0, 360], 1000, 1);
Y = randi([0, 180], 1000, 1);
Z = randi([-100, 100], 1000, 1);

Nx = 36;
M = 18;

edgesX = linspace(0, 360, Nx+1);
edgesY = linspace(0, 180, M+1);
quantizedX = discretize(X, edgesX);
quantizedY = discretize(Y, edgesY);

uniquePairs = unique([quantizedX, quantizedY], 'rows');
meanZ = zeros(size(uniquePairs, 1), 1);
for i = 1:size(uniquePairs, 1)
    idx = quantizedX == uniquePairs(i, 1) & quantizedY == uniquePairs(i, 2);
    meanZ(i) = mean(Z(idx));
end

Zgrid = nan(Nx, M);
for i = 1:size(uniquePairs, 1)
    Zgrid(uniquePairs(i, 1), uniquePairs(i, 2)) = meanZ(i);
end

figure;
imagesc(Zgrid);
colorbar;
colormap([linspace(1,0,256)', linspace(0,1,256)', zeros(256,1)]);
caxis([-100 100]);
xlabel('Quantized X');
ylabel('Quantized Y');
title('Mean Z Values Represented by Color');
axis xy;

Here, we primarily make use of the "discretize()" function to divide the X and Y data into bins. Through a loop, we process each of the bins and assign the corresponding mean value of Z to the X and Y data. We then make a "Zgrid()", which would help us in plotting the required colour map.

You can find the documentation for each of the mentioned functions below:

https://www.mathworks.com/help/matlab/ref/double.discretize.html

https://www.mathworks.com/help/control/ref/zgrid.html

Hope this helps!