Handbook of Research on Geoinformatics - Hassan A. Karimi Part 4 pot

120
Network Modeling
and methods for describing and measuring net-
works and proving properties of networks are
well-developed. There are a variety of network
models in GISystems, which are primarily dif-
ferentiated by the topological relationships they
maintain. Network models can act as the basis for
location through the process of linear referenc-
ing. Network analyses such as routing and ow
modeling have to some extent been implemented,
although there are substantial opportunities for
additional theoretical advances and diversied
application.
references
Ahuja, R. K., Magnanti, T. L., & Orlin, J. B.
(1993). Network Flows: Theory, Algorithms, and
Applications. Upper Saddle River, NJ: Prentice-
Hall, Inc.
Cooke, D. F. (1998). Topology and TIGER: The
Census Bureau’s Contribution. In T. W. Foresman
(Ed.), The History of Geographic Information
Systems. Upper Saddle River, NJ: Prentice Hall.
Curtin, K. M., Noronha, V., Goodchild, M. F.,
& Grise, S. (2001). ArcGIS Transportation Data
Model. Redlands, CA: Environmental Systems
Research Institute.
Curtin, K. M., Qiu, F., Hayslett-McCall, K., &
Bray, T. (2005). Integrating GIS and Maximal
Covering Models to Determine Optimal Police
Patrol Areas. In F. Wang (Ed.), Geographic In-

formation Systems and Crime Analysis. Hershey:
Idea Group.
Dueker, K. J., & Butler, J. A. (2000). A geographic
information system framework for transportation
data sharing. Transportation Research Part C-
Emerging Technologies, 8(1-6), 13-36.
Evans, J. R., & Minieka, E. (1992). Optimization
Algorithms for Networks and Graphs (2nd ed.).
New York: Marcel Dekker.
Federal Highway Administration. (2001). Imple-
mentation of GIS Based Highway Safety Analy-
sis: Bridging the Gap (No. FHWA-RD-01-039).
McLean, VA: U.S. Department of Transporta-
tion.
Federal Transit Administration. (2003). Best
Practices for Using Geographic Data in Transit:
A Location Referencing Guidebook (No. FTA-NJ-
26-7044-2003.1). Washington, DC: U.S. Depart-
ment of Transportation.
Fletcher, D., Expinoza, J., Mackoy, R. D., Gordon,
S., Spear, B., & Vonderohe, A. (1998). The Case
for a Unied Linear Reference System. URISA
Journal, 10(1).
Fohl, P., Curtin, K. M., Goodchild, M. F., &
Church, R. L. (1996). A Non-Planar, Lane-Based
Navigable Data Model for ITS. Paper presented
at the International Symposium on Spatial Data
Handling, Delft, The Netherlands.
Harary, F. (1982). Graph Theory. Reading: Ad-
dison Wesley.

Kansky, K. (1963). Structure of transportation net-
works: relationships between network geogrpahy
and regional characteristics (No. 84). Chicago,
IL: University of Chicago.
Koncz, N. A., & Adams, T. M. (2002). A data
model for multi-dimensional transportation ap-
plications. International Journal of Geographical
Information Science, 16(6), 551-569.
Noronha, V., & Church, R. L. (2002). Linear Ref-
erencing and Other Forms of Location Expression
for Transportation (No. Task Order 3021). Santa
Barbara: Vehicle Intelligence & Transportation
Analysis Laboratory, University of California.
Nyerges, T. L. (1990). Locational Referencing and
Highway Segmentation in a Geographic Informa-
tion System. ITE Journal, March, 27-31.
Rodrigue, J., Comtois, C., & Slack, B. (2006).
The Geography of Transport Systems. London:
Routledge.
121
Network Modeling
Scarponcini, P. (2001). Linear reference system
for life-cycle integration. Journal of Computing
in Civil Engineering, 15(1), 81-88.
Sutton, J. C., & Wyman, M. M. (2000). Dynamic
location: an iconic model to synchronize temporal
and spatial transportation data. Transportation
Research Part C-Emerging Technologies, 8(1-
6), 37-52.
Vonderohe, A., Chou, C., Sun, F., & Adams, T.

