concept of sma presentation march 5 2016

8/18/2019 Concept of SMA Presentation March 5 2016

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A Concept in Sub-pixelClassifcation: Spectral Mixture

Analysis

March 5, 2016

Presented by

Kaleab Woldemariam


2/19

Pixel: represents a ~square area in the scene that is a

measure of the sensor's ability to resolve objects .

A Mixed Pixel:

• Spectral images measure mixed or integratedspectra over a pixel. Often each pixel contains

different materials, many with distinctive spectra.

• Refers to a pixel with different materials and hencedifferent spectral signatures within the smallest unit

( a pixel ) of an image.


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Image Processing Sequence

(single image)

Raw Satellite Image

Product

• Pre-Processing(Calibration)

• Spectral analysis (Multiband

Image, Ratio Image, PCA, etc.)

• Initial Classification or oter type

of analysis

• Interpretation!"erification• or furter analysis.

Processing

Spectral Mi#ture Analysis isa sub-pi#el classification

metod usually used in

Medium Resolution Satellite

Images suc as $andsat %.


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Distinguishing Earth’s Surface Materials using Spectral

Reflectance

Reectance: Is the ratioo reected energy toincident energy.

Varies withwavelength

Function of themolecular propertiesof the material.

Passive sensors usesun’s light as EMR(ElectromagneticRadiation)

Reectance Signature: A plot o the reectanceo a aterial as aunction o !a"elength.


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Spectral Mixture Analysis (SMA) #he reectance o an iage pixel is a linear cobination o reectances

ro $typically% se"eral &pure' substances $or endebers% contained

!ithin the ground-spot sapled by the reote sensing syste.

SMA is a techni(ue or estiating the proportion o each pixel that is co"ered by a

series o )no!n co"er types or attepts to deterine the li)ely coposition o each

iage pixel.

&*ure' pixels contain only one eature or class. A pure pixel !ould contain only oneeature+ such as "egetation.

*ixels that contain ore than one co"er type are called ixed pixels. Mixed *ixelscause *robles in #raditional iage classifcations $e.g.+ super"ised or unsuper"ised classifcation%

because the pixel belongs to ore than one class but can be assigned to only asingle class.

ead to overestimation or underestimation o land co"ers.

In a -I-S odel $ egetation-Iper"ious-Soil%+ a ixed pixel ight containegetation+ Iper"ious Surace + Soil and /ater. 0ach o these are oten calledendmembers.

1ne Solution to ixed pixel proble : SMA $soeties called subpixel analysis%.


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Spectral Mixture Analysis (SMA)

• An area of ground of, say 30 m by 30 m may contain 3 materials: A, B, and C.

• SMA is an inversion technique to determine the quantities of A, B, and C

in the ‘Mixture’ spectrum.

• SMA is physically-based on the spectral interaction of photons of light and matter.

• SMA is in widespread use today in all sectors utilizing spectral remote sensing

• Variations include different constraints on the inversion; linear SMA; nonlinear SMA

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40

Wavelength (micrometers)

R e l e c t a n c e

!

"

#

$i%t&re

‘Mixture’ = 25%A + 35%B + 40%C


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Linear vs. Non-Linear Mixing

1. Linear Mixing(additive).

Assues that endeber substances are

sitting side-by-side !ithin the 21.2. Non-Linear Mixing

– Intimate mixtures,

Beer’s Law.

Assues that endeber coponents arerandoly distributed throughout the 21.

Multiple scattering e3ects.

r = f g&rg+ rs &(1- f g)

r = f g·rg+ rs&(1- f g)&exp(-k g&d)

d


8/19

2 Endmember Spectra (Soil & Vegetation)

The extreme spectra

that mix and that

correspond to scenecomponents are

called spectral

endmembers.

0 1 2

Wavelength, µ m


9/19

Spectral Mixtures

25% Green Vegetation (GV)75% Soil

T M B a n d 4

TM Band 3

0

60

40

20

0 40

75% GV

50% GV

A pixel with 25% GV

100% GV

100% Soil

0 20 60

4

54

64

74

84

944

:;4 8;4 9:;4 98;4 5:;4

Spectral Plot (TM B3 (Red) vs. TM B4 (NIR))


10/19

Spectral Mixtures

25% Green Vegetation

70% Soil

5% Shade

T M B a n d 4

TM Band 3

0

60

40

20

0 20 40 60

100% GV

100% Shade

100%

Soil

4

54

64

74

84

944

:;4 8;4 9:;4 98;4 5:;4

3 endmember spectral plot


11/19

Linear Spectral Mixtures

r mix,b

f em

rem,b

= Reflectance of observed (mixed) image spectrum at each band b

= Fraction of pixel filled by endmember em

= Reflectance of each endmember at each band

= Reflectance in band b that could not be modeled

= number of image bands, endmembers

εb

bbem

m

em

embmix r f r ε +=∑=

)( ,'

, '

'

=∑=

m

em

em f

There can be at most m=n+1 endmembers

or else you cannot solve for the fractions funiquely ∑==n

b

bnrms

'

('ε

n,m


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LSMA- Assumptions & Process Assuptions

#here exist at least one pure pixel or each class.

#he aterial signature atrix is the sae or all iage pixels in the scene.

#he nuber o endebers is )no!n.

#he su o raction o a pixel is 9.

2raction o pixels lie bet!een 4 and 9.

#he spectral "ariation in an iage is caused by ixtures o a liited nuber osurace aterials

#!o-step process 0ndeber detection

Con"ex geoetry-based approach $M#+ **I+ SCS+ >


13/19

In order to analyze an image in terms of mixtures, We must

estimate the endmember spectra and the number of endmembers

you need to use.

• Endmember spectra can be pulled from the image

itself , or from a reference library (requires calib-

ration to reflectance).

• To get the right number and identity of endmembers, trial-and-error

usually works. But for Urban Mapping, the endmembers are

usually Vegetation, Impervious Surface, and Soil, after Water

pixels are masked.• Often, “shade” will be an endmember.

• “shade”: a spectral endmember (often the null vector) used to

model darkening due to terrain slopes and unresolved shadows


14/19

Inverse SMA (“spectral unmixing”)

A process by which mixed pixel spectra are decomposedinto endmember signatures and their fractional abundances.

Objective of SMA:

•to find the spectral endmember fractions that areproportional to the amount of the physical endmember

component in the pixel.


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As a rule of thumb, the number of useful endmembersin a cohort is 4-5 for Landsat TM data.

It rises to about 8-10 for imaging spectroscopy.

There are many more spectrally distinctive

components in many scenes, but they are rare or don’t

mix, so they are not useful endmembers.


16/19

Landsat TM image

of part of theGifford Pinchot

National Forest


17/19

urnedMature

regro*t

+ld gro*t

Immature

regro*t

roadleaf

eciduous

Clearcutrasses

Shadow


18/19

reen

"egetationClearcut

Sade

Spectral mixture analysis from the

Gifford Pinchot National Forest

R = NPV

G = green veg.

B = shade

In fraction images, light tones

indicate high abundance


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Importance of SMA

Mixing analysis is useul because

9.It a)es raction pictures that are almostsynonymous as abundance of physicallymeaningful scene components $ e.g. area o"egetation%

5.It helps reduce dimensionality o data sets toanageable le"els !ithout thro!ing a!ay uch data.

.By isolating topographic shading+ it pro"ides a

ore stable basis or classifcation and a useulstarting point or IS analysis.

4.Better Classication accuracy copared to

traditional super"ised and unsuper"ised classifcation.

concept of sma presentation march 5 2016

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