Application of Pattern Recognition to Concept
Discovery in Geography
Ian Turton
Submitted in accordance with the requirements of the degree
of Master of Science
The University of Leeds, School of Geography
September 1997
Abstract
This thesis starts from the premise that geography must learn to generalise the
oods of geographic data that are now being created. This data is a by-product
of the geographical information systems (GIS) revolution that started in the 1980s.
Almost every piece of data collected by computer these days is geocoded in some
way and as such should be analysed as part of a geographical dataset. However if
geography is to survive this growth then more of the simple generalisation work,
that is commonly applied to a dataset before detailed analysis, must be passed to
computers.
This thesis takes a large dataset, the SURPOP population surfaces derived from
the 1991 census of population, and rstly uses image processing techniques to segment the surface into urban and rural areas. The urban areas are then processed
using computer vision methods to determine how like the theoretical models of the
rst half 19th century modern British cities are. The urban areas are then compared
to each other to see if there are any groups of similar towns and cities to be found.
Several urban areas are found that are similar in social structure to the theoretical
models developed earlier in the century. There are also a number of groupings of
modern British cities that can be made in terms of their social structure.
i
Acknowledgements
I would like to acknowledge the support of Professor Stan Openshaw as both my
supervisor and my employer without whom this work would not have been possible.
The surface data used in this work were generated by Ian Bracken and David
Martin, and obtained from the University of Manchester Computing Centre. They
are derived from the 1991 census of population and are Crown Copyright. I am also
grateful to the ESRC/JISC for the academic purchase of the data.
Finally I wish to express my gratitude to my wife Lesley, who having suered
through my rst thesis has now put up with the trauma of my second with good
grace throughout.
Contents
1 Introduction
2
1.1 Why Classify Cities? . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 What is a City? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Review of Urban Social Structure
8
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 The Zonal Model of Burgess . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 Assumptions of the Zonal Model . . . . . . . . . . . . . . . . 11
2.2.2 Criticisms of the Zonal Model . . . . . . . . . . . . . . . . . . 13
2.3 The Sectoral Model of Hoyt . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.1 Assumptions of the Sectoral Model . . . . . . . . . . . . . . . 15
2.3.2 Criticism of the Sectoral model . . . . . . . . . . . . . . . . . 16
2.4 Combining the Zonal and Sectoral Models . . . . . . . . . . . . . . . 17
2.5 The Multiple Nuclei Model of Harris
and Ullman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.6 The Zonal and Sectoral Models Revisited . . . . . . . . . . . . . . . . 18
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1
3 Investigation of image analysis and computer vision methods
20
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2 Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3 Image Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3.1 Low Level Image Processing . . . . . . . . . . . . . . . . . . . 22
3.3.2 Medium Level Image Processing, Initial segmentation . . . . . 27
3.3.3 High Level Image Processing, feature extraction . . . . . . . . 31
3.4 Pattern detection and classication . . . . . . . . . . . . . . . . . . . 32
3.4.1 Discussion of the Fourier{Mellin Invariant Descriptor . . . . . 34
4 Operationalisation of image processing methods
37
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2 Computing Needs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.3 Population Surface Models . . . . . . . . . . . . . . . . . . . . . . . . 38
4.4 Low level image processing . . . . . . . . . . . . . . . . . . . . . . . . 39
4.5 Medium level image processing . . . . . . . . . . . . . . . . . . . . . 43
5 Tests of pattern discovery using the 1991 GB Census of Population 51
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.2 Social Structure and the 1991 Census of
Population . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
6 Conclusions
64
6.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Chapter 1
Introduction
Openshaw (1994) argues that as the amount of data that is collected as a result
of the GIS revolution increases geographers must start to apply new methods to
these new data riches. It is no longer enough to merely catalogue the data and draw
simple maps of it. It is also no longer acceptable to use crude statistical measures
that average over a whole map or region and in so doing throw away the geographical
content of the data.
In other words geography must generalise or drown in the ood of spatial data
that has increased many fold during the 1980s and 1990s and which will continue
to grow into the next century. As the amount of data increases, increasing the
accuracy of maps will cease to tell us anything new about the areas under study.
As the amount of data grows, it becomes increasingly dicult for humans to nd
the time to study and interpret the data; the only solution is to pass more of the
routine analysis to computers leaving the researcher with more time to study the
truly interesting parts of the output.
2
3
This thesis is a rst attempt to apply these ideas to a geographical data set.
One data set will be studied in detail though the ideas and methods developed will
be applicable to many other data sets. The data set selected for this study is a
population density surface derived from the 1991 census of population by Bracken
and Martin (1989). Using this data set the aim is to take the data{poor geographical
theories of urban social structure of the rst half of the century and make use of
the data{rich environments of the 1990s to test the theories in a general and robust
manner. To achieve this pattern matching techniques used in computer vision and
other elds will be applied to raster data of population density and social and
economic variables for Great Britain.
1.1 Why Classify Cities?
This is one of the key questions that needs to be addressed in this work: is it simply a
relic of the simplistic geography of the past, where when stuck for a theory to explain
satisfactorily the growth and formation of urban areas geographers fell back on
classication to cover their lack of knowledge? Berry (1972) discusses this question
and concludes \We would never have learned anything if we had never thought how
objects resemble each other, and whether they manifest the same properties. If every
object in the world were taken as distinct and unique, our perceptions of the world
would disintegrate into complete meaninglessness. The purpose of classication is to
give order to the things we experience. We classify things so that we may learn more
about them." It is clear from this that classication must be a step towards greater
4
understanding rather than an end in itself. Simply classifying cities does not help
our understanding of urban structure, however if we make use of the urban types
discovered during the classication process to create theories and new knowledge
then it is a valuable activity.
Chapter 2 looks in more detail at how classications of cities and urban social
structure have developed over time and what these theories can tell us about the
environment that we live in. Chapter 3 contains a review and discussion of image
processing and computer vision techniques that can be usefully applied to raster
maps and other geographic datasets. Chapter 4 then shows the results of applying
these techniques to the population surfaces to \discover" the locations of urban areas
in Great Britain.
Chapter 5 then takes the locations of these urban areas and by applying the
computer vision analysis techniques described in chapter 3 investigates whether the
patterns discussed in chapter 2 can be seen in British urban areas. It also looks at
the possibilities that British urban areas show common patterns amongst themselves
that can lead to new classications of of urban areas and the possibilities of new
theories of urban development that can be derived from this new classication.
1.2 What is a City?
Clearly before it is possible to attempt to answer questions such as can cities be classied? and where are Britain's cities? it is necessary to rst answer the fundamental
question of what is a city?
5
At rst glance this seems to be a simple question: anyone looking at a map
of population density (such as gure 1.1) can point immediately to the centres of
concentration and say \that is a city!" and can equally easily point to the blank
areas and say \there is countryside". In fact this seems to be child's play, until
you ask them \why is that a city?" and \where are its edges?" How do we dene
where one city ends and another starts, for instance are Leeds and Bradford separate
cities? is Salford part of Manchester or a city in its own right?
There are three problems in dening what is an urban area and what is a rural
area.
1. The settlement continuum:
Clarke (1982) says \Towns and cities are inherently dicult to dene because
they are members of a continuum of nucleated settlements that grade into one
another ... The problems of denition arise because towns and cities may dier
from rural centres in so many dierent ways." The problem was also considered
by The United Nations (1955) who conclude \There is no point in the continuum
from large agglomeration to small clusters or scattered dwellings where urbanity
disappears and rurality begins; the division between urban and rural populations is
necessarily arbitrary."
Thus while it is clear that size is one of the dening characteristics of a town or
city any specic threshold is necessarily arbitrary and often is a result of historical
concerns.
