1 Spatial Modelling of the Terrestrial Environment - Georeferencial

208 Spatial Modelling of the Terrestrial Environment
10.2.2 A Region-Based, Graph-Topological Implementation
Although Kruger’s (1979a, b) studies provide the conceptual basis for the work presented in
this chapter, a number of modifications have been made to the original built-form connectivity
model, taking into account the type of information that might reasonably be derived
from the new generation of satellite-sensor images. For example, the land-cover parcels produced
by multi-spectral image classification do not, in general, permit individual dwellings
in a row of terraced houses to be distinguished as separate entities: in other words, several
dwellings will typically be represented as a single parcel. Thus, as a general rule, we are
unable to characterize the topological interconnections between built-form units in a builtform
array. For this reason, we limit the built-form connectivity models used here to a subset
of the complete hierarchy considered by Kruger (1979a), i.e., Constellation → Built-Form
Units (Regions) , as opposed to Constellation → Built-Form Arrays ↔ Built-Form Units.
On the other hand, the use of a parcel- or region-based representation of land cover
allows us to analyse built-form morphology (i.e., size and shape) – a feature not included
in Kruger’s original studies – which is likely to assist in the identification of different urban
land-use types (Barr and Barnsley, 1999; Barnsley and Barr, 2001). Moreover, the advent of
high-level, dynamic programming languages, which were less widely available at the time
of Kruger’s studies, means that we are able to implement an automated, graph-theoretic
system to analyse built-form connectivity.
Representation of Region Morphology and Spatial Structure. In this study, a regionbased
structural analysis system, Structural Analysis and Mapping System (SAMS), is
used to analyse the built-form constellations present in a raster land-cover dataset (Barr
and Barnsley, 1997). SAMS operates by deriving structural information about the regions
(i.e., land-cover parcels) present in these data. The boundaries of each region are identified
using a simple contour-tracing algorithm (Gonzalez and Wintz, 1987; Gonzalez and Woods,
1993), represented by using Freeman chain codes (Freeman, 1975), and stored in a Region
Search Map (RSM). The RSM can be processed to derive further information about the
structural characteristics of the observed scene, including various morphological properties
(e.g. region area, perimeter and various measures of shape) and spatial relations (e.g. region
adjacency, containment, distance and direction). This information is used to populate a
graph-theoretic data model, known as XRAG (eXtended Relational Attribute Graph), which
is defined by the heptuple:
XRAG = {N, E, EP, I, L, G, C} (2)
where N is the set of nodes (i.e., regions), such that N ≠∅, E is the set of spatial relations
between n ∈ N (e.g. adjacency and containment), EPis the set of properties associated with
the relations in E (e.g. distance and direction), I is the set of properties relating to n ∈ N
(e.g. area and perimeter), L is the set of labels (interpretations) assigned to n ∈ N (e.g.
grass, tree, urban, non-urban, etc.), G is the set of groups ‘binding’ ∀l ∈ L to the context of
a scene interpretation (e.g. the label tarmac is bound to the group land cover, while the label
residential is bound to the group land use) and C is the set stating the confidence to which
l ∈ L → n ∈ N (e.g. ‘the probability that region n belongs to land-cover class l is 0.9’).
Each region is represented by a node, n ∈ N, in the XRAG model. A relationship between
two regions n x and n y for a given relation, r i ∈ E, is represented by an edge (i.e., (n x , n y ) ∈
r i ). Thus, the node set N, in combination with the relation r i , is equivalent to a standard