Discussion

Soft classification methods have attracted considerable attention for reducing the mixed pixel problem that is often encountered in RS applications. The exact nature of the derived unmixing results is a function of classification algorithm and endmember definitions. Correlation for all the estimated classes with actual/reference proportion of those classes greatly improved when endmembers were selected based on the spectral variability of materials within the scene. The effect of decreasing correlation between reference and modelled fractions due to decrease inspatial resolution was an expected result for several reasons: (a) decreasing the pixel size would increase the impact of geolocation error and this would affect accuracy assessment while comparing the results with a high spatial resolution classified reference map; (b) the signal recorded at the sensor for a single pixel is affected by the spectral properties of surrounding pixels (Forster, 1985; Townshend et al., 2000); and (c) the process of averaging fractions over larger areas reduces the variance of each dataset thereby, decreases correlation between fractions, with the assumption that the means of the two datasets are similar. Actually, similarity between endmembers results in a high correlation between the endmember spectra, which in turn leads to an unstable inverse matrix and a dramatic drop in estimation accuracy (Gong & Zhang, 1999).Under ideal conditions, most accurate fractional estimates can be achieved using the minimum number of endmembers required to account spectral variability within a mixed pixel (Sabol et al., 1992). Fractional errors occur either when too few endmembers are used resulting in spectral information that cannot be accounted by the existing endmembers, or too many, in which case minor departures between measured and modelled spectra are often assigned to an endmember that is used in the model, but not actually present (Roberts et al., 1998). Urban environments are particularly difficult for a simple mixture model because a single endmember cannot account for considerable spectral variation within a class. In contrast, endmember variability can account for within-class variability and thus is likely to be more suitable for urban RS (Frankeet al., 2009).Using theVECLS approach, pixel-scale limits in spectral dimensionality were acknowledged while also accounting for considerable spectral variability within a scene. The uncertainties in endmember fraction estimates that are usually caused by brightness differences due to the wide FOV (Field of view) of sensors or particularly due to the complex structure of urban objects are minimised(Franke et al., 2009). This work highlights that it is not sufficient to use a spectral library based on the most representative endmembers of each category. The ‘purest’ endmember fractions are not necessarily representative of materials within the scene and representative spectra may not necessarily be selected as ‘pure’ endmembers (Song, 2005). An endmember that is most representative of its class, in this case of endmember selection may not capture LC with distinct spectra that occupy small areas within the scene (Powell et al., 2007). Therefore, accounting endmember variability for each class is important for estimating correct class proportions.

Usually, two common problems are encountered while identifying endmembers and performing unmixing. Firstly, the sub-pixel abundances generated generally do not correspond to a single class of LC materials. For example, in densely builtup areas, bare soil tend to occur and mix with roof tiles made up of clay in addition to some surrounding materials. This results in wrong estimation of LC fractions. Secondly, when two classes of materials exist as mixtures within a sub-pixel, such as soil mixed with vegetation, the chances of identifying proper endmember and correct estimation of fractions reduces. In the absence of pure pixels, alternative algorithms (Plaza et al., 2002 and Plaza et al., 2004) can be used for endmember extraction. VECLS can be applied in other cities and different landscapes with diverse natural environments to assess its generality.There are several challenges on which future research can be based:

1. Incorporating endmember variability in the absence of endmembers.
2. Integration of spatial, temporal and spectral information for reducing endmember variability.
3. Combining non-linear mixture models (Kumar et al., 2012) with VECLS methodto account both the effects of endmember variability and multiple scattering.
4. Development of methods to account for the bidirectional reflectance (Asner et al., 1997), adjacency effects and atmospheric interferences (Somers et al., 2011, Settle, 2005).