(1997). A generic data model for linear referenc-
ing systems (No. Research Results Digest Number
218). Washington D.C.: National Cooperative
Highway Research Program, Transportation
Research Board.
Wilson, R. J. (1996). Introduction to Graph
Theory. Essex: Longman.
keywords
Capacity: The largest amount of ow permit-
ted on an edge or through a vertex.
Graph Theory: The mathematical discipline
related to the properties of networks.
Linear Referencing: The process of associat-
ing events with a network datum.
Network: A connected set of edges and
vertices.
Network Design Problems: A set of com-
binatorially complex network analysis problems
where routes across (or ows through) the network
must be determined.
Network Indices: Comparisons of network
measures designed to describe the level of con-
nectivity, level of efciency, level of development,
or shape of a network.
Topology: The study of those properties of net-
works that are not altered by elastic deformations.
These properties include adjacency, incidence,
connectivity, and containment.
122
Chapter XVI

Articial Neural Networks
Xiaojun Yang
Florida State University, USA
Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited.
Abstr Act
Articial neural networks are increasingly being used to model complex, nonlinear phenomena. The
purpose of this chapter is to review the fundamentals of articial neural networks and their major
applications in geoinformatics. It begins with a discussion on the basic structure of articial neural
networks with the focus on the multilayer perceptron networks given their robustness and popularity.
This is followed by a review on the major applications of articial neural networks in geoinformat-
ics, including pattern recognition and image classication, hydrological modeling, and urban growth
prediction. Finally, several areas are identied for further research in order to improve the success of
articial neural networks for problem solving in geoinformatics.
Introduct Ion
An articial neural network (commonly just
neural network) is an interconnected assemblage
of articial neurons that uses a mathematical or
computational model of theorized mind and brain
activity, attempting to parallel and simulate the
powerful capabilities for knowledge acquisi-
tion, recall, synthesis, and problem solving. It
originated from the concept of articial neuron
introduced by McCulloch and Pitts in 1943. Over
the past six decades, articial neural networks
have evolved from the preliminary development
of articial neuron, through the rediscovery and
popularization of the back-propagation training
algorithm, to the implementation of articial neu-
123
Articial Neural Networks

ral networks using dedicated hardware. Theoreti-
cally, articial neural networks are highly robust
in data distribution, and can handle incomplete,
noisy and ambiguous data. They are well suited
for modeling complex, nonlinear phenomena
ranging from nancial management, hydrologi-
cal modeling to natural hazard prediction. The
purpose of the article is to introduce the basic
structure of articial neural networks, review
their major applications in geoinformatics, and
discuss future and emerging trends.
bAckground
The basic structure of an articial neural network
involves a network of many interconnected neu-
rons. These neurons are very simple processing
elements that individually handle pieces of a big
problem. A neuron computes an output using an
activation function that considers the weighted
sum of all its inputs. These activation functions
can have many different types but the logistic
sigmoid function is quite common:
1
f ( x )
1 e
x
where f(x) is the output of a neuron and x rep-
resents the weighted sum of inputs to a neuron.
As suggested from Equation 1, the principles
of computation at the neuron level are quite
simple, and the power of neural computation

relies upon the use of distributed, adaptive and
nonlinear computing. The distributed comput-
ing environment is realized through the massive
interconnected neurons that share the load of the
overall processing task. The adaptive property
is embedded with the network by adjusting the
weights that interconnect the neurons during the
training phase. The use of an activation function
in each neuron introduces the nonlinear behavior
to the network.
There are many different types of neural net-
works, but most can fall into one of the ve major
paradigms listed in Table 1. Each paradigm has
advantages and disadvantages depending upon
specic applications. A detailed discussion about
these paradigms can be found elsewhere (e.g.,
Bishop, 1995; Rojas, 1996; Haykin, 1999; and
Principe et al., 2000). This article will concentrate
upon multilayer perceptron networks due to their
technological robustness and popularity (Bishop,
1
995
).
Figure 1 illustrates a simple multilayer per-
ceptron neural network with a 4×5×4×1 structure.
This is a typical feed-forward network that al-
lows the connections between neurons to ow in
one direction. Information ow starts from the
neurons in the input layer, and then moves along
weighted links to neurons in the hidden layers for

processing. The weights are normally determined
through training. Each neuron contains a nonlinear
activation function that combines information
from all neurons in the preceding layers.The
output layer is a complex function of inputs and
internal network transformations.
The topology of a neural network is critical
for neural computing to solve problems with
reasonable training time and performance. For
any neural computing, training time is always
the biggest bottleneck and thus, every effort is
needed to make training effective and affordable.
Training time is a function of the complexity of
the network topology which is ultimately deter-
mined by the combination of hidden layers and
neurons. A trade-off is needed to balance the
processing purpose of the hidden layers and the
training time needed. A network without a hidden
layer is only able to solve a linear problem. To
tackle a nonlinear problem, a reasonable number
of hidden layers is needed. A network with one
hidden layer has the power to approximate any
function provided that the number of neurons and
the training time are not constrained (Hornik,
1993). But in practice, many functions are dif-
cult to approximate with one hidden layer and
thus, Flood and Kartam (1994) suggested using
two hidden layers as a starting point.
124
Articial Neural Networks

