Commit f223a1df authored by Cédric Traizet's avatar Cédric Traizet

DOC: add a paragraph on spectral classification in the hyperspectral recipe.

parent 8e47d3c3
Pipeline #4287 passed with stages
in 75 minutes and 33 seconds
......@@ -106,6 +106,68 @@ image is shown below:
Resulting unmixed image, here the first three bands are displayed.
Classification
--------------
A common task in hyperspectral image processing is to classify a data cube. For example
one might want to match pixels to reference endmembers. The Spectral Angle Mapper (SAM) algorithm
[1] does that by computing a spectral measure between each pixel and the references.
The spectral angle of a pixel `x` with a reference pixel `r` is defined by :
.. math::
sam[x, r] = cos^{-1}(\frac{<x,r>}{\|x\| * \|r\| } )
where `<x,r>` denotes the scalar product between x and r.
This is also called the spectral angle between `x` and `r`.
In SAM classification the spectral angle is computed for each pixel with a set of reference pixels,
the class associated with the pixel is the index of the reference pixel that has the lowest spectral angle.
::
otbcli_SpectralAngleClassification -in inputImage.tif
-ie endmembers.tif
-out classification.tif
-mode sam
The result of the classification is shown below :
.. figure:: ../Art/HyperspectralImages/classification.png
:width: 70%
:align: center
Resulting unmixed classified image.
Another algorithm is available in this application based on spectral information divergence [1],
if we define the probability mass function p of a pixel x by :
.. math::
x = [x_1, x_2 ,..., x_L ]^T \\
p = [p_1, p_2 ,..., p_L ]^T \\
p_i = \frac{x_i}{\sum_{j=1}^L x_j}
The spectral information divergence between a pixel `x` and a reference `r` is defined by :
.. math::
sid[x, r] = \sum_{j=1}^{L} p_j *log(\frac{p_j}{q_j}) + \sum_{j=1}^{L} q_j * log(\frac{q_j}{p_j})
where p and q are respectively the probability mass function of x and r. As with the SAM algorithm,
the class associated with the pixel is the index of the reference pixel that has the lowest spectral information
divergence.
Note that the framework described in the
:ref:`classification recipe<classif>` can also be applied to hyperspectral data.
Anomaly detection
-----------------
......@@ -183,6 +245,10 @@ The value of the threshold depends on how sensitive the anomaly detector should
Left: Computed Rx score, right: detected anomalies (in red)
*[1] Du, Yingzi & Chang, Chein-I & Ren, Hsuan & Chang, Chein-Chi & Jensen, James & D'Amico, Francis. (2004).
New Hyperspectral Discrimination Measure for Spectral Characterization. Optical Engineering - OPT ENG. 43.*
.. _here: http://www.ehu.eus/ccwintco/index.php/Hyperspectral_Remote_Sensing_Scenes#Cuprite
.. _AVIRIS: https://aviris.jpl.nasa.gov/
.. _Pavia: http://www.ehu.eus/ccwintco/index.php/Hyperspectral_Remote_Sensing_Scenes#Pavia_University_scene
.. _classif:
Classification
==============
......
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