In the computation of DN distributions, again determining the means and covariances for the classes that fall within the training sites, a statistical (Bayesian) Probability Function is also calculated for the class data. The class DN distribution, again for a two-dimensional case, gives rise to elliptical boundaries which define the equiprobability envelope for each class. Here is a scatter plot that shows the outer envelope bounding each class:
Not shown is the fact that inside each ellipse are contours that indicate the degree of probability. Associated with each ellipse is a separate plot that expresses a statistical surface (bell-shaped in three dimensions) called probability density functions. Using these functions, which relate to the contours, a likelihood that any unknown point U is most probably associated with some one ellipse is determined. A Bayesian Classifier is a special case in which the likely occurrence of each class (common to rare) is assessed and integrated into the decision making.
We made this Supervised Classification using the Maximum Likelihood classifier acting on all seven bands. Again, multiband classes are derived statistically and each unknown pixel is assigned to a class using the maximum likelihood method.
In this image we omit thermal Band 6 and define 16 classes (this is the maximum allowable in the IDRISI program). These classes are identical to the previous ones recorded in the Minimum Distance image. In both instances, the Sediment class has been subdivided into three levels (I and II in the ocean and a third in the Bay) and two Urban classes (I = Morro Bay; II = Los Osos) are attempted, to account for visual differences between them (mainly street patterns). Look at this image classification and decide how believable it is. Compare it with the minimum distance image as well. To assist you in comparing similar classes, we used the same color assignments. Next, look at a Supervised Classification that uses Band 6 and again specifies 16 classes. Notice how each urban area becomes more homogeneous. There is a similar increase in spatial homogeneity of vegetation and slopes in general with Band 6 added, but overall adding Band 6 didn't show much differences.
Each 16-class Maximum Likelihood version is a fairly dazzling image, with many classes "right on". Both Breakers and sand bar (Beach) seem uniformly classified. The sediment load distribution is credible. There are enough color tone differences between Morro Bay and Los Osos to justify the decision to make them two Urban classes (Los Osos differs in its street patterns and in the presence of the orange-brown soil, seen in the composite of Bands 1,2, and 3). However, color elements of one Urban class are mixed with the other, in differing proportions, as one would expect. The bright orange given to the coastal Marsh area occupies a slightly larger area than its equivalent does in the Minimum Distance classification and is also distributed in small patches around the Los Osos coastline, and again along the river. Thus it is probably a true condition, in that, we expect such vegetation to be more widespread. No doubt the most uncertain group of classes is spread over the hills. The categories SunLit Slope and Shadow Slope are somewhat artificial, in that they refer mostly to an illumination condition. Whereas the grass and trees classes may be a mix of lighting effects and a lighter or darker surface. The class Cleared Land is, again, a depiction of land surfaces that may support, not only thin natural vegetation or even be partially barren but also may in some places have a shadowing effect. The Grasslands is properly placed in this image but appears to spread over wider areas than indicated in several other images, so it is doubtless a valid case. The Green Vegetation category proxies well for the actual distribution of reflective organic material (in Band 4) but in this choice of class assignments, several types of growing ground cover are not singled out. Thus, elements of the golf course and the mountain crest forest are shown as "like" and are not distinguished from field crops, etc. We could tell them apart to some degree of correctness, if we had given each its own class and selected training sites.
Nearly two years after the above Supervised Classifications were generated, an occasion arose to redo the same scene using new IDRISI software that operates from Windows, Version 1, rather than DOS 3.1. In performing this Supervised Classification, we used the same Maximum Likelihood classifier with all seven TM bands and 15 classes. But, as an experiment, we decided to drop several class categories and select new ones instead. Also, we established some slightly different training site polygons for each class. In effect, we achieved an independent classification without peeking at the results, shown above, for guidance. And, instead of using the natural color scene from which to pick training sites, we used the false color image. This is the result:
(ERROR: For some reason, the Windows IDRISI does not show the 15th class in the legend. This class should be "Trees", in dark green, present mainly in the upper right corner of the class map. Also, the first legend box (black here; blue in the two other classifications above) has no label; it is not a named class but refers to the color used outside the map image as background.)
Note that for some of the classes, we assigned different colors than used in the first two maxlike classifications, which makes it rather difficult to compare the results with the earlier classifications. Nevertheless, scrolling between this and the 7-band, Supervised Classification just above, reveals differences and similarities.
In the Windows version, the two Sediment classes are combined. Also, the class, called Fields in the DOS 3.1 version, is here renamed GreenVeg, and includes fields with crops and also some natural vegetation (probably local woodlands). Both show bright red in the false color rendition. The distribution of the class Trees is similar in both classifications but is a bit more widespread in the Windows version (but harder to see because dark green and black shadows do not show contrast well). The classes Scrubland and Cleared in the DOS 3.1 version are partially represented by Scrub in the Windows version. In DOS 3.1, Urban II (focused on the Los Osos street pattern) is olive and is orange in the Windows version. In both cases, the distribution of the Urban II class pattern is much more extensive than is the real situation. Town structures or clusters of buildings do not exist in the long orange strip near the highway, nor in the lower right part of the image. Apparently, some natural surfaces, as interpreted from the true and false color composite images, give rise to signatures that resemble this urban class. In the Windows version, several very bright areas, mainly around Los Osos, have been named Sandpit. This is a guess, because they may be excavated ground or inland remnants of beach sand (although they classify as distinct from the Sand Class); only an on-site visit could ascertain a correct identity.
The point in running and comparing these two classifications is probably obvious: the precise end result is sensitive to the variables involved and the choices we made - mainly in extrapolating classes from their training sites to the identities and distribution of the selected classes, i.e., the overall appearance and accuracy of the classifications. Interpretations differ depending on the colors and other factors present in the training image, by which we choose separable classes and block efficient training sites. The number of classes, the validity (purity) of the enclosed space in the training sites (and the number of pixels in the polygons assigned to each class), the nature of a class (the Urban division is somewhat artificial and Scrub may be rather dissimilar classes or features in the real world), the colors assigned to the final map, and other considerations all contribute to differences. Once again, we emphasize the argument that field work, if logistically possible, before and after computer-based classification of an image, is the key to selecting and then checking class locations. Thus it is the best insurance for achieving a quality product. But, if an on-site visit is not feasible, a skilled interpreter can develop a fairly reasonable classification based mainly on his/her abilities in recognizing obvious ground features in the scene. The writer (NMS) has achieved believable classifications of many parts of the world without any field work, but just from his knowledge of the appearance of the common components of a landscape or land-use categories. You, the reader have the same option of scene interpretation based on your general experience; surprisingly, this often works well.
Several of the commercial satellites described in the Introduction have supplied 4-band multispectral imagery and a higher resolution panchromatic band. A check of websites on the Internet indicates that use of the highest resolution band set increases the accuracy of class/feature identification, in some cases to the 90+% level. Here is an IKONOS image of part of the town of Columbia, Missouri (where the writer lived in 1954 while teaching at the University of Missouri), and beneath it a supervised classification involving classes pertinent to evaluation of neighborhood construction; the result had a 93% accuracy level.