Two Models Representing World Features Real World Features Raster Vector •

The problem with raster representation of the real world

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

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?

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?

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?

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

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

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

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

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

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

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

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

What about more complicated Probilities?

End member fractions