6.2. Classification—Simple classes
Figure 6.2.1 displays the model areas for each class in the classification. The chosen classes are water (blue), buildings (red), roads (brown) and snow (yellow). This is a low number of classes compared to previously made classifications of Longyearbyen, but since it was overcasted during our flight it was not necessary to divide the classes into sunlit/shadowed objects.
Figure 6.2.1: Model areas for the classes water, buildings, roads and snow.
Figure 6.2.2 illustrates the mean spectra of each class for the 15 first images in selected wavelengths. The snow is clearly different from the three other classes, by exhibiting a clear white surface (fairly constant intensity over wavelength in the visible range of the spectra), which is very characteristic for snow. As expected, the water absorbs the most light. The curves of the roads and buildings follow each other closely. These curves are used to identify the different regions in the images, by comparing the measured spectra from each image with the theoretical spectra shown in Figure 6.2.2. A Gaussian fit is used in the Bayes classification.
Figure 6.2.2: Spectral fingerprint of each class defined as wavelength vs. intensity.
The ImageCalculator is then running a Bayes classification (the loss for correct decision is 0 and wrong decision is 1), and producing a resulting classified image (figure 6.2.3). Note the similarities between Figure 6.1.2 and Figure 6.2.3.
Figure 6.2.3: Classified image by ImageCalculator. The classes are: Water (blue), buildings (red), roads (brown) and snow (yellow).
A cluster plot is created by the Image Calculator to show the scatter within each class. Figure 6.2.4 shows the plot of the intensity of each pixel, where 414 nm intensity is plotted against 656 nm intensity. The smaller a cluster is, the more specified is the class. In our data, water is well defined and the intensity of the pixels classified as water has a very low standard deviation. This could be a result of low S/N value, as the albedo of the water is low. Thus there is a big uncertainty of that data. Buildings and roads have a great overlap, but houses tend to have a lower intensity in a redder wavelength. In snow the S/N ratio is better, since the albedo of the snow is much higher. This also results in a larger spread of the intensity values.
Figure 6.2.4: Scatter plot, showing the spread of intensity for the different classes.
Figure 6.2.5, 6.2.6 and 6.2.7 show the probability distribution functions (pdf’s) for the classes, in three different wavelengths. Figure 6.2.4 displays the functions for the central wavelength 436 nm. The Gaussian fits are also shown. We see that the distribution of the class “water” is much narrower than the rest. This means that this class is very well determined. The same applies for the class “snow”, since its distribution is clearly separated from the others. The pdf’s for the classes buildings and roads are just separated, since they appear with similar intensities in all wavelengths. From Figure 6.2.5, 6.2.6 and 6.2.7 we see that the best separation between these two classes is found in shorter wavelengths. The probability of higher intensity of water is larger for longer wavelengths, i.e. when observing water in a redder wavelength we get a larger intensity. This is in accordance with the fact that water has a highest albedo in NIR.
Figure 6.2.5: Probability distribution functions for the different classes in wavelength 436 nm.
Figure 6.2.6: Probability distribution functions for the different classes in wavelength 524 nm.
Figure 6.2.7: Probability distribution functions for the different classes in wavelength 634 nm.
The classes need to be numerically separated, to make sure that the classification is good. To make sure this is the case, we need a measure of class separability. This is given by the Jeffries-Matusita (J-M) distance. The J-M distance has values between 0 and sqrt(2), where a value of 0 means no separation and a value of sqrt(2) full separation. We see from Figure 6.2.8 that water and snow are completely separated from all other classes, whereas buildings and roads have a J-M distance of 1.13, so they are not fully separated. This is in accordance to our earlier observations from the probability distribution functions.
Figure 6.2.8: J-M distance for the different classes, where a value of 1.41 means that the classes are fully separated.