2. The changing urban character.
In early times a town was synonymous with a market town. Once a market or
6
Figure 1.1: SURPOP Population Density of Great Britain
fair was established then a town would tend to grow around it. There would also be
a clear demarcation between the town and the surrounding rural area often in the
form of town walls. However during the 18th and 19th centuries industrialisation
led to the rapid growth both of existing towns and the formation of new towns. The
growth of suburbs during the 20th century as transport improved rst with buses
and trams and then with cars, still further blurred the boundaries of towns and
7
cities.
In the past it was possible to dene a town by the presence of certain services
or facilities such as a market, a cathedral or garrison. This is no longer possible as
even a small village will have a shop and post oce whereas many large cities now
nd that their shopping centre has relocated to a green eld site on the outskirts of
the city.
3. Ocial Designation
Ocial boundaries of urban areas are often historical and may now bear little
relationship to the current state and extent of the city or town. If an area is in decline
the ocial boundary may well encompass a much larger area than the actual area
of the city or in the case of areas of expansion the ocial area may be much smaller
than the city or in some cases the city may not be ocially recognised by the state,
for very recent new growth.
The answer that will be adopted here is to throw out any preconceived ideas
as to where is a city and where is not and allow an unbiased computer program to
make the decision for us. However the program will need some guidelines. Chapter 4
explores this in greater detail but the common features of cities are that they are
contiguous areas with a higher population density than the surrounding area with
some sort of smooth decay in population density from a central point to the edges.
Chapter 2
Review of Urban Social Structure
2.1 Introduction
Over time as a city grows dierent areas of cities become associated with dierent
types of population and this leads to systematic relationships between geographic
and social space. Bourne (1971) says \All cities display a degree of internal organisation. In terms of urban space, this order is frequently described by regularities
in land use patterns." A seasoned traveller will soon notice that while each city is
obviously dierent in its precise layout there are striking similarities between them,
for instance they will all have an area of shops and oces, usually in the centre
which is well served by transport links while residential areas tend to locate around
this area with the areas of better housing being found farthest from the centre of the
city. These observations lead to questions about how these patterns can be modelled
to allow comparisons to be made between cities and to attempt to give insights into
the growth and formation of these patterns.
8
9
Much of the dening work on these questions was undertaken by the Chicago
ecologists who where concerned with the dierences in environment and behaviour
in dierent parts of the city. From this descriptive research into behaviour in various
parts of the city grew an interest in the general structure of the city and its evolution
over time. In this work they introduced terms from the classical ecology such as
dominance, succession and invasion. The majority of this work was conned to the
study of the large industrial city of Chicago. The work of the Chicago group can
be traced back to the work of Hurd (1903) who developed several theories of urban
expansion which stressed two main methods of growth: central and axial growth.
Some may doubt the applicability of the models described below to British urban
areas, since they were developed mostly with respect to large cities in the United
States. The development of urban areas in the United States can reasonably be
considered to be signicantly dierent to the development of urban areas in Great
Britain due to dierences in planning controls and history, few cities in the US are
older then 200 years. However it must be considered that theories of urban social
structure must be broadly comparable between countries if they are to be considered
useful theories at all.
2.2 The Zonal Model of Burgess
The zonal system developed by Burgess (1925) is based solely on the central growth
element and radial expansion. This is closely linked to the general assumptions of
impersonal competition of ecological theory. The zonal model came about almost
10
as an aside in the discussion of how urban areas expand.
The innermost and smallest zone is the central business district. This is the
centre of the city's commercial, social and cultural life. This is the area of highest
land values and so can only be used by activities that can generate the prots
necessary to pay the high rents and taxes charged in this area. Thus this area
contains the retail district with large department stores and other expensive outlets.
It also contains the main oces of nancial institutions as well as expensive hotels,
civic buildings and some leisure outlets. The city's main transport terminals are
here and it has the greatest number of people moving into and out of it each day.
Therefore in terms of residential type this is a sparsely settled area with few people
being able to aord, or in fact choosing, to live in the central zone. Surrounding the
central zone in Burgess's model is the warehousing district with light industries and
possibly the market. Again this is a sparsely populated with only scattered pockets
of residents remaining.
Zone II, the \zone in transition", is the remnant of the city's rst suburban area
where originally merchants and other successful citizens lived. However as the city
has grown with businesses encroaching from the CBD the area has deteriorated and
the once ne houses have been converted into industrial units in the inner area of the
zone and subdivided into ats and bed-sits in the remainder of the zone. This is an
area of rst generation immigrants and social mists. It is a very mixed population
with high crime rates and a highly mobile population. Rents are high as landlords
make a short term prot with an eye to the expansion of the CBD into the area.
There are very few children and families except in newly arrived immigrant areas.
11
As members of the population prosper they move outward to better areas of the
city, leaving behind the elderly and less t members of the population.
Zone III is the zone of independent working men's homes, providing housing for
the families of shop and factory workers who have prospered suciently to move
out from zone II. This area is still easily accessible to the central business district
where the majority of the population work. Burgess characterised this area as
being predominately working class. All age groups are represented in this area with
traditional family forms being dominant.
Zone IV is an area of better residences, a zone of middle class population living
in large private houses or good apartment blocks. Within this zone satellite shopping centres are found to compete with the more expensive central shops. Burgess
suggests that women outnumber men in this zone.
Farthest out is zone V, the commuters' belt within a journey time of 30-60
minutes from the CBD. This is suburbia, characterised by single family dwellings.
The majority of the men work in the CBD leaving the area as a dormitory town in
the day. Burgess however points out that zone V is the least homogeneous zone of
the city being highly segregated.
2.2.1 Assumptions of the Zonal Model
Burgess was at pains to point out that the zonal model was designed as an idealised
model rather than as a particular picture of urban evolution. In Burgess (1953)
\My name has been identied with a zonal theory of growth of the city as would
be interpreted graphically if only one factor, namely, radial expansion, determined
12
city growth. ..... At no time .... have I denied the existence of other possible factors
which might also be regarded as idea constructs. For example, sectors, climatic
conditions, types of street plan, barriers (hills, lakes, mountains, rail{roads) can
each have an eect upon the formation of city structure."
The essential feature of the model is the tendency for each inner zone to expand
outward under the pressure of new population and invade the outer zones. Thus the
model depicts a dynamic process as opposed to a static picture. Burgess does however believe that at any given time it is possible to delimit the ve zones. Attempts
to apply the model to empirical city data have consistently ignored the implicit and
explicit assumptions of the model. The Burgess model assumes a constantly growing
population to drive the rapid urban growth that is required. It also assumes that
much of this increase is as a result of overseas and ethnically diverse immigration.
The model assumes that the population is disaggregated by migration experience,
ethnic background and occupation. It also assumes a particular type of economic
and political background, such that wealth and power are interchangeable. It is
implicit that there is no city or centralised planning, so that the rich may locate
where they wish and make use of their property in any way which they feel t.
The main driving force of the model is the demand for city centre locations:
this is based on the assumption that accessibility is greatest in the city centre and
declines with increasing distance. Transportation is assumed to be relatively ecient
with all members of the population being able to travel to the CBD with ease, and
with cost being a function of radial distance. The dominance of the city centre and
the decline in land values from the centre outward is very similar to the Von Thunen
13
model of agricultural land use.
Burgess appears to consider dierences in life stage to be reected entirely in
dierences in wealth. Thus the zonal variation is entirely a result of the wealthy
being able to preempt the newer and more desirable housing areas on the outskirts
of the city.
