Plot a heatmap from a matix

I implemented the minutia heat map presented in this paper (page 7): https://arxiv.org/pdf/1909.09901.pdf

The result is that i have 6 matrixes and i am looking for a way to plot these as shown in the paper (same page), like this:

Basically, the low values is presented in dark, and it gets lighter when it increase.

[darova]

What about pcolor?

[Katie]

pcolor, image, imagesc, imshow, or heatmap could all give you results that look similar to those in the paper figure you've shared. pcolor doesn't exactly color grid locations in accordance to the value at that grid location. Instead, it's doing a bilinear interpolation based on the colors at the verticies of that grid cell. There's some discussion about the difference between pcolor and image here: https://www.mathworks.com/matlabcentral/answers/37049-removing-grid-edge-lines-in-pcolor-figure

If you're set on using heatmap to plot your matricies, you could do a 2 by 3 subplot setup with the 'gray' colormap (or a custom colormap) and with the grid turned off.

subplot(2,3,1)
heatmap(x1,'Colormap',gray,'GridVisible','off')

[Ahmed Madhun]

Thanks it seems to work, however, it sees to not be accurate. Because all my 6 matrixes are different, but when i use:

 heatmap(Mx, 'Colormap',gray,'GridVisible','off'));

all the figures are the same, any idea of why this happen ?

[darova]

Make range for color axis the same for each figure

min = % minimum of 6 matrix
max = % maximum of 6 matrix
caxis([min max])

[Ahmed Madhun]

Sorry didn't get you comment: how to apply that for my code ?

% Function to create the HeatMap matrix of a minutia set in "TestData" file
function HeatMapCreator()
    % Start plotting minutia 
    [X, Y, A] = GetMinData("TestData");
    % Minutia 1 has X1, Y1, and A1 => X and Y is the position and A is the angle between 0-359
    % Count Minutiea
    n = length(X);

    % set Width and Hight
    W = 600;
    H = 750;
    K = 6;
    
    % Create the matixes
    MM = cell(K, 1);
    M = zeros(H,W);
    
    % Define the gussian paramater
    GP = 2*2^2;
    
    % Go throw each pixel
    for k = 1:6
        for i = 1 : W
           for j = 1 : H
              Hijk = 0; 
              for t = 1 : n
                Xt = X(t);
                Yt = Y(t);
                At = A(t);

                %Calculate Cs
                ED = sqrt((i-Xt)^2+(j-Yt)^2);
                Cs = exp(-ED/GP);

                %Calculate Co
                DO = At - (2 * k * pi / K);
                if (DO < -pi) || (DO > pi)
                    DO = 2 * pi - DO;
                end                       
                Co = exp(-DO/GP);

                Hijk = Hijk + (Cs * Co);
              end
              M(i,j) = Hijk;
           end
        end
        MM{k} = M;
    end
    
    % Show the 6 figures
    for k = 1:6
        figure(k)
        heatmap(MM{k},'Colormap',gray,'GridVisible','off');
    end
end

Comment: I set the Gussian paramater to test weather it works or not.

Answer 1

[darova]

You are using H for rows and W for columns

M1 = zeros(H,W);
% ...
for i = 1 : W
    for j = 1 : H
        % ...
        M1(i,j) = Hijk;        % looks like mistake

You can use cells to create 6 matrices automatically

MM = cell(6,1);
M = zeros(H,W);
for k = 1:6
    for i 
        for j
            for t
                % do stuff
            end
            % ...
            M(i,j) = %...
        end
    end
    MM{k} = M;
end

After you found max and min values (global) use loop to visualize

for k = 1:6
    figure(k)
    heatmap(MM{k});
    caxis([minx maxx])
    colormap gray
end

[Ahmed Madhun]

Yeah, i saw the mistake of the i and j, and corrected it.

But how do you define the minx and maxx for:

    caxis([minx maxx])

[darova]

Find max value of each matrix and choose biggest. Do the same for minimum

[Ahmed Madhun]

Not really, no value is now displayed on the heatmap figures at all.

I change my code as you advised:

    minV = 0;
    maxV = 0;
    
    for k = 1:6
        for i = 1 : W
           for j = 1 : H
              Hijk = 0; 
              for t = 1 : n
                Xt = X(t);
                Yt = Y(t);
                At = A(t);

                %Calculate Cs
                ED = sqrt((i-Xt)^2+(j-Yt)^2);
                Cs = exp(-ED/GP);

                %Calculate Co
                DO = At - (2 * k * pi / K);
                if (DO < -pi) || (DO > pi)
                    DO = 2 * pi - DO;
                end                       
                Co = exp(-DO/GP);

                Hijk = Hijk + (Cs * Co);
              end
              M(i,j) = Hijk;
           end
        end
        MM{k} = M;
        
        % Get the maximum and minimum cell from all matrixes
        if minV > min(M(:))
            minV = min(M(:));
        end
        
        if maxV < max(M(:))
            maxV = max(M(:));
        end
    end
    
    for k = 1:6
        figure(k)
        heatmap(MM{k})
        caxis([minV maxV])
        colormap gray
    end

the result is:

However, if i use the old code to display the heatmap as:

    heatmap(MM{1},'Colormap',gray,'GridVisible','off');

the result is:

But this is equal for all matrixes!, which is not correct as all matrixes are different!

[darova]

Is color range caxis the same for each matrix?

[Ahmed Madhun]

Yes, because i only store the highest and loweat value of all matrixes.

[darova]

Please attach the data

[Ahmed Madhun]

Here is it in a .mat format, that contains X, Y, A. => X(1), Y(1) and A(1) is for the same object.

[darova]

There is difference but only in intensity

for k = 1:5
    subplot(3,2,k)
%     figure(k)
    h = pcolor(MM{k}-MM{k+1});
    set(h,'edgecolor','none');
%     caxis([minV maxV])
    colormap gray
end

[Ahmed Madhun]

Not sure, because according to the paper. If it's implemented correctly each heat map should highlight only minutia in the same degree range.

[darova]

Can you attach a screenshot or something? The file is too large, can't donwload .pdf (i have low internet speed)

[Ahmed Madhun]

The paper is only 8 Mb. You can find it if you search on google for: "Learning a Fixed-Length Fingerprint Representation"