No. Type Example Brief description
1
Feed-forward neural
network
Multi-layer perceptron It consists of multiple layers of processing units that are usually
interconnected in a feed-forward way
Radial basis functions As powerful interpolation techniques, they are used to replace the
sigmoidal hidden layer transfer function in multi-layer perceptrons
Kohonen self-organiz-
ing networks
They use a form of unsupervised learning method to map points in
an input space to coordinate in an output space.
2
Recurrent network Simple recurrent
networks
Contrary to feed-forward networks, recurrent neural networks use
bi-directional data ow and propagate data from later processing
stages to earlier stages
Hopeld network
3
Stochastic neural
networks
Boltzmann machine They introduce random variations, often viewed as a form of statis-
tical sampling, into the networks
4
Modular neural
networks
Committee of machine They use several small networks that cooperate or compete to solve
problems.
5

Other types Dynamic neural net-
works
They not only deal with nonlinear multivariate behavior, but also
include learning of time-dependent behavior.
Cascading neural
networks
They begin their training without any hidden neurons. When the
output error reaches a predened error threshold, the networks add
a new hidden neuron.
Neuro-fuzzy networks They are a fuzzy inference system in the body which introduces the
processes such as fuzzication, inference, aggregation and defuzzi-
cation into a neural network.
Table 1. Classication of articial neural networks (Source: Haykin, 1999)
Figure 1. A simple multilayer perceptron(MLP) neutral network with a 4 X 5 X 4 X 1 structure
125
Articial Neural Networks
The number of neurons for the input and output
layers can be dened according to the research
problem identied in an actual application. The
critical aspect is related to the choice of the number
of neurons in hidden layers and hence the number
of connection weights. If there are too few neu-
rons in hidden layers, the network may be unable
to approximate very complex functions because
of insufcient degrees of freedom. On the other
hand, if there are too many neurons, the network
tends to have a large number of degrees of free-
dom which may lead to overtraining and hence
poor performance in generalization (Rojas, 1996).
Thus, it is crucial to nd the ‘optimum’ number of

neurons in hidden layers that adequately capture
the relationship in the training data. This optimi-
zation can be achieved by using trial and error
or several systematic approaches such as pruning
and constructive algorithms (Reed, 1993).
Training is a learning process by which the
connection weights are adjusted until the network
is optimal. This involves the use of training sam-
ples, an error measure and a learning algorithm.
Training samples are presented to the network
with input and output data over many iterations.
They should not only be large in size but also
be representative of the entire data set to ensure
sufcient generalization ability. There are several
different error measures such as the mean squared
error (MSE), the mean squared relative error
(MSRE), the coefcient of efciency (CE), and
the coefcient of determination (r
2
) (Dawson and
Wilby, 2001). The MSE has been most commonly
used. The overall goal of training is to optimize
errors through either a local or global learning
algorithm. Local methods adjust weights of the
network by using its localized input signals and
localized rst- or second- derivative of the error
function. They are computationally effective for
changing the weights in a feed-forward network
but are susceptible to local minima in the er-
ror surface. Global methods are able to escape

local minima in the error surface and thus can
nd optimal weight congurations (Maier and
Dandy, 2000).
By far the most popular algorithm for opti-
mizing feed-forward neural networks is error
back-propagation (Rumelhart et al., 1986). This
is a rst-order local method. It is based on the
method of steepest descent, in which the descent
direction is equal to the negative of the gradient of
the error. The drawback of this method is that its
search for the optimal weight can become caught
in local minima, thus resulting in suboptimal
solutions. This vulnerability could increase when
the step size taken in weight space becomes too
small. Increasing the step size can help escape lo-
cal error minima, but when the step size becomes
too large, training can fall into oscillatory traps
(Rojas, 1996). If that happens, the algorithm will
diverge and the error will increase rather than
decrease.
Apparently, it is difcult to nd a step size that
can balance high learning speed and minimiza-
tion of the risk of divergence. Recently, several
algorithms have been introduced to help adapt
step sizes during training (e.g., Maier and Dandy,
2000). In practice, however, a trial-and-error
approach has often been used to optimize step
size. Another sensitive issue in back-propagation
training is the choice of initial weights. In the
absence of any a priori knowledge, random values