2.2.2 Criticisms of the Zonal Model
The most severe misgivings about the Burgess model are over the empirical status
of the zone as a classication device. Each zone is presented as a homogeneous
area despite the fact that zones I, II and V are said to be in-homogeneous, diering
considerably in income and ethnic groupings. Empirical tests of zonal homogeneity
have generally been negative (Timms 1971). The major problem has been in dening
the boundaries of the zones. In the model these are presented as crisp lines dividing
one zone from the next. In reality urban structures tend to vary from one type to
another through a transitional area which reects some of the characteristics of each
of the zones. Also the residential structure of a city tends to change gradually with
radial distance rather than as a series of distinct step changes as predicted by the
Burgess model.
The zonal model has been tested by many social scientists during the 1960s
(Mehta 1968), (Berry and Rees 1967). In general these studies have attempted to
t a specic model to the empirical data collected to describe the city's residential
population. However this requires a great degree of precision and the specication
of exact radii for the zones.
14
2.3 The Sectoral Model of Hoyt
The sectoral model developed by Hoyt (1939) has a much narrower focus than the
zonal model of Burgess being primarily concerned with the distribution of rental
classes. Based upon a block by block analysis of changes in a variety of housing
characteristics in 142 US cities, Hoyt concludes that: \The high rent neighbourhoods
do not skip about at random in the process of movement, they follow a denite path
in one or more sectors of the city. ... the dierent types of residential areas tend to
grow outward along rather distinct radii, and a new growth on the arc of a given
sector tends to take on the character of the initial growth of that sector."
Again the spatial expression of the model is an aside to the main thrust of the
model which is the dynamics of rental patterns. Movement of the areas of high
rent provide the main driving force of the model. As rich neighbourhoods move
outward they are replaced by intermediate and lower class groups moving into the
abandoned housing. Hoyt notes: \The high-grade residential neighbourhoods must
almost necessarily move outward towards the periphery of the city. The wealthy
seldom reverse their steps and move backwards into the obsolete houses which they
are giving up. On each side of them is usually an intermediate rental area so they
cannot move sideways. As they represent the highest{income group, there are no
houses above them abandoned by another group. They must build new houses on
vacant land. Usually this vacant ground lies available just ahead of the line of march
of the area because, anticipating the trend of fashionable growth, land promoters
have restricted it to high{grade use or speculators have placed a value on the land
15
that is too high for the low{rent or intermediate rental group. Hence the natural
trend of the high{rent area is outward, towards the periphery of the city in the very
sector in which the high{rent area started."
The high status area is assumed to have started near the CBD which provides
the employment and services for the residents of the high{rental area. It is on the
far side of the city from the factories and warehouses. This can be aected by the
prevailing wind conditions, for example many British cities have a rich area to the
west of the city since the prevailing wind is from the west, so blowing clean fresh
air into the best areas of the city and then blowing away any pollution from the
industrial area in the east.
The movement of high status populations outward from the city centre along
the main transport routes has been accompanied by changes in the methods of
transport, which have lead to more expansive settlement patterns. Therefore the
high{rental areas do not grow out in a linear fashion but form fans loosely centred
on the transport links to the city centre.
2.3.1 Assumptions of the Sectoral Model
The sectoral model was developed as an empirical model, as opposed to the zonal
model, and was intended to allow future predictions to be made. Since these decisions were of a nancial nature, the model concentrates on rental income and on
the ability to pay. The sectoral model shares many of the assumptions of the zonal
model. The model assumes a growing population with a range of commercial and
industrial activities. There is a single central nucleus and a lack of planning control
16
from government which allows competition to completely shape the development of
the city.
Hoyt's theory was developed before the wide spread use of the car as a means of
individual transport, so while it makes some reference to road transport for industry
it fails to take account of the growth of residential areas made possible by greater
transport freedom brought about by the car. Before the car, access to the city was
only easy and quick if you lived along a transport route to the centre, which leads
to the development of the sectors of Hoyt's model.
2.3.2 Criticism of the Sectoral model
It has been pointed out that the prime movers in the growth of the sectoral patterns
in the model appear to be the leaders of society. These leaders are however somewhat
indistinct as is their attraction to the rest of the residents of the city (Rodwin 1950).
The homes of these leaders are variously represented by highest rent, the high grade
districts and the most fashionable districts, however Rodwin points out that these
areas are often not synonymous. During the construction of the model Hoyt made
use of rental data since it was the most accurate available to him. The actual
relationship between rental price, prestige and income was not investigated.
Firey (1950) points out that the sectors of a city can be aected by geography,
such as the sea or a lake as well as topographic constraints on transport routes.
There are also restrictions on where suitable residential areas can be located.
17
2.4 Combining the Zonal and Sectoral Models
Berry (1965) suggests that overlaying the zonal and sectoral models would produce
a number of cells that would be remarkably homogeneous in terms of their social and
economic characteristics. Around any band there will be similar densities, tenure
types and family types, although there will be some variation in income. Along any
axis communities will have relatively similar income characteristics but the types of
family will change as you move outward from the city centre. Thus it is possible to
use a system of polar coordinates centred on the CBD to describe the socio-economic
characteristics of the population of the city. He concludes \Although the skeleton of
the city is determined by the broader regional and supra{regional forces, the esh
shows certain systematic regularities which are tightly knit into a locational system
of simultaneous concentric and axial dimensions. Segregated housing patterns are
responsible for the current inability to develop a single model of the whole covering
both spatial structure and change."
2.5 The Multiple Nuclei Model of Harris
and Ullman
Harris and Ullman (1945) argue that land use patterns do not grow from a single
central point in a city but from multiple points or nuclei. Some of these points
existed before the city began to grow, while others develop as the city grows. Nuclei
may include the original retail or market area of the city and important transport
18
links such as railway stations, ports or the airport.
The areas of the city that they recognise are similar to the ones noted by Hoyt
and Burgess but the location of these areas will be dierent in dierent cities. The
central business district will often be found near the original retail area of the city.
Warehousing and light industrial areas will develop adjacent to the CBD and along
transport links such as railways and roads. Heavy industry will locate on the outskirts of towns or where the outskirts were when the development took place, since
growth of the urban area may have overrun this area by now. Residential areas
will be found in the remaining space, with high class housing situated in the better
areas with good drainage, often on high ground and away from nuisances such as
noise and poor air quality. Lower quality housing will be forced to occupy the less
attractive areas of the city.
2.6 The Zonal and Sectoral Models Revisited
Hoyt (1964) reviews the developments in urban structure since his and Burgess's
earlier work. The major revision to the earlier work was that the car had allowed
cities to expand far further than they had previously allowed for and had allowed
people to trade longer commuting times for greater space on the outskirts of the
city.
While both of the initial models had recognised the development of some satellite
shopping areas on the periphery of cities, these areas have greatly expanded with the
increase of car ownership. The early shopping centres had been located on suburban
19
railway networks whereas the location of later developments is constrained only by
the availability of land to provide parking for cars.
He notes that the light manufacturing and warehousing that Burgess placed in
zone II of his model have now mostly moved to the suburbs, with the exception of
certain specialised industries such as garment making. In the 1980s and 1990s other
light \industries" such as computer consultancies, media and training rms can now
be found occupying this area of the city since they need to be close to the rms in
the CBD but can often not aord the high rents of the CBD. Heavy industry, where
it survives at all, is now located on the outskirts of the city since the factory workers
can now commute to the plant by car. This allows the factories to be constructed
on larger sites due to the lower land values outside the city and to escape more
stringent air controls and the higher local taxes needed by the city to support its
functions, especially with a declining tax base.
The other main change that Hoyt notes is the development of the suburbs which
were poorly developed in the 1920s and 1930s. They are now more heavily populated
and are no longer the exclusive preserve of the very wealthy. Complete communities
with their own services, schools and industries are being developed around cities,
either on green eld sites or by aggregating around an existing village or small town
which was once separate from the city that has now swallowed it.
