1. Two Models Representing World Features
Real World Features
Raster
Vector •

2. The problem with raster representation of the real world

3. Assumptions for SMA
Landscape is composed of a few major components, called end members
Spectral signatures of end members are constant within the scope of areas of interest

4. Mathematical Solutions for SMA
Given n (j=1, …,n) end members and m (i=1, …,m) bands, fj is the fraction of end member j in a pixel with spectral signature Sij in band i, then
How many bands do we need in order to solve for n end members?

5. An SMA Example
The simplest case: one band (NDVI image) two end members (Vegetation, Impervious Surface).
NDVI=0.5
NDVIveg=0.7
NDVIis=-0.1
What is the fraction of vegetation cover within the pixel?

6. Another Example of SMA
Assuming we have three end members (Vegetation, Impervious Surface, and Water), can we still solve for vegetation cover with the following information?.
NDVI=0.5
NDVIveg=0.7
NDVIis=-0.1
Why?

7. Key information for SMA
Number of End Members
Spectral Signature of End members

8. How many end members? Land Cover Classes: IGBP 17 classes
Landsat TM 6 reflective bands
Hyperspectral: Hundreds of bands

9. Assumptions for SMA
Landscape is composed of a few major components, called end members
Spectral signatures of end members are constant within the scope of areas of interest

10. Where do we get end member signatures?
Image end members
(1) find the purest pixels
(2) find the corner pixels in feature space
NIR
Red

11. Where do we get end member signatures?
Reference End members
End member spectral signatures obtained from a spectral library.

12. Are End Member Signatures Constant?
Here is an example of Landsat image for the FACE site at Duke. There are
tremendous variations in each endmember,such as vegetation

13. How do we handle variable end member signatures?
End member bundles: Each end member spans a signature space. An end member is estimated as the mean of the minimum and maximum fractions. Assumption (s)?
Multiple end members: Allows end member signature to vary from pixel to pixel. The end member signature is derived from a spectral library based on the goodness of fit.
Other options
NIR
Red

14. Bayesian SMA? Bayes Theorem: Convolution of Probabilities : NDVI=0.5
Pr(NDVIveg=0.7)=0.6
Pr(NDVIveg=0.6)=0.4
NDVIveg=0.7
NDVIurb=-0.1fv=, Pr=0.6*0.7=0.42
NDVIurb=-0.2fv=, Pr=0.6*0.3=0.18
NDVI=0.6
NDVIurb=-0.1fv=, Pr=0.4*0.7=0.28
NDVIurb=-0.2fv=, Pr=0.4*0.3=0.12
Pr(NDVIurb=-0.1)=0.7
Pr(NDVIurb=-0.2)=0.3

15. What about more complicated Probilities?

16. End member fractions