sam

Measure spectral similarity using spectral angle mapper

Syntax

score = sam(inputData,refSpectrum)

score = sam(testSpectrum,refSpectrum)

Description

score = sam(inputData,refSpectrum) measures the spectral similarity between the spectrum of each pixel in the hyperspectral data inputData and the specified reference spectrum refSpectrum by using the spectral angle mapper (SAM) classification algorithm. Use this syntax to identify different regions or materials in a hyperspectral data cube.

score = sam(testSpectrum,refSpectrum) measures the spectral similarity between the specified test spectrum testSpectrum and reference spectrum refSpectrum by using the SAM classification algorithm. Use this syntax to compare the spectral signature of an unknown material against the reference spectrum or to compute spectral variability between two spectral signatures.

Note

This function requires the Image Processing Toolbox™ Hyperspectral Imaging Library. You can install the Image Processing Toolbox Hyperspectral Imaging Library from Add-On Explorer. For more information about installing add-ons, see Get and Manage Add-Ons.

Examples

Distinguish Hyperspectral Regions Using Spectral Angle Mapper

Distinguish different regions in a hyperspectral data cube by computing the spectral angle distance between each pixel and the endmember spectra of the data cube.

Read hyperspectral data into the workspace.

hcube = hypercube('jasperRidge2_R198.hdr');

Identify the number of spectrally distinct bands in the data cube by using the countEndmembersHFC function.

numEndmembers = countEndmembersHFC(hcube)

numEndmembers = 14

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

endmembers = nfindr(hcube,numEndmembers);

Plot the spectral signatures of the endmembers. The result shows the 14 spectrally distinct regions in the data cube.

figure
plot(endmembers)
legend('Location','Bestoutside')

Compute the spectral angular distance between each endmember and the spectra of each pixel in the data cube.

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

Compute the minimum score value from the distance scores obtained for each pixel spectra with respect to all the endmembers. The index of each minimum score identifies the endmember spectra to which a pixel spectra 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 0.15 0.4 0.8])
imagesc(rgbImg)
axis off
title('RGB Image of Hyperspectral Data')
subplot('Position',[0.45 0.15 0.4 0.8])
imagesc(matchingIndx)
axis off
title('Indices of Matching Endmembers')
colorbar

Determine Similarity of Endmember Spectra Using SAM

Read hyperspectral data into the workspace.

hcube = hypercube('indian_pines.dat');

Find ten endmembers of the hyperspectral data.

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

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

score = zeros(1,numEndmembers-1);
refSpectra = endmembers(:,1);
for i = 2:numEndmembers
    testSpectra = endmembers(:,i);
    score(i-1) = sam(testSpectra,refSpectra);
end

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

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

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

figure
plot(refSpectra)
hold on
plot(maxMatch,'k')
plot(minMatch,'r')
xlabel('Band Number')
ylabel('Data Values')
legend('Reference spectra','Minimum match test spectra','Maximum match test spectra',...
       'Location','Southoutside')
title('Similarity Between Spectra')
annotation('textarrow',[0.25 0.25],[0.4 0.5],'String',['Max score: ' num2str(maxval)])
annotation('textarrow',[0.6 0.55],[0.6 0.45],'String',['Min score: ' num2str(minval)])

Input Arguments

inputData — Input hyperspectral data

hypercube object | 3-D numeric array

Input hyperspectral data, specified as a hypercube object or a 3-D numeric array containing the data cube. If the input is a hypercube object, the data is read from the DataCube property of the object.

testSpectrum — Test spectrum

C-element vector

Test spectrum, specified as a C-element vector. The test spectrum is the spectral signature of an unknown region or material.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

refSpectrum — Reference spectrum

C-element vector

Reference spectrum, specified as a C-element vector. The reference spectrum is the spectral signature of a known region or material. The function matches the test spectrum against these values.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Output Arguments

score — SAM score

scalar | matrix

SAM score, returned as a scalar or matrix. The output is a

• scalar — If you specify the testSpectrum input argument. The function matches the test spectral signature against the reference spectral signature and returns a scalar value. Both the test and the reference spectra must be vectors of same length.

• matrix — If you specify the inputData input argument. The function matches the spectral signature of each pixel in the data cube against the reference spectral signature and returns a matrix. If the data cube is of size M-by-N-by-C and the reference spectra is a vector of length C, the output matrix is of size M-by-N.

Each element of the SAM score is a spectral angle in radians in the range [0, 3.142]. A smaller SAM score indicates a strong match between the test signature and the reference signature.

Data Types: single | double

More About

Spectral angle mapper

Given the test spectrum t and a reference spectrum r of length C, the SAM score α is calculated as

$$\alpha ={\cos }^{-1}\left(\frac{{\displaystyle \sum _{i=1}^C{t}_i{r}_i}}{\sqrt{{\displaystyle \sum _{i=1}^C{t}_i^2}}\sqrt{{\displaystyle \sum _{i=1}^C{r}_i^2}}}\right).$$

References

[1] Kruse, F.A., A.B. Lefkoff, J.W. Boardman, K.B. Heidebrecht, A.T. Shapiro, P.J. Barloon, and A.F.H. Goetz. “The Spectral Image Processing System (SIPS)—Interactive Visualization and Analysis of Imaging Spectrometer Data.” Remote Sensing of Environment 44, no. 2–3 (May 1993): 145–63. https://doi.org/10.1016/0034-4257(93)90013-N.