should be used for initial weights.
The stop criteria for learning are very im-
portant. Training can be stopped when the total
number of iterations specied or a targeted value
of error is reached, or when the training is at the
point of diminishing returns. It should be noted
that using low error level is not always safe to
stop the training because of possible overtraining
or overtting. When this happens, the network
memorizes the training patterns, thus losing the
ability to generalize. A highly recommended
method for stopping the training is through cross
validation (e.g., Amari et al., 1997). In doing so,
an independent data set is required for test pur-
poses, and close monitoring of the error in the
training set and the test set is needed. Once the
error in the test set increases, the training should
126
Articial Neural Networks
be stopped since the point of best generalization
has been reached.
AppLIcAt Ions
Articial neural networks are applicable when a
relationship between the independent variables
and dependent variables exists. They have been
applied for such generic tasks as regression analy-
sis, time series prediction and modeling, pattern
recognition and image classication, and data
processing. The applications of articial neural
networks in geoinformatics have concentrated

on a few major areas such as pattern recognition
and image classication (Bruzzone et al., 1999),
hydrological modeling (Maier and Dandy, 2000)
and urban growth prediction (Yang, 2009). The
following paragraphs will provide a brief review
on these areas.
Pattern recognition and image classication
are among the most common applications of
articial neural networks in remote sensing, and
the documented cases overwhelmingly relied upon
the use of multi-layer perceptron networks. The
major advantages of articial neural networks over
conventional parametric statistical approaches to
image classication, such as the Euclidean, maxi-
mum likelihood (ML), and Mahalanobis distance
classiers, are that they are distribution-free with
less severe statistical assumptions needed and that
they are suitable for data integration from various
sources (Foody, 1995). Articial neural networks
are found to be accurate in the classication of
remotely sensed data, although improvements in
accuracies have generally been small or modest
(Campbell, 2002).
Articial neural networks are being used in-
creasingly to predict and forecast water resource
variables such as algae concentration, nitrogen
concentration, runoff, total volume, discharge,
or ow (Maier and Dandy, 2000; Dawson and
Wilby, 2001). Most of the documented cases used
a multi-layer perceptron that was trained by using

the back-propagation algorithm. Based on the
results obtained so far, there is little doubt that
articial neural networks have the potential to be
a useful tool for the prediction and forecasting of
water resource variables.
The application of articial neural networks
for urban predictive modeling is a new but rapidly
expanding area of research (Yang, 2009). Neural
networks have been used to compute develop-
ment probability by integrating a set of predictive
variables as the core of a land transformation
model (e.g., Pijanowski et al., 2002) or a cellular
automata-based model (e.g., Yeh and Li, 2003). All
the applications documented so far involved the
use of the multilayer perceptron network, a grid-
based modeling framework, and a Geographic
Information Systems (GIS) that was loosely or
tightly integrated with the network for input data
preparation, modeling validation and analysis.

conc Lus Ion And future
trends
Based on many documented applications within
recent years, the prospect of articial neural
networks in geoinformatics seems to be quite
promising. On the other hand, the capability of
neural networks tends to be oversold as an all-
inclusive ‘black box’ that is capable to formulate
an optimal solution to any problem regardless
of network architecture, system conceptualiza-

tion, or data quality. Thus, this eld has been
characterized by inconsistent research design
and poor modeling practice. Several researchers
recently emphasized the need to adopt a system-
atic approach for effective neural network model
development that considers problem conceptual-
ization, data preprocessing, network architecture
design, training methods, and model validation in
a sequential mode (e.g., Mailer and Dandy, 2000;
Dawson and Wilby, 2001; Yang, 2009).
T
here
are a few areas where further research is
needed. Firstly, there are many arbitrary decisions
127
Articial Neural Networks
involved in the construction of a neural network
model, and therefore, there is a need to develop
guidance that helps identify the circumstances
under which particular approaches should be
adopted and how to optimize the parameters that
control them. For this purpose, more empirical,
inter-model comparisons and rigorous assessment
of neural network performance with different
inputs, architectures, and internal parameters are
needed. Secondly, data preprocessing is an area
where little guidance can be found. There are
many theoretical assumptions that have not been
conrmed by empirical trials. It is not clear how
different preprocessing methods could affect the

model outcome. Future investigation is needed to
explore the impact of data quality and different
methods in data division, data standardization,
or data reduction. Thirdly, continuing research is
needed to develop effective strategies and prob-
ing tools for mining the knowledge contained in
the connection weights of trained neural network
models for prediction purposes. This can help
uncover the ‘black-box’ construction of the neural
network, thus facilitating the understanding of
the physical meanings of spatial factors and their
contribution to geoinformatics. This should help
improve the success of neural network applica-
tions for problem solving in geoinformatics.

