Ambiguity in linear spectral unmixing

Ambiguity arises due to the enormous intraclass variability found in nature. For example, figure 6 shows a typical scattergram for a 3-class problem.

Figure 6

 The pure classes are soil (its pixels are represented by squares), aleppo pine (its pixels are represented by triangles), and other vegetation (its pixels are represented by circles), in a 2-band coordinate system. We measure the reflectance (scaled to a range from 0 to 255) of each pixel in the two bands (red and infrared) along the two axes. We see that each class consists of such varied pixels, that if we had a mixed pixel in the middle trying to assess its proportions using equations (1) and (2), we would not know which values to use for x,y and z to represent the pure classes. This is a genuine ambiguity and ignoring it simply means that we are forcing the data to give us more information than they contain. The extra information is clearly inaccurate and unreliable. The Fuzzy approach based on model mixtures avoids drawing forced conclusions.

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