SHARAF ALKHEDER & JIE SHAN

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Indiana GIS Conference, March 7
-
8, 2006

1

URBAN GROWTH MODELING USING

MULTI
-
TEMPORAL IMAGES AND CELLULAR
AUTOMATA


A CASE STUDY OF INDIANAPOLIS


















SHARAF ALKHEDER & JIE SHAN


GEOMATICS ENGINEERING AREA

SCHOOL OF CIVIL ENGINEERING

PURDUE UNIVERSITY

Indiana GIS Conference, March 7
-
8, 2006

2

OUTLINE




Introduction.



Statement of the problem.



Focus of our work.



Cellular Automata (CA) urban growth modeling:


Artificial city modeling (synthetic data).


Real city modeling (Indianapolis).



Conclusions.



Work in progress.

Indiana GIS Conference, March 7
-
8, 2006

3

INTRODUCTION



Urban growth process is complex in its nature.



Urban growth modeling is a necessity for each
municipality.



Simulation & prediction of urbanization process
help infrastructure planning.



Cellular Automata (CA) is promising due to its
ability to learn and simulate complex processes that
not possible with mathematical models.



Cellular Automata (CA) for 2D spatial modelling.



Indiana GIS Conference, March 7
-
8, 2006

4

STATEMENT OF THE PROBLEM


Urban areas undergo accelerated urban growth rates.



Multi
-
temporary images are useful resource.



The objective is to use CA with satellite images to model
the spatial & temporal growth of Indianapolis.



CA for complex processes modeling in a grid space.

1973

1987

2003

Indiana GIS Conference, March 7
-
8, 2006

5

FOCUS OF OUR WORK


Development and calibration of CA model.



Spatial & temporal calibration algorithm design.



CA rules calibration:


Using Multi
-
temporal data.


Based on neighborhood structure and input data.


Based on modeling error feedback (over/under estimate).



Township based evaluation.



Integrate with commercial GIS (ArcGIS, VBA).

Indiana GIS Conference, March 7
-
8, 2006

6

CELLULAR AUTOMATA (CA) THEORY


CA introduced by Ulam and von Neumann in 1940s to study the
behaviour of complex systems.



CA: An iterative dynamical discrete system in space and time that
operates on a uniform grid under certain rules.



Four components of CA:

Cells/pixels, States, Neighborhood &
Transition rules.




Let
I

represents integers set. For a cellular space over the set
I
x
I

;
the neighborhood function for cell
α

is
defined as:





Where;
δ
i
(i = 1…n) is index of the neighborhood pixels.





The CA system in a symbolic notation is defined as:





Where; is distinct element of cellular states V & is the local transition function.
(rules on neighborhood).


Indiana GIS Conference, March 7
-
8, 2006

7

CELLULAR AUTOMATA (CA) THEORY


The neighborhood function
is defined as:




Where; are the current states of tested pixel
and its neighborhood.




Relation between the state of cell
α

at time (t+1) and its
neighborhood states at time t is expressed as:



represents the CA transition rules defined on
α

and
neighborhood states to drive the modelling process.



The neighborhood (e.g. square) over the
I
x
I

space
presented as a
city
-
block metric :

Indiana GIS Conference, March 7
-
8, 2006

8

CA FOR URBAN GROWTH MODELLING


CA mechanism:


complex phenomenon
can be modeled by a
# of simpler ones.



CA composed of cell
,
state, neighborhood
and transition rules.



The future state of a
cell depends on:


-

Its current state.


-

Neighborhood


states.


-

T
ransition rules
.

Indiana GIS Conference, March 7
-
8, 2006

9

ARTIFICIAL CITY CA URBAN GROWTH


OBJECTIVES:



M
imic the reality by introducing complex structures for
an urban system.




To test the effect of a number of factors and constraints
on urban growth.



To design the CA system transition rules as a function
of neighborhood structure.



CA
design is based on the effect of each land use. E.g.,
roads encourage and drive the urban development.

Indiana GIS Conference, March 7
-
8, 2006

10

ARTIFICIAL CITY CA URBAN GROWTH


200x200 pixels image input to the CA algorithm.



The CA rules are defined with the


motivation that they represent each


land use effect on the growth process.



Growth constraints are take into


consideration in rules definition.




CA rules:

for tested pixel


IF it is river, road, lake, urban


or pollution source, THEN no growth.


IF it is non
-
urban
AND

1 or more


of neighborhood are pollution,


THEN keep non
-
urban.


IF it is non
-
urban AND the # urban pixels in the neighborhood is >=
than 3 AND there is no pollution pixel THEN change it to urban.


IF non
-
urban AND
1 or more of the neighborhood road AND 1 or
more urban AND no pollution pixel, THEN change to urban.


Indiana GIS Conference, March 7
-
8, 2006

11

ARTIFICIAL CITY CA URBAN GROWTH


CA rules (cont’d):


IF
non
-
urban AND 1 or
more of the neighborhood
are lake AND 1 or more are
urban AND no pollution
pixel, THEN change to
urban.



ELSE keep non
-
urban.



Moore 3 by 3 rectangle
neighborhood.



CA
simulates urban growth at
0, 25, 50 and 60 growth steps.



Effect of road and lakes in
driving growth.



Pollution source buffer zones.



Conservation of water.

