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The potential of neural networks for mixed pixel classification is recognised by several authors (e.g. Foody, 1996; Schouten and Gebbinck, 1997). Foody uses a multilayer perception (Sections 2.3.5 and 3.1) to retrieve class proportions. The network was trained using mixed pixels. Each input vector generates a corresponding output membership value for each of the candidate information classes. The key point is to teach the network to learn the (output) class proportions from the input (mixed) spectral vector. The results produced by the multilayer perception to identify the proportions of different land cover categories within a mixed pixel show considerable promise.

Since the output activations from a multilayer perception generally do not sum to unity, the output values must be rescaled through a normalisation process in order to achieve mixed pixel estimation. Although this normalisation operation offers a simple solution, further theoretical studies are needed to clarify its effects. Neural networks other than the perceptron have not been used to analyse mixed pixels. Possible solutions could be based on counter-propagation or fuzzy ARTMAP networks, because both output floating-point values and, logically, fuzzy ARTMAP is able to classify mixed pixels.

4.6.3 Spectral mixture analysis

Spectral mixture analysis provides an alternative way of determining the relative proportions of ground cover components within a mixed pixel. The method uses a set of end members (defined as pure information classes) representing ideal types from which all mixtures present in the image are formed. Each end member has a location in an n-dimensional feature space, where n is the number of features used to describe the pixel. A polyhedron is formed by linking the positions of the end members in this hyperspace. All possible mixtures with non-negative proportions of end members should be enclosed by this polyhedron (Settle and Drake, 1993). Figure 4.18 shows three end members in a two-dimension space, forming a triangle, and all possible non-negative mixtures fill the triangle. The use of this method to solve the mixed pixel problem is called spectral unmixing.

Spectral unmixing is most often performed using the linear mixture model (Settle and Drake, 1993). The basic physical assumption underlying the linear mixture model is that there is no multiple scattering between the different cover types; so that each photon that reaches the sensor has interacted with just one land cover type. Under these conditions, the energy received at the sensor can be considered as the simple linear sum of the energy received from each cover component. As noted by Bork et al. (1999, p. 3642), ‘One problem with the use of mixing models is that they tend to be reliable under conditions where only one (or a few) vegetation components exist’, which is unlikely.

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