8/18/2019 Concept of SMA Presentation March 5 2016
1/19
A Concept in Sub-pixelClassifcation: Spectral Mixture
Analysis
March 5, 2016
Presented by
Kaleab Woldemariam
8/18/2019 Concept of SMA Presentation March 5 2016
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.
8/18/2019 Concept of SMA Presentation March 5 2016
3/19
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 %.
8/18/2019 Concept of SMA Presentation March 5 2016
4/19
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.
8/18/2019 Concept of SMA Presentation March 5 2016
5/19
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%.
8/18/2019 Concept of SMA Presentation March 5 2016
6/19
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
8/18/2019 Concept of SMA Presentation March 5 2016
7/19
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
8/18/2019 Concept of SMA Presentation March 5 2016
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
8/18/2019 Concept of SMA Presentation March 5 2016
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))
8/18/2019 Concept of SMA Presentation March 5 2016
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
8/18/2019 Concept of SMA Presentation March 5 2016
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
8/18/2019 Concept of SMA Presentation March 5 2016
12/19
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+ >
8/18/2019 Concept of SMA Presentation March 5 2016
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
8/18/2019 Concept of SMA Presentation March 5 2016
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.
8/18/2019 Concept of SMA Presentation March 5 2016
15/19
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.
8/18/2019 Concept of SMA Presentation March 5 2016
16/19
Landsat TM image
of part of theGifford Pinchot
National Forest
8/18/2019 Concept of SMA Presentation March 5 2016
17/19
urnedMature
regro*t
+ld gro*t
Immature
regro*t
roadleaf
eciduous
Clearcutrasses
Shadow
8/18/2019 Concept of SMA Presentation March 5 2016
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
8/18/2019 Concept of SMA Presentation March 5 2016
19/19
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.