Chapter 3
Investigation of image analysis and
computer vision methods
3.1 Introduction
There are three sections to this chapter: the rst deals with image processing techniques that are applied to process an image or map before further processing takes
place. The second looks at methods that can be used for feature extraction from
the image, and the nal one deals with how to use pattern matching to classify the
features extracted.
There are many possible denitions of image processing and computer vision,
one of the most common that will be used in this thesis is that image processing
refers to processing an image (usually by a computer) to produce another image,
whereas computer vision takes an image and processes it into some sort of generalised information about the image, such as labelled regions. However Ballard and
20
21
Brown (1982) say that \Computer Vision is the enterprise of automating and integrating a wide range of processes and representations for visual perception." They
go on to include the term image processing within this denition, there by implying
that image processing is one step in computer vision. Niblack (1986) describes image processing as \the computer processing of pictures" whereas \Computer Vision
includes many techniques from image processing but is broader in the sense it is
concerned with a complete system, a `seeing machine'." Boyle and Thomas (1988)
also suggest that computer vision is more than recognition, they also present their
`low level processing' operations as purely image processing algorithms and again
subsume image processing into computer vision.
Image processing can be subdivided in to three groups: low, medium and high
level which are usually applied in that order. Low level routines are concerned with
improving and enhancing the image, medium level routines are used to carry out
local neighbourhood operations and high level routines are used to bring together
results from the medium level routines for the whole image.
3.2 Aims
The aim of using image processing and computer vision within the context of this
thesis is twofold. First the computer must take a raster population density map of
Great Britain, process it to provide a clean image for later processes to work with,
then segment the image to nd the urban areas. A second stage must extract these
areas and use the locations of the towns and cities discovered in the rst stage for
22
classication against existing theoretical models of urban structure and also as inputs
to a classier that attempts to discover new structures within the British urban
environment. In the second stage it is important that possible matches between
an observed urban area and a theoretical template or another observed area are
not overlooked due to changes in orientation, size or possible distortions caused by
local topology. It is therefore necessary that the second stage of the process makes
corrections for these dierences without losing sight of the underlying structure of
the area.
3.3 Image Processing
3.3.1 Low Level Image Processing
Low level image processing is concerned with cleaning and improving the quality of
the image before later operations are applied to start extracting information from
the image.
One of the main causes of poor image quality is high frequency noise in the
image. In the specic context of the population density and other raster maps used
in this thesis high frequencies are caused by small variations in the variable surface.
The simplest method of removing these unwanted frequencies is to simply average
the values of a pixels surrounding neighbours and replace the pixel with this value.
This is a relatively unsophisticated technique and takes no account of the position
of the pixels.
Figure 3.1 shows an example of this, the numbers at the top of the gure represent
23
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Figure 3.1: An example of averaging
an input image and the numbers at the bottom of the gure represent the output
image. Each cell in the output image is the average of the three by three block
around its position in the input image. It can be seen that the overall pattern of
the image is retained but that the variation between a pixel and its neighbours is
reduced. It should also be noted that the output image is one pixel smaller in each
direction than the input image due to the need to have a full three by three block for
each output pixel. These cells can either be ignored or lled with zero in the output
image. An alternative would be to pad the input image with zeros around the edges
which would lead to a gradual lowering of the values at the edges of the output
image. This could be benecial in some contexts such as fourier transformation
where it is usual to apply a windowing function to the input to deal with boundary
conditions.
24
Another relatively simple process is the aggregation of pixels. In this process
groups of neighbouring pixels are added together to create an image with fewer
pixels. This causes some smoothing of the image and can be used to make a very
large image easier to handle. In the case of the population data it also lls in some of
the \holes" found in urban areas caused by parks or factories where the population
density goes to zero at a sharp boundary. This sort of sharp transition causes
problems for the medium level routines outlined in the next section. Figure 3.2
shows an example of this process. In aggregation a block of three by three (or
larger) pixels in the input image are summed and placed in the output image. This
is then repeated at the next non{overlapping block in the input image. The resulting
output image is one third the size of the input image in both the horizontal and
vertical directions, or the output image can be can be considered to be the same size
as the input image but with pixels that are three times the size of the input image,
depending on the context of the data under consideration. This process diers from
averaging in that the number of output pixels is substantially less than the input and
that each input pixel only contributes to one output pixel rather than in averaging
where each input pixel contributes to nine output pixels.
Another process that is applied commonly to images is a low pass lter to remove
any high frequencies from the image. A low pass lter can either be implemented in
the frequency domain by simply setting high frequencies to zero before the image is
transformed back to the space domain, or by convolution with a smoothing template.
Convolution in this context is carried out by taking a template or two dimensional
array of values and placing it over the image step by step and at each step multiplying
25
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Figure 3.2: An example of aggregation
the elements in the template with the corresponding element in the image and
summing all the products to give a new value. If T (x; y) is the template (n m)
and the image is I (X; Y ) of size (N M ) then convolving of T with I is represented
by:
T I (X; Y ) =
Xn= m=X
2
2
i=?n=2 j =?m=2
I (X + i; Y + j )
(3.1)
Technically this is the cross{correlation term rather than the convolution term which
would be given by:
T I (X; Y ) =
Xn= m=X
2
2
i=?n=2 j =?m=2
I (X ? i; Y ? j )
(3.2)
However the term convolution is used to refer to the rst (3.1) and not the second
equation in nearly all image processing literature.
26
Template
-1 0
1 0
1
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4
Image
Result
2 1 4 4
1 1 0 -1 *
3 1 3 6
1 1 0 0 *
4 1 3 2
1 1 0 1 *
5 1 2 1
* * * * *
Figure 3.3: An example of convolution
An example of this operation is shown in gure 3.3, an edge detection template
is shown on the left of the gure. This template is then applied to the image in the
centre to give the result shown on the right. The template is rst located over the
top left hand cell of the image and each element of the template is multiplied by
the corresponding cell of the image, these values are summed and the sum placed
in the top left hand corner of the output image. The template is then moved to the
right by one cell and the process repeated. The output image is one cell smaller
than the input image in each direction since the template can not be moved o the
input image.
In the context of smoothing a template like the one shown in gure 3.4 would
be convolved with the image. This replaces the value of the image at the centre
of the template with the sum of the surrounding pixels while giving more weight
to the pixels that are nearest the central pixel. As gure 3.4 shows this increases
the values of all the output pixels which may cause problems for later processing.
If this is the case then the output pixels can be divided by the sum of the cells in
the smoothing template (shown on the right of gure 3.4). This type of smoothing
operation is similar in eect to averaging, which can be considered to be a special
case of convolution with a three by three template of all ones. Again the output
image is one pixel smaller than the input along each edge. However the weighting
27
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111 128 165 194
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Figure 3.4: A typical smoothing template
factors used in the template reduce the blurring of features in the original image,
since while each input pixel still contributes to nine output pixels the amount by
which it contributes varies depending on its distance to the position of the output
pixel.
In all these examples a three by three block is used for convenience and there is
no reason why larger templates could not be used.
3.3.2 Medium Level Image Processing, Initial segmentation
Medium level image processing techniques are usually concerned with modifying
the image to start to determine which are the areas of interest where high level
segmentation techniques can be applied most protably. In general they concentrate
on nding edges and regions with in the image.
28
The simplest segmentation technique is to threshold the image. This is simply to
set all values below (or above) the threshold to zero and all pixels with a value above
(or below) the threshold at one. The areas of interest can be taken to have values
above or below the threshold depending on the context. This technique is very simple
but can be very eective if the image has a simple structure such that the dierence
in pixel values between two areas, one of which is of interest and the other which is
not, is quite large. This is particularly true in applications such as text recognition
where the text is black and the paper is white. In the detection of urban areas the
distinction between urban areas with their high population density and rural areas
with low population density once a suitable threshold value has been determined,
can be carried out easily. However it can be dicult to select the best threshold
value without some experimentation and the application of domain knowledge. The
operation outlined above is known as absolute thresholding: an alternative method
is part thresholding, where pixels with values below the threshold are set to zero
and pixels above the threshold are left unchanged.
