sid

Distinguish different regions in a hyperspectral data cube by computing the spectral information divergence (SID) between each pixel spectrum and the endmember spectrum of the data cube.

Read hyperspectral data into the workspace.

 hcube = hypercube('jasperRidge2_R198.hdr');

Specify the number of spectrally distinct bands to identify in the data cube.

numEndmembers = 7;

Extract endmember spectral signatures from the data cube by using the NFINDR algorithm.

endmembers = nfindr(hcube,numEndmembers);

Plot the spectral signatures of the endmembers.

figure  
plot(endmembers)   
xlabel('Band Number')
ylabel('Data Value')
legend('Location','Bestoutside')

Compute the spectral information divergence between each endmember and the spectrum of each pixel in the data cube.

score = zeros(size(hcube.DataCube,1),size(hcube.DataCube,2),numEndmembers);
for i= 1:numEndmembers
    score(:,:,i) = sid(hcube,endmembers(:,i));
end

Compute the minimum score value from the distance scores obtained for each pixel spectrum with respect to all the endmembers. The index of each minimum score identifies the endmember spectrum to which a pixel spectrum exhibits maximum similarity. An index value, n, at the spatial location (x, y) in the score matrix indicates that the spectral signature of the pixel at spatial location (x, y) in the data cube best matches the spectral signature of the nth endmember.

[~,matchingIndx] = min(score,[],3);

Estimate an RGB image of the hyperspectral data cube by using the colorize function. Display both the RGB image and the matrix of matched index values.

rgbImg = colorize(hcube,'Method','RGB');
figure('Position',[0 0 1100 500])
subplot('Position',[0 0.2 0.4 0.7])
imagesc(rgbImg)
axis off
colormap default
title('RGB Image of Hyperspectral Data')
subplot('Position',[0.5 0.2 0.4 0.7])
imagesc(matchingIndx);
axis off
title('Indices of Matching Endmembers')
colorbar

Read hyperspectral data into the workspace.

hcube = hypercube("jasperRidge2_R198.hdr");

Find 10 endmembers of the hyperspectral data cube by using the N-FINDR method.

numEndmembers = 10;
endmembers = nfindr(hcube,numEndmembers);

Consider the first endmember as the reference spectrum and the rest of the endmembers as the test spectrum. Compute the SID score between the reference and test spectra.

score = zeros(1,numEndmembers-1);
refSpectrum = endmembers(:,1);
for i = 2:numEndmembers
    testSpectrum = endmembers(:,i);
    score(i-1) = sid(testSpectrum,refSpectrum);
end

Find the test spectrum that exhibit maximum similarity (minimum distance) to the reference spectrum. Then find the test spectrum that exhibit minimum similarity (maximum distance) to the reference spectrum.

[minval,minidx] = min(score);
maxMatch = endmembers(:,minidx);
[maxval,maxidx] = max(score);
minMatch = endmembers(:,maxidx);

Plot the reference spectrum, maximum similarity test spectrum, and the minimum similarity test spectrum. The test spectrum with the minimum score has the highest similarity to the reference endmember. On the other hand, the test spectrum with maximum score has the highest spectral variability and characterises the spectral behavior of two different materials.

figure
plot(refSpectrum)
hold on
plot(maxMatch,"k")
plot(minMatch,"r")
legend("Reference spectrum","Minimum match test spectrum","Maximum match test spectrum", ...
       Location="southoutside");
title("Similarity Between Spectra")
annotation("textarrow",[0.3 0.3],[0.4 0.52],String="Min score: "+minval)
annotation("textarrow",[0.6 0.6],[0.4 0.55],String="Max score: "+maxval)
xlabel("Band Number")
ylabel("Data Values")