 # Calculate percentage of endmember abundance in Hyperspectral Unmixing resut?

Hi, my first time here, I fell in love with ORFEO only a few weeks ago.

I am unsure on how to calculate the percentage each endmember has in the result of Hyperspectral unmixing. For an example RGB Pixel I have the values: [137.75, 123.70, 58.39] which with 4 endmembers gives me an abundance matrix of : [0.76, 0.03, -0.35, 0.92].

Am I right by assuming these are the coefficients of the linear equation that when multiplied with my endmembers results in the pixel value? How could I calculate a percentage of each endmember present in the pixel?

King reguards,

Hello,

this is weird, I think the output abundances should lie between 0 and 1, and should sum to 1. Have you tried to verify the result of unmixing by manually applying the linear model using the endmembers and the output abundances ? Which unmixing algorithm did you use ?

Where do the endmembers come from ? Have they been generated using the VertexComponentAnalysis application ?

Cédric

1 Like

Dear Cédric,
I used the ucls-algorithm, and the endmembers do come from the VertexComponentAnalysis application. I tried to verify the result after your advice using different pixel values as the example above, and it gives back the correct values:

``````import numpy as np
# observed pixels
R = np.array([146.21552, 142.08421, 80.00875])

# endmembers
A = np.array([
[212.6503, 10.482534, 136.97844],
[267.92877, 32.882927, 108.81945],
[181.8901, -5.3892436, 41.599026]
])

# abundance matrix
S = np.array([0.294039,-0.129561, 0.620872])

print(A.dot(S))

``````

Returns:

``````[146.21543197 142.08411226  80.00868937]
``````

Here a link to my testdata:

Raphael

Hello Raphael,

the result are weird, in particular I think the endmembers produced by the VCA should all be positive. I tested another implementation of the algorithm (available here) and obtained the same output endmembers, so I don’t think the problem comes form OTB implementation (note that both implementation are based on the same Matlab code provided by the author of the VCA paper ).

perhaps the problem comes from the input data ? I am not sure the linear mixing model and use VCA to compute endmembers for a RGB image. Maybe the algorithm should be used on an actual hyperspectral image of high dimension ?

Cédric

 Vertex Component Analysis: A Fast Algorithm to Unmix Hyperspectral Data, José M. P. Nascimento, and José M. Bioucas Dias, IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 43, NO. 4, APRIL 2005

Thank you very much! I think you are right the reasons is probably that I need an actual hyperspectral image instead RGB.

Raphael