Another technique that is of relevance to the detection of urban areas with a
population density surface is the determination of the gradient of the surface. This
is analogous to the dierentiation of a mathematical function. To determine where a
maxima of a function are, the function can be dierentiated. Where dy=dx is zero the
function is either at a maximum, minimum or a point of inection. To distinguish
between these the function is dierentiated again to give the second dierential
(d y=dx ) which is negative at maxima. A similar process can be applied to images.
2
2
The usual way to calculate a gradient of an image is to apply a pair of Sobel lters
29
X Gradient
lter
-1 0 1
-2 0 2
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Y Gradient
lter
-1 -2 -1
0 0 0
1 2 1
Figure 3.5: Sobel lters
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Figure 3.6: First derivative of an image using a Sobel lter
(see gure 3.5) to the image. Figure 3.6 shows an example of how this pair of lters
are convolved with an image to give an X and Y gradient, which are then combined
by using the sum of the absolutes to give the gradient of the image.
In the upper left hand section of the gure we can see the input image which
contains a peak in the centre of the image. In the upper right hand corner we see
the Y or vertical gradient of the input image. The lower left hand section contains
the X or horizontal gradient of the image. In the lower right hand corner is the sum
of the absolutes of the two gradients. Both the horizontal and vertical gradients
show a zero crossing at the centre, however this information is lost in the sum of
the absolutes of the gradients.
To discover if the zero crossings found in the gradients are maxima or minima
it is necessary to calculate the second derivative of the image. This is done by
30
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Figure 3.7: Second derivative of the image in gure 3.6
applying the same Sobel templates to the X and Y gradients. Figure 3.7 shows this
process; the X Sobel lter is applied to the horizontal gradient in gure 3.6 and the
Y Sobel lter is applied to the vertical gradient. In both cases the second derivative
is negative indicating that the original input image was a maximum. The two second
derivatives can be combined by summing the absolutes of the two gradients. If the
sign of the output is required then the sign of the sum can be set to the sign of the
largest absolute value of the two gradients.
By combining the information obtained from the two steps in the gradient process
peaks can be detected. Areas that have a low gradient and a high negative second
derivative are easily selected after processing; thresholding can be applied to limit
the areas selected.
31
3.3.3 High Level Image Processing, feature extraction
High level image processing operations are used to take an image that has been
processed using low and medium level processing to give areas of interest and to
convert these areas of interest into well dened regions that can be used for further
investigation.
Once areas of interest have been identied in the image or map it is usual to
convert the image into a bit map with areas of interest valued at one and the
remainder of the image set to zero. This type of image can be processed in a
variety of ways; one of the most common ways is to label the regions in the image
by assigning each area a unique identication label. There are also a variety of
more complex methods that can extract basic shape information from the processed
image.
Area labelling is a relatively simple operation that splits a segmented image into
distinctly labelled areas. The image is scanned row by row to nd the rst lled
pixel and then the output image is labelled as far to the right and left of that pixel as
possible while the input image is zeroed. Then the labelled area is scanned from left
to right checking for connected pixels above and below the line. When a connected
pixel is found the procedure is repeated recursively starting from the connected
pixel. This recursive procedure is continued until the whole area has been labelled
and there are no more connected pixels. Then scanning recommences to nd the
next area in the input image to be labelled.
A more complex technique is to detect basic shapes within the image, which is
32
known as a Hough transform (Low 1991). At its simplest the Hough transform can
be used to detect straight lines from edges detected in an earlier processing step.
If the pixels detected fall on a straight line then they can be expressed by the
equation:
y = mx + c
The basis of the Hough transform is to translate the points in (x; y) space into (m; c)
space using the equation:
c = (?x)m + y
Thus each point in (x; y) space (i.e. the image) represents a line in (m; c) space.
Where three or more of these lines intersect a value can be found for the gradient
(m) and intercept (c) of the line that connects the (x; y) space points.
The Hough transform can be expanded to consider circles by transforming the
(x; y) space into a \circle centre" space, and even to arbitrary objects providing that
their shape and orientation are known before hand. However this assumption often
does not hold for the type of general object detection being attempted here.
3.4 Pattern detection and classication
Once features have been extracted the process moves on to the detection of patterns
within the features and the classication of the features discovered.
To classify patterns successfully it is essential to remove the eects of scale
changes, rotations and translations. For instance it is required to classify all cir-
33
cles regardless of their size; a rectangle should be recognised and classied as a
rectangle regardless of its orientation.
To achieve this aim it is possible to make use of many techniques that are based
on template matching. This technique takes a pattern template that is being sought
in the image and compares it to the image making use of a metric such as the sum
of the absolute errors or the sum of the square of the errors between the template
and the image. When an image closely resembles the template then these measures
will be small whereas if the template is very dierent from the image then the error
measures will be larger.
There are many problems that have to be overcome to make this technique work
well in a general case. For instance if the pattern to be detected is non-symmetric
then consideration must be taken as to how to compare the template in dierent
orientations or to preproccess the image in such a way that the asymmetry is always
in the same orientation (Schalko 1989). It is also necessary to consider the eects
of scaling on the image under consideration since it is nearly always important to
recognise the target pattern regardless of its size.
Many authors have investigated the problems of rotation, scaling and translation
invariant systems of template matching. All the systems considered apply some
sort of transformation to either the image, the template or both to correct for
these eects before attempting the matching process. For instance Yuceer and
Oazer (1993) recommend a method that transforms the image under consideration
to reduce the number of templates to be considered to two. However they admit
that there are some problems to be overcome in the process as a certain amount
34
of distortion is introduced to the image as a result of the transformation process.
Perantonis and Lisbon (1992) discuss how to make use of a neural net to perform the
template matching process with scale, rotation and translation invariance. There
are some problems with this technique as it requires a dierent neural network to be
constructed for each template to be matched, which must be trained using as many
distorted templates as possible.
This study will be restricted to the implementation of the Fourier{Mellin transform. The approach consists of calculating the Fourier{Mellin Invariant (FMI) for
each image to be matched and then correlating the FMI descriptors. A high correlation indicates that the two images being compared are similar. Since the FMI is
rotation, scale and translation invariant there is no need to carry out any extensive
pre{processing before classifying images (Schalko 1989).
3.4.1 Discussion of the Fourier{Mellin Invariant Descriptor
Consider an image b(x; y) which is a rotated, scaled and translated copy of a(x; y),
b(x; y) = a([cos x + sin y] ? x ; [? sin x + cos y] ? y )
0
0
where is the rotation angle, the scale factor, and x and y are the translation
0
0
osets. The fourier transforms, B (u; v) and A(u; v) of b and a respectively are
related by:
B (u; v) = e?i
u;v) ?2 jA( ?1[u cos + v sin ]; ?1 [?u sin + v cos ])j
b(
35
where b(u; v) is the spectral phase of the image b(x; y). This phase depends on the
rotation, translation, and scaling, but the spectral magnitude
jB (u; v)j = ? jA(? [u cos + v sin ]; ? [?u sin + v cos ])j
2
1
1
(3.3)
is invariant for translations.
Equation 3.3 shows that a rotation of image a(x; y) rotates the spectral magnitude by the same angle and that a scaling of scales the spectral magnitude by
? . However at the spectral origin (u = 0; v = 0) there is no change to scaling or
1
rotation. Rotation and scaling can thus be decoupled around this spectral origin by
dening the spectral magnitudes of a and b in polar coordinates (; r).
