Likewise, li2 = Pr(M/2|Xi>*2) and /# = Pr(M/3|xf-,Z3 ) may also be found, and, of course, the sum of the three posterior probabilities equals 1.0:
Before the modified ML classifier is implemented, a series of hierarchical segmentations are carried out in order to partition the image and generate the housing stratum from which the three housing types are ultimately derived. Segmentations are applied within standard unsupervised classifica tions using the ISODATA (Iterative Self-Organizing DATA analysis) algorithm. These produce generalized urban and non-urban strata, from which the urban stratum is subdivided into built-up and non-built-up. The built-up stratum is then segmented into housing and non-housing. Using the housing stratum, prior probabilities for each housing type are calculated at the local level. This means that area proportions for each of three housing types (detached, semi-detached and terraced) are calculated for each of the census EDs that represent a settlement. In Figure 9.1, EDs (e.g., 09DDFH31) from the city of Bristol are illustrated along with their respective areal proportions of housing types. These proportions are normalized to create a probability distribution, and modified to take into account their relative size ratios (average prior probabilities are given in Table 9.2). The size ratio transformation helps to preserve the relative areal proportions of each housing type, where for instance detached housing occupies a larger physical space than terrace dwellings. Using stereoscopic aerial photographs, twenty samples of dwelling type sizes were generated and average relative size ratios between dwelling types were established. The ratios stabilized at 1 detached dwelling to 1.5 semi-detached and 1 detached to 2.25 terraced. Although
Table 9.2 Average prior probabilities for the three housing types derived from census estimates (with scaling factors)
Settlement Average census prior probabilities Low density Medium density High density Total
Bristol 0.0946 0.2786 0.6268 1.0 Swindon 0.1545 0.2659 0.5795 1.0 Bath 0.2472 0.2374 0.5154 1.0 Taunton 0.1044 0.3022 0.5935 1.0 Scaling 1.00 1.50 2.25 -
Figure 9.2 Methodology for inserting prior probabilities within a spatially segmen ted and Bayes-modified ML classification.