11.hyperspectral

8/10/2019 11.Hyperspectral

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Spectral Angle Mapper:

The Spectral Angle Mapper (SAM) performs supervised classification of hyper-spectral

imagery, given a set of spectral records. SAM computes the "spectral angle" beteen

each n-dimensional pixel of image and a set of n-dimensional reference spectra of a

spectral library file. The result is a classification image here each pi!el is assigned to the

class, hich has the smallest spectral angle. i!els are assigned to the #$%% (&) class if

the minimum spectral angle is greater than a threshold value.The spectral angle is a '-bit

real value beteen & and *&.

$nli+e other classifiers, SAM has the advantage that similarity beteen an image pi!el

and a reference spectrum can be determined ithout regard to their relative brightness.

The SAM algorithm assumes that hyper-spectral image data have been reduced to

"apparent reflectance", ith path radiance biases removed.

onsider a "reference spectrum" and a "test spectrum" from a to-band data set

represented on a to-dimensional plot a to points. The lines connecting each spectrum-

point and the origin contain all possible positions for that material, corresponding to the

range of possible illuminations. oorly illuminated pi!els ould fall closer to the origin (the

dar+ point) than pi!els ith the same spectral signature but greater illumination. The angle

beteen the to vectors is the same regardless of their length. The calculation consists of

ta+ing the arccosine of the dot product of the to spectra. SAM determines the similarity(or "spectral angle") of a test spectrum T to a reference spectrum using the folloing

euation/

angle = arccos ( (Sum of (T(i)*R(i))) / ( |T| * |R| ) )

T(i) = test spectrum values (i = 1 to n) , R(i) = refer spectrum values (i = 1 to n)

|T| = s!uare root of ( sum of (T(i)*T(i)) ), |R| = s!uare root of ( sum of (R(i)*R(i)) )

This measure of similarity is insensitive to gain factors because the angle beteen to

vectors is invariant ith respect to the lengths of the vectors0 As a result, laboratory

spectra (from spectral libraries) can be directly compared to remotely sensed apparent

reflectance spectra (from hyper-spectral images), hich inherently have an un+non gain

factor related to topographic illumination effects.


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Spectral Mi"ture Anal#sis of $#per%spectral &ata

1'ntrouction

1n remote-sensing imagery, the measured spectral radiance of a pi!el is the integration of

the radiance reflected from all the ob2ects ithin the ground instantaneous field of view

(31456). Mi!ed pi!els are generated if the si7e of the pi!el includes more than one type of

terrain cover. 5bviously, spectral mi!ing is inherent in any finite-resolution digital imagery

of a heterogeneous surface.

Solving the spectral mi!ture problem is, therefore, involved in image classification,

referring to the techniue of spectral unmi!ing. The application of spectral unmi!ing as

limited due to the lo spectral resolution of the sensors in the past. The large number of

spectral bands in hyperspectral data allos the unmi!ing of very comple! scenes to avoid

intrinsic singular problems. 1n addition, the hyperspectral data permits the direct

identification of image-derived endmember spectra.

onceptually, the occurrence of multiple materials, or endmembers, ithin the 31456 of a

single pi!el leads to a composite or mi!ed spectral signal. The spectra of an endmember

ideally represent the signatures that ould be recorded for pure or single-component

pi!els.

%inear mi!ture modeling is commonly applied ith the assumptions that electromagnetic

energy reflected from the surface interacts ith a single component and a uniform

eighting of radiance over the 31456 area. 8oever, non-linear mi!ing may dominate

freuently in reality hen incident electromagnetic energy reacts ith more than one

component before being reflected from the surface, for e!ample the reflectance from

vegetation canopy. 1n addition, due to the fact that the sensor spatial spread function

results in a non-uniform response, spectrally determinate fraction coefficients do not

correspond ith the proportions of endmembers distributed ithin a pi!el.

Spectral nmi"ing:

%inearly unmi!es +non endmembers from a spectral image. reates endmember fraction

images on output, ith pi!el values being an estimate of the fractional contribution to that


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pi!el by that endmember. 1t performs a "sub-pi!el" classification, and is normally used to

classify mi!ed pi!els in hyper-spectral images.

Spectral unmi!ing is a technology, hich allos the user to trade spectral information for

spatial information. As such it can be used to determine information on a "subpi!el" scale.

1t is a method ideally suited to separating "mi!ed pi!els", and therefore has many

applications in geology, ecology, and hydrology.

Traditional image classifiers are used to classify each image pi!el into one of a number of

classes. Spectral unmi!ing, hoever, is used to assign fractional class membership to

each image pi!el. Therefore, rather than producing one classification image, spectral

unmi!ing produces one classification image per class, here the image values indicate

the fraction of the pi!el assigned to the class (in spectral unmi!ing, the classes are called

"9ndmembers").

:etermining endmember fractions for each image pi!el is useful hen/

- image pi!els are mi!ed, and traditional classification methods cannot effectively be

used

- one is loo+ing for the presence of some particular endmember, hich is relatively rare,

and ishes to narro the search to a subset of the image area.

This linear mi!ture model can be mathematically described as a linear vector-matri!euation,

here/

i;,..,m (number of bands)

11.hyperspectral

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