Ap(; r) = jA(r cos ; r sin )j; 0 < 2; 0 r < 1
Bp(; r) = jB (r cos ; r sin )j; 0 < 2; 0 r < 1
which leads to
Bp(; r) = Ap( ? ; r=)
2
Hence an image rotation () shifts the image along the angular axis, and a scale
change () is reduced to a scaling along the radial axis and magnies the intensity
by a constant ( ). This scaling can be further reduced by using a logarithmic scale
2
for the radial coordinate:
36
Apl(; ) = Ap(; r)
and
Bpl(; ) = Bp(; r) = Ap( ? ; ? )
2
where = log(r) and = log(). This leads to both rotation and scaling now
being simple translations, so that taking a fourier transform of this polar-logarithmic
representation reduces these eects to phase shifts, so that the magnitudes of the
two images are the same.
This is known as a Fourier{Mellin transform and can be used to compare a single
template against an unknown image which will be matched even if it has undergone
rotation, scaling or translation.
Chapter 4
Operationalisation of image
processing methods
4.1 Introduction
This chapter rst discusses the SURPOP population surfaces of Great Britain and
then takes some of the methods discussed in chapter 3 and applies them to the
population density surface of Great Britain. The aim of this chapter is to segment
the population surface into urban and rural areas. Once this process has been
satisfactorily carried out the results can be analysed for evidence of urban social
structure in chapter 5.
37
38
4.2 Computing Needs
The computational requirements of the methods discussed in this chapter are modest, a large workstation (such as a Sun Ultrasparc system) is suitable for the all
the tasks undertaken in this chapter. The main computing constraint encountered
is the large amount of disk space required to store the data les used and to store
intermediate results. However the work described in chapter 5 while still possible on
a workstation really requires access to a high performance compute facility to make
the run times of the tasks reasonable. In this case the programs were developed
and tested on small problems on a workstation and then transfered to the Cray
T3D in Edinburgh for the production runs. To facilitate this transfer the programs
were developed using FORTRAN90 and converted to High Performance FORTRAN
(HPF) as the easiest route to parallelisation.
4.3 Population Surface Models
The data used in the dissertation are the population surfaces developed by Bracken
and Martin (1989). Their work concentrated on the use of zone centroids with
associated population counts though other methods exist such as the pychnoplactic
method of Tobler (1979). In the case of the 1991 census of population the population
weighted centroid of an enumeration district (ED) (the smallest areal unit of the
census) is used as a starting point to redistribute the population of the ED into
a regular grid of cells. The sum of these cells is constrained to be equal to the
population total associated with the centroid, that is no population is lost or created
39
by the method.
Each centroid was visited in turn by the algorithm and a linear distance decay
function calculated based on the local density of centroids, such that it falls o more
quickly in a region comprising small zones and more slowly in a rural area with larger
zones. Each cell is then allocated a weight based on the decay function and it then
receives this proportion of population from the centroid. For other census variables
a similar process is carried out which also preserves the totals.
For the SURPOP surfaces the grid size is 200 metres square, which gives a potential matrix of 22,750,000 cells. However the population surface for Great Britain
is much sparser than this with only 369,174 cells being populated.
4.4 Low level image processing
The rst step in the processing of the population density surface is to smooth out
the \holes" in the 200 metre resolution data. Figure 4.1 shows the city of Leeds at
a 200m resolution. There are areas where the population density is either zero or
very low. Such areas are often caused by the central business district in the centre
of the city, by parks and open spaces around the city and by linear transport and
geographic features such as roads and rivers.
To attempt to remove these \holes" several of the methods discussed in chapter 3
were applied rst to the test area of Leeds and then to the whole country.
The rst technique applied was averaging which can be seen in gure 4.2. As
can be seen there are still \holes" in the population density surface which would
40
Figure 4.1: Population Density of Leeds at 200m resolution with roads overlaid
cause problems for medium level techniques applied later. There are also some
problems with storing the whole of Great Britain at a resolution of 200 metres,
since this would require matrixes of 6500 by 3500, which while not insurmountable
does require a machine with very large quantities of memory. There are methods
that could be used to take advantage of the sparsity of this matrix, however there
are many computational advantages to storing the data as a full, at matrix. There
is always a trade o between computation and memory in tasks of this nature and
in this instance it was felt that the reduction in resolution of the data set was
41
acceptable for the task in hand.
Figure 4.2: Averaged Population Density of Leeds at 200m resolution
Another technique described in chapter 3 is that of aggregating, this is the equivalent of changing the scale or resolution of geographic data. The examples in chapter 3 used a base square of side three for the aggregation, however in the case of
the SURPOP data it makes more sense to use a base of side 5 to convert the 200
metre resolution data to a grid of 1 kilometre. As can be seen in gure 4.3 while the
central business district is still visible many of the smaller \holes" have been lled
in by the aggregation procedure. This procedure also has the advantage that the
42
matrix required to store the surface for the whole of Great Britain is now reduced
to 1300 by 700 which reduces memory problems and processing times accordingly.
Figure 4.3: Population density of Leeds at 1km resolution
43
4.5 Medium level image processing
The next step is to apply some of the medium level techniques discussed in chapter 3
to select which parts of Great Britain are urban areas. This requires a technique that
can take the population density surface of Great Britain (gure 4.4) and segment it
in to areas of high population and low population.
Figure 4.4: GB Population Density
The rst technique that was tried was thresholding where any cell with a value
below the threshold is set to zero. Figures 4.5, 4.6 and 4.7 show the population surface after thresholding at 2000 people/km , 4000 people/km and 8000 people/km .
2
2
2
Figure 4.5 retains the most areas but has picked out many small peaks from the sur-
44
face that cannot really be considered to be urban areas. Figure 4.6, with a threshold
of 4000 people/km , has selected a smaller number of areas but these areas are not
2
complete with new holes being introduced into the urban areas by the thresholding
process. Finally gure 4.7 has successfully located part of London and some small
areas in the Midlands but clearly the threshold has been set too high to capture the
full range of urban areas in Great Britain.
Figure 4.5: GB Population Density, thresholded at 2000 persons/km
2
45
Figure 4.6: GB Population Density, thresholded at 4000 persons/km
2
46
Figure 4.7: GB Population Density, thresholded at 8000 persons/km
2
47
140
120
100
Count
80
60
40
20
0
-350
-300
-250
-200
-150
2nd Derivative
-100
-50
0
Figure 4.8: Number of points having 2nd derivative values for the whole map
The second technique to be applied to the population surface was to take the
second derivative of the population surface. This makes use of the fact that, following
aggregation, the surface is relatively smooth and that urban areas are maxima of
the surface. This means that no assumptions about the maximum of population
density of the urban area are required and that both large cities and smaller towns
can be detected by the same process.
As can be seen in gure 4.9 a range of city sizes from London to Aberdeen can be
seen, in the map of the second derivative. This gure was constructed by calculating
the second derivative of the population density surface as described in chapter 3 and
then applying a threshold that removed all cells with a value greater than -45. This
threshold was chosen as it is the lowest point on a histogram of second derivative
48
values for the map (see gure 4.8).
Figure 4.9: Second Derivative of GB Population, thresholded at -45
Once this map had been created a set of 129 urban areas was dened using
the area labelling method described in chapter 3. The next step was to convert
the boxes extracted and to determine which town was within the box. A gazetteer
sorted by population size was used in conjunction with a point in polygon program
to determine the largest town in each box. The output was then modied by hand
49
where two large urban areas had be conglomerated by the exaction program, for
example Leeds and Bradford are a single output box, but only Leeds was inserted
by the point in polygon method, so Bradford was inserted by hand. Table 4.1 gives
a list of the urban areas shown in gure 4.9. Most of the urban areas selected by
this method are single distinct locations, however some are connurbations formed by
the merging of two large towns or cities, such as Birmingham and Wolverhampton
and Leeds and Bradford.