references
Amari, S., Murata, N., Muller, K. R., Finke, M., &
Yang, H. H. (1997). Asymptotic statistical theory
of overtraining and cross-validation. IEEE Trans-
actions On Neural Networks, 8(5), 985-996.
Bishop, C. ( 1995). Neural Networks for Pattern
Recognition (p. 504). Oxford: University Press.
Bruzzone, L., Prieto, D. F., & Serpico, S. B. (1999).
A neural-statistical approach to multitemporal and
multisource remote-sensing image classication.
IEEE Transactions on Geoscience and Remote
Sensing, 37(3), 1350-1359.
Campbell, J. B. (2002). Introduction to Remote
Sensing (3
rd

) (p. 620). New York: The Guiford
Press.
Dawson, C. W., & Wilby, R. L. (2001). Hydro-
logical modelling using articial neural networks.
Progress in Physical Geography, 25(1), 80-108.
Flood, I., & Kartam, N. (1994). Neural networks
in civil engineering.2. systems and application.
Journal of Computing in Civil Engineering, 8(2),
149-162.
Foody, G. M. (1995). Land cover classication
using an articial neural network with ancillary
information. International Journal of Geographi-
cal Information Systems, 9, 527- 542.
Haykin, S. (1999). Neural Networks: A Compre-
hensive Foundation (p. 842). Prentice Hall.
Hornik, K. (1993). Some new results on neural-
network approximation. Neural Networks, 6(8),
1069-1072.
Kwok, T. Y., & Yeung, D. Y. (1997). Constructive
algorithms for structure learning in feed-forward
neural networks for regression problems. IEEE
Transactions On Neural Networks, 8(3), 630-
645.
Maier, H. R., & Dandy, G. C. (2000). Neural
networks for the prediction and forecasting of
water resources variables: A review of modeling
issues and applications. Environmental Modelling
& Software, 15, 101-124.
Pijanowski, B. C., Brown, D., Shellito, B., &
Manik, G. (2002). Using neural networks and GIS

to forecast land use changes: A land transforma-
tion model. Computers, Environment and Urban
Systems, 26, 553–575.
Principe, J. C., Euliano, N. R., & Lefebvre, W.
C. (2000). Neural and Adaptive Systems: Fun-
damentals Through Simulations (p. 565). New
York: John Wiley & Sons.
128
Articial Neural Networks
Reed, R. (1993). Pruning algorithms - a survey.
IEEE Transactions On Neural Networks, 4(5),
740-747.
Rojas, R. (1996). Neural Networks: A Systematic
Introduction (p. 502). Springer-Verlag, Berlin.
Rumelhart, D. E., Hinton, G. E., & Williams, R. J.
(1986). Learning internal representations by error
propagation. In Parallel Distributed Processing
D. E. Rumelhart, & J. L. McClelland. Cambridge:
MIT Press.
Yang, X. (2009). Articial neural networks
for urban modeling. In Manual of Geographic
Information Systems, M. Madden. American
Society for Photogrammetry and Remote Sens-
ing (in press).
Yeh, A. G. O., & Li, X. (2003). Simulation of
development alternatives using neural networks,
cellular automata, and GIS for urban planning.
Photogrammetric Engineering and Remote Sens-
ing, 69(9), 1043-1052.
key ter Ms