Indiana GIS Conference, March 7
-
8, 2006

12

REAL CITY (INDIANAPOLIS) CA GROWTH


Extending the artificial city CA model for real city.



Complex structure and interaction of development
factors result in growth pattern.



Careful design of CA transition rules.



Model calibration and evaluation is needed.



Indianapolis is located in Marion County at latitude
39
°
44'N and longitude of 86
°
17'W.



Grown from part of Marion in 70’s to the whole
County and parts of the neighboring in 2003.



Indiana GIS Conference, March 7
-
8, 2006

13

INDIANAPOLIS CA GROWTH
-

INPUT DATA

1.
Multitemporal Satellite Imagery:



5 historical MSS/TM satellite images : (1973, 1982,
1987, 1992 and 2003).



Images are projected to UTM NAD1983 zone 16N &
registered.




Ground reference data are used to classify the
images.



7 classes are defined: water, road, commercial, forest,
residential, pasture and row crops.



High classification accuracy (>92%).



Commercial and residential classes represent urban
class.

Indiana GIS Conference, March 7
-
8, 2006

14

INDIANAPOLIS CA GROWTH
-

INPUT DATA

2.
Population Density Maps:



Another input to CA model.



A population density model for each growth year is
prepared.



2000 Census tract map is used.



Area for each census tract


is calculated.



Population density is


computed per census tract.











(Source, IGS)

Indiana GIS Conference, March 7
-
8, 2006

15

INDIANAPOLIS CA GROWTH
-

INPUT DATA

2.
Population Density Maps:


An exponential model is fitted between density and
distance from city center.




The model is used to calculate population density per
pixel for entire image for each growth year.



Model parameters are updated yearly based on
population growth rate.



Population density is used as another CA input.

Indiana GIS Conference, March 7
-
8, 2006

16

CA TRANSITION RULES

CA rules based on:



Land use effect
:
growth constraints.




Closeness to city
:


positive effect.




Population density.



3 by 3 Moore
neighborhood.



CA calibration
involves two aspects:
Spatial and Temporal
calibration.

Future

Indiana GIS Conference, March 7
-
8, 2006

17

CA ALGORITHM DESIGN



CA Modelling in ArcGIS through VBA.



CA transition rules are defined as a function of
neighborhood structure and population density.



Two set of multitemporal imagery:


-

Training images 1982 & 1987 to calibrate the CA
rules.


-

Testing images of 1992 and 2003 for validation
purposes only.



CA rules are initialized to run the simulation from
1973 till 1982
.

Indiana GIS Conference, March 7
-
8, 2006

18

CA ALGORITHM DESIGN


Spatial calibration at 1982


on a township basis.


Rules are calibrated based


on township site specific


features.


Evaluate urban class per


region for simulated and


real images at 1982.


Calculate region &


average accuracy as a ratio


between simulated and


real urban amount.

Indiana GIS Conference, March 7
-
8, 2006

19

CA ALGORITHM DESIGN


IF over/under estimate increase/decrease urban
growth rate through modifying the rules, respectively.



Run the simulation again from 1973 to 1982 and
evaluate.



Run till simulated results closely estimate real growth.



For temporal calibration, Recalibrate again spatially
at 1987 to adapt growth pattern over time.



Predict urban growth at 1992 (from 1987) for 5 years
interval and 2003 for 11 years interval (from 1992).

Indiana GIS Conference, March 7
-
8, 2006

20

ARCGIS
-
CA TOOL DEVELOPMENT

Indiana GIS Conference, March 7
-
8, 2006

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CA MODELING RESULTS
-

CALIRATION


Close


match


Spatial

calibration

effect.





Indiana GIS Conference, March 7
-
8, 2006

22

CA MODELING RESULTS
-

CALIRATION

Temporal

calibration

Effect.



Indiana GIS Conference, March 7
-
8, 2006

23

CA MODELING RESULTS


PREDICTION (1992)


Short term prediction (5 years).



Good


accuracy

Indiana GIS Conference, March 7
-
8, 2006

24

CA MODELING RESULTS


PREDICTION (2003)



Good


accuracy



Pattern


match


Indiana GIS Conference, March 7
-
8, 2006

25

CA
PREDICTION

RESULTS ACCURACY


Higher


accuracy for


short term.



Township effect


on improving


accuracy.




Low variability.



Indiana GIS Conference, March 7
-
8, 2006

26

CONCLUSIONS


Multitemporal imagery is a rich source for urban
growth modeling.



CA show great potential to model the 2D growth
process.



Error model of comparing the real and simulated
images on a township basis is the basis of calibration
process.



Importance of spatial calibration on township basis to
improve the spatial prediction accuracy.



Temporal calibration to adapt the growth pattern over
time.

Indiana GIS Conference, March 7
-
8, 2006

27

WORK IN PROGRESS….


Fuzzy CA modeling to preserve the continuous nature
of the growth process.



Genetics algorithms for efficient and automatic CA
transition rules calibration.



Indiana GIS Conference, March 7
-
8, 2006

28


Thanks For Listening. Questions!!







SHARAF ALKHEDER & JIE SHAN

GEOMATICS ENGINEERING AREA

SCHOOL OF CIVIL ENGINEERING

(salkhede,jshan )@ecn.purdue.edu

PURDUE UNIVERSITY