Any area with an area of less than one kilometre square was eliminated from
the study since it was felt that these areas would be too small to show any internal
structure even at the 200 metre resolution. Bounding boxes for each area were then
calculated so that data could be extracted at a 200 metre resolution for the urban
areas. Analysis of these datasets is discussed in chapter 5.
50
Table 4.1: The 129 urban areas extracted from the population surface
Aberdeen
Aldershot
Barrow in Furness
Basingstoke
Birkenhead
Blackpool
Bracknel
Burnley
Cardi
Chelmsford
Chestereld
Corby
Crewe
Dewsbury
East Kilbride
Ellesmere Port
Gateshead
Gravesend
Guildford
Harrogate
Hemel Hempsted
Hull
Leeds{Bradford
Leamington Spa
London
Maccleseld
Manchester
Milton Keynes
Newport
Nottingham
Peterborough
Portsmouth
Reading
Rotherham
Scunthorpe
Slough
Southport
Staord
Stoke on Trent
Swindon
Wakeeld
Widnes
Worcester
Accrington
Aylesbury
Barry
Bath
Birmingham{Wolverhampton
Bolton
Brighton
Bury
Carlisle
Cheltenham
Coatbridge
Coventry
Darlington
Doncaster
Eastbourne
Exeter
Glasgow
Greenock
Halifax
Hartlepool
High Wycombe
Ipswich
Leicester
Licheld
Lowestoft
Maidenhead
Manseld
Motherwell
Northampton
Nuneaton
Peterseld
Preston
Redditch
Runcorn
Sheeld
Southampton
St Albans
Stevenage
Sunderland
Torbay
Warrington
Wigan
Worthing
Airdrie
Barnsley
Basildon
Bedford
Blackburn
Bournemouth
Bristol
Cambridge
Chatham{Gillingham
Chester
Colchester
Crawley
Derby
Dundee
Edinburgh
Farnborough
Gloucester
Grimsby
Harlow
Hastings
Hudderseld
Kidderminster
Leigh
Liverpool
Luton
Maidstone
Middlesbourgh
Newcastle
Norwich
Oxford
Plymouth
Ramsgate
Rochdale
Scarbourgh
Skipton
Southend
St Helens
Stockton{on{Tees
Swansea
Tunbridge Wells
Weston{Super{Mare
Woking
York
Chapter 5
Tests of pattern discovery using
the 1991 GB Census of Population
5.1 Introduction
In this chapter the high level pattern detection methods of chapter 3 are applied to
the urban areas that were extracted from the population density surface in chapter 4 to attempt to rstly detect the theoretically dened patterns of urban social
structure as discussed in chapter 2 and secondly to discover if there are groups of
cities in contemporary Britain that exhibit similarity in terms of social structure.
51
52
5.2 Social Structure and the 1991 Census of
Population
Before any patterns of social structure can be considered it is necessary to determine
a variable or series of variables available in the 1991 census of population that can
be considered to be a proxy for social status.
There have been many attempts of recent years as to what constitutes deprivation
both for an individual and for an area, and how best to measure this using variables
that are collected in the censuses of population. It is generally recognised that
it is important to avoid focusing on groups who are venerable to deprivation but
not of themselves deprived. The question also arises are the deprived always poor?
or are the poor always deprived? (Townsend and Gordon 1991). There has also
been considerable work carried out on the links between deprivation and ill health
(e.g. Campbell, Radford and Burton (1991), Morris and Cairstairs (1991), Jarman
(1984)). This study however requires a less specic denition since a proxy for
social class is required rather than a specic indicator of deprivation. So for the
purposes of this study it was decided to use a combination of local authority rented
households (gure 5.1), unemployment (gure 5.2), overcrowded households (more
than one person per room) (gure 5.3) and households lacking a car (gure 5.4) and
lacking central heating (gure 5.5).
For example gure 5.1 shows the distribution of local authority housing in Leeds.
The surface has been normalised so that the highest cell value is 100 and the remainder are scaled relative to the value of that cell. The darkest cells are the highest
53
Figure 5.1: Local Authority Renting Surface, 200m resolution. Leeds
with lighter areas being lower and white being areas with no population. A similar
scheme is used for the remainder of the gures. The actual values of the indicator
are not important since the absolute value of the cells only contributes a DC term
to the rst FFT of the FMI calculation. In all cases the small triangular cells are an
artifact of the GIS used to create the gures and are not real features of the dataset
or the analysis.
To generate a pattern of the social structure of Leeds (and for the other selected
urban areas) the normalised variables are added together to give a single \deprivation" variable. This can be seen for Leeds in gure 5.6. The pattern can be clearly
seen with the concentration of low social status seen to the north east of the city
centre and a smaller centre of low status seen in the Headingly area to the north
west of the centre.
54
Figure 5.2: Unemployment Surface, 200m resolution. Leeds
Figure 5.3: Overcrowding Surface, 200m resolution. Leeds
55
Figure 5.4: Households Lacking a Car Surface, 200m resolution. Leeds
Figure 5.5: Households lacking central heating Surface, 200m resolution. Leeds
56
Figure 5.6: Social Structure of Leeds, see text for details
57
Figure 5.7: Bounding boxes of the selected urban areas of Great Britain
The \deprivation" variable surface was then created for each of the 129 urban
areas extracted in chapter 4 (gure 5.7). Once this operation was completed the
Fourier{Mellin invariant transform was calculated for each urban area as described
in chapter 3.
The rst step for the pattern recognition exercise was to investigate the theoretical patterns of urban social structure discussed in chapter 2. This was undertaken
58
Figure 5.8: Three synthetic cities used for pattern detection: a) Simple radial decay;
b) Stepped radial decay; c) Sectoral Model
by creating synthetic patterns that matched the structures that were predicted by
theory. Figure 5.8a shows a simple radial decay from high deprivation in the centre
to low deprivation at the outskirts, gure 5.8b shows a stepped radial decay pattern
as proposed by Burgess (1925) and gure 5.8c shows one of the sectoral models used.
Sectoral patterns with 4, 6 and 8 sectors were used, as discussed by Hoyt (1939).
Both the combined radial{sectoral model of Berry (1965) and the multiple nuclei
model of Harris and Ullman (1945) are ignored here. Berry's theory is impossible
to model using the simple single variable approach used here, as it requires both
income and family type to be changed. Harris and Ullman's model is a descriptive
model and as such is not amenable to being reduced to a single example pattern
that could be used as a template in the pattern recognition process. For each of the
synthetic patterns used the Fourier{Mellin invariant transform was calculated.
The next step was to discover which, if any, of the selected urban areas had
any similarity with the theoretical models by calculating the root mean square error
between the FMI of each urban areas and each theoretical pattern.
The results of this process were then ranked by level of similarity. It was found
59
that the stepped radial decay model was most similar to any of the urban areas
tested, but that the simple linear decay model was also similar to a similar group of
urban areas. These towns and cities are listed in table 5.1. The gure in brackets
that follows each town name is the level of similarity between that town and the
model. As can be seen the same towns can be seen to match the stepped and
linear models of radial decay although the levels of similarity are lower for the linear
models compared to the stepped model. This is to be expected due to the similarity
of the two theoretical models. However the sectoral model is similar to a very
dierent group of towns and the levels of similarity are much worse than for the
radial models.
The towns that are most similar to the radial models all tend to be small, inland towns, the exceptions being Doncaster, Scarbourgh and Corby. It seems likely
that the majority of these towns grew slowly around markets before the industrial
revolution and have retained their compact shape since.
In contrast, the sectoral towns are larger industrial towns and also include a
number of seaports (Bristol, Weston{Super{Mare, Hull, Plymouth, Aberdeen and
Cardi). There is a possibility that this was caused by the similarity of a half radial
model to a sectoral model. This possibility was tested by calculating the cross
correlation of a half radial model with the sectoral models and the radial model.
