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This document describes Mixture Modeling research
in the HPCC Grand Challenge Project at the Institute
for Advanced Computer Studies.
The Data
This is an AVHRR image of a large portion of the African
continent. Very frequently, estimates of the surface cover
types are needed from data like this.
Classification
A common method to obtain information on surface cover
types, from
remotely sensed data, is classification. This technique
assigns a single label to each pixel in the image.
This label belongs to one of the
cover types present in the image. The result is a thematic
map of the
different cover types in the image.
Mixture Modeling
There are situations when this technique does not accurately represent the
ground truth. This happens, for example, when the ground area corresponding
to a pixel is very large. For instance, in AVHRR imagery, each pixel could
correspond to an area of a few square miles.
What is it ?
In situations like these, a single class label for each pixel is not
a very accurate representation of the ground truth. This is where
mixture modeling comes in. In this technique, we model each pixel
as being composed of fractions of the different cover types. For example,
a certain pixel in an image may contain 50% desert, 40% shrub, and 10%
water. We attempt to estimate these fractions (or percentages), for each pixel
in the image. The number of fractions estimated per pixel is equal
to the number of surface cover types present in the scene.
Click here for a mathematical
formulation of the problem, and a description of our
algorithms
The result of mixture modeling is a set of quantitative maps, unlike the single
thematic map produced by classification. There is a fraction map corresponding
to each surface cover type. For instance, the fractional map corresponding to
the desert component will indicate the amount of desert in
every pixel in the image. Therefore, there are as many of these fractional
maps, as there are cover types. The images shown below help to illuminate
these notions.
Here are the fractional map estimates of the four different cover types,
obtained by our algorithm.
Desert fraction
Grass fraction
Forest fraction
Water fraction