The sectoral model had a correlation coeciant of 9.20 with the half radial model
while the radial model had a correlation coeciaent of 5.93. If the correlation was
spurious it would have been expected that the sectoral model would have been more
similar to the half radial model than the radial model was to the half radial model.
60
Table 5.1: Towns and cities ranked in order of similarity to theoretical models,
the number in brackets after the name is the correlation coecient and the second
number in the sectoral group is the number of sectors in the model matched.
Stepped Radial
Decay Model
Skipton (0.43)
Corby (0.44)
Harrogate (0.46)
Doncaster (0.49)
Blackburn (0.51)
Colchester (0.52)
Scarbourgh (0.56)
Chestereld (0.57)
Gateshead (0.57)
Redditch (0.58)
Wakeeld (0.59)
Maccleseld (0.60)
Linear Radial
Decay Model
Corby (0.48)
Skipton (0.50)
Harrogate (0.54)
Doncaster (0.57)
Blackburn (0.59)
Colchester (0.61)
Scarbourgh (0.64)
Redditch (0.65)
Gateshead (0.66)
Chestereld (0.67)
Wakeeld (0.67)
Maccleseld (0.68)
Sectoral
Model
Sheeld (3.80) 8
Leicester (3.28) 8
Coventry (3.83) 8
Nottingham (3.97) 6
Bristol (4.13) 4
Weston{Super{Mare (4.23) 4
Derby (4.35) 8
Hull (4.36) 4
Bury (4.39) 8
Plymouth (4.40) 6
Aberdeen (4.42) 6
Cardi (4.50) 8
Therefore the patterns are really sectoral and it is probable that their location on
the sea has forced a more sectoral growth pattern since growth is constrained to be
away from the sea and also that seaports are more likely to require distinct transport
routes to their hinterland. The remaining industrial towns in the sectoral group are
also likely to have developed strong transport links to allow both the import of raw
materials and the export of nished goods to the surrounding areas.
To investigate the hypothesis that urban areas in Great Britain show similarity
amongst themselves the root mean square errors between each of 129 selected areas
and all the other areas were calculated. Then for each town or city it is possible
to select the other urban areas that the most similar to this town. From these lists
it is possible to determine groups of towns and cities that are more similar to each
other than to other groups.
The seven groups with the highest internal similarity are shown in table 5.2.
61
In each group the largest dierence in similarity between two urban areas within
the group is 0.5 and in most cases is much smaller. Therefore it can be seen that
the similarity levels within these groups is much smaller than the levels reported in
the experiment above that compared theoretical models and urban areas where the
lowest level of similarity found was 0.43.
Group 1 contains mostly small inland towns with the exception of Scarbourgh
which is on the coast and Chester which is larger than the remainder. The group
appears to be a mix of (ex{)industrial towns (Corby, Maccleseld), and towns where
service industries predominate (High Wycombe and Skipton).
Group 2 is a more homogeneous group being predominately towns that have
grown up around a single industry: Motherwell and steel, Grimsby and shing,
Runcorn and chemicals, Barnsley and coal. The exceptions to this are St. Albans
and Oxford, although Oxford does have a car manufacturing area on the outskirts
of the historic town.
Group 3 is a mixture of new towns (East Kilbride and Bracknell) which were
either planned or underwent less structured but rapid growth in the 1980s, ports
such as Lowestoft, Ellesmere Port and Hastings, and northern manufacturing towns
(Accrington, Crewe, Manseld). The common feature seems to be that all the towns
in this group under went some sort of rapid growth at some time in their history.
Group 4 seems to be a very mixed group of towns with no common feature
readily apparent, whereas group 5 is a group of larger towns and cities though
none of them is the largest in its immediate area. They are also all towns with
major railways passing through them which may account for the similarity of social
62
structure between them.
Group 6 is a grouping of smaller towns which have not experienced the rapid
growth of some of the other groups but that have grown steadily from markets and
ports that date back to medieval times. The only exception to this is Warrington
which is a major industrial centre.
Group 7 is the smallest group and comprises cities that were extensively rebuilt
after the second world war; they are also all transport nodes and may have had their
development shaped by these two factors.
63
Table 5.2: Groups of similar urban areas
Group 1
Airdrie
Woking
Maccleseld
Aylesbury
Chester
High Wycombe
Corby
Scarbourgh
Harrogate
Skipton
Redditch
Aldershot
Group 4
Dundee
Preston
Reading
Northampton
Newport
Peterseld
Ipswich
Wigan
Lowestoft
Group 7
Cardi
Portsmouth
Coventry
Farnborough
Nottingham
Group2
Motherwell
Grimsby
Scunthorpe
Stevenage
Barrow{in{Furness
Runcorn
Leamington Spa
Bedford
Barnsley
Chestereld
St Albans
Oxford
Group 5
York
Darlington
Hartlepool
Edinburgh
Gateshead
Carlisle
Group3
East Kilbride
Southport
Bath
Accrington
Crewe
Lowestoft
Bracknell
Hastings
Basingstoke
Ellesmere Port
Manseld
Halifax
Group 6
Aberdeen
Peterseld
Preston
Warrington
Reading
Swansea
Northampton
Dewsbury
Leicester
Peterborough
Chapter 6
Conclusions
The aim of this thesis was to investigate the potential for the use of computerised
generalisation to the problem of large geographic datasets. It sought to demonstrate that image processing methods that had been developed for the use of other
disciplines could be successfully transfered to geography and to investigate the use
of computer vision methods in the specic context of the social structure of urban
areas.
The rst step was demonstrated in chapter 4 which showed how, after some
suitable preprocessing of the raster dataset, the SURPOP population surface could
be successfully segmented into urban and rural areas. This led to the extraction of
129 urban areas for Great Britain. The second stage was discussed in chapter 5.
This showed how the urban areas of Great Britain could be compared to theoretical
models of social structure that were developed predominantly in the United States.
It should also be noted that this method of analysis allows the researcher to ignore
many of the problems that have occurred in previous statistical studies of social
64
65
structure, such as where is the centre of a city? where are the boundaries of the
city? How wide should the rings in the model be? and such like.
Therefore, in conclusion, it appears that large geographical datasets can be processed by computer to extract both simplications of the dataset and to carry on
beyond this point to extract new concepts which can lead to new theory formulation with relatively little input from the human researcher. This process, if widely
adopted, could prevent geographers drowning in the sea of new data that is being
collected both by industry and new satellites every day.
6.1 Future Work
In the future it is hoped to carry on the work described in this thesis in a variety of
ways. The primary area of urban social structure is an interesting and useful area
of geography. It would be useful and interesting to revisit the results produced in
chapter 5 and make use of developments in the eld of neurocomputing to classify
the British cities found. One possible method that could be of relevance here is
the Kohonen self organising map (Openshaw and Turton 1996). The use of this
technique would allow a more objective classication of the urban areas, it might also
be useful to use several individual variables rather than the collapsed \deprivation"
variable used. This would obviously increase the compute times required for the
work to as several FMI transforms would be required for each individual area to be
studied as well as the extra data storage.
On a more general note it should be noted that the rst step of this work was to
66
demonstrate the applicability of generalisation methods from image processing to
large raster datasets. This work could be developed further especially with reference
to satellite imagery. It would be possible to use similar techniques to the ones
described in chapter 4 to study the movement of icebergs in the oceans of the world,
this would provide useful information on ocean circulation and allow comparison of
present and paleoiceberg tracks. There are also applications to studies of slash and
burn agriculture in tropical rainforrests. The analysis of imagery from several years
would allow estimates to be made of the amounts of forest aected and the speed
that groups of farmers moved through the forest.
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