Architecture: The structure of a neural
network including the number and connectivity
of neurons. A network generally consists of an
input layer, one or more hidden layers, and an
output layer.
Back-Propagation: The training algorithm for
the feed-forward, multi-layer perceptron networks
which works by propagating errors back through
a network and adjusting weights in the direction
opposite to the largest local gradient.
Error Space: The n-dimensional surface in
which weights in a networks are adjusted by the
back-propagation algorithm to minimize model
error.
Feed-Forward: A network in which all the
connections between neurons ow in one direc-
tion from an input layer, through hidden layers,
to an output layer.
Multiplayer Perceptron: The most popular
network which consists of multiple layers of in-
terconnected processing units in a feed-forward
way.
Neuron: The basic building block of a neural
network. A neuron sums the weighed inputs,
processes them using an activation function, and
produces an output response.
Pruning Algorithm: A training algorithm
that optimizes the number of hidden layer
neurons by removing or disabling unnecessary
weights or neurons from a large network that is

initially constructed to capture the input-output
relationship.
Training/Learning: The processing by which
the connection weights are adjusted until the
network is optimal.
129
Chapter XVII
Spatial Interpolation
Xiaojun Yang
Florida State University, USA
Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited.
Abstr Act
Spatial interpolation is a core component of data processing and analysis in geoinformatics. The purpose
of this chapter is to discuss the concept and techniques of spatial interpolation. It begins with an over-
view of the concept and brief history of spatial interpolation. Then, the chapter reviews some commonly
used interpolations that are specically designed for working with point data, including inverse distance
weighting, kriging, triangulation, Thiessen polygons, radial basis functions, minimum curvature, and
trend surface. This is followed by a discussion on some criteria that are proposed to help select an ap-
propriate interpolator; these criteria include global accuracy, local accuracy, visual pleasantness and
faithfulness, sensitivity, and computational intensity. Finally, future research needs and new, emerging
applications are presented.
Introduct Ion
Spatial interpolation is a core component of data
processing and analysis in geographic informa-
tion systems. It is also an important subject in
spatial statistics and geostatistics. By denition,
spatial interpolation is the procedure of predi-
cating the value of properties from known sites
to un-sampled, missing, or obscured locations.
The rationale behind interpolation is the very

common observation that values at points close
together in space are more likely to be similar
than points further apart. This observation has
been formulated as the First Law of Geography
(Tobler, 1970). Data sources for spatial interpola-
tion are normally scattered sample points such as
soil proles, water wells, meteorological stations
or counts of species, people or market outlets
130
Spatial Interpolation
that are summarized by basic spatial units such
as grids or administrative areas. These discrete
data are interpolated into continuous surfaces that
can be quite useful for data exploration, spatial
analysis, and environmental modeling (Yang and
Hodler, 2000). On the other hand, we often think
about some kinds of data as continuous rather
than discrete even though we can only measure
them discretely. Thus, spatial interpolation al-
lows us to view and predict data over space in
an intuitive way, thereby making the real-world
decision-making process easier.
The history of spatial interpolation is quite
long, and a group of optimal interpolation methods
using geostatistics can be traced to the early 1950s
when Danie G. Krige, a South African mining
engineer, published his seminal work on the theory
of Kriging (Krige, 1951). Krige’s empirical work
to evaluate mineral resources was formalized in
the 1960s by French engineer Georges Matheron

(1961). By now, there are several dozens of interpo-
lators that have been designed to work with point,
line, or polygon data (Lancaster and Salkauskas,
1986; Isaaks and Srivastava, 1989; Bailey and
Gatrell, 1995). While this chapter focuses on the
methods designed for working with point data,
readers who are interested in the group of inter-
polators for line or polygon data should refer to
Hutchinson (1989), Tobler (1979), or Goodchild
and Lam (1980).
The purpose of this chapter is to introduce
the concept of spatial interpolation, review some
commonly used interpolators that are specically
designed for point data, provide several criteria for
selecting an appropriate interpolator, and discuss
further research needs.
spAt IAL Interpo LAt Ion
Methods
There is a rich pool of spatial interpolation ap-
proaches available, such as distance weighting,
tting functions, triangulation, rectangle-based
interpolation, and neighborhood-based interpola-
tion. These methods vary in their assumptions,
local or global perspective, deterministic or
stochastic nature, and exact or approximate t-
ting. Thus, they may require different types of
input data and varying computation time, and
most importantly, generate surfaces with various
accuracy and appearance. This article will focus
on several methods that have been widely used

in geographic information systems.
Inverse Distance Weighting (IDW)
Inverse distance weighting (IDW) is one of the
most popular interpolators that have been used
in many different elds. It is a local, exact inter-
polator. The weight of a sampled point value is
inversely proportional to its geometric distance
from the estimated value that is raised to a specic
power or exponent. This has been considered a
direct implementation of Tobler’s First Law of
Geography (Tobler, 1970). Normally, a search
space or kernel is used to help nd a local neigh-
borhood. The size of the kernel or the minimum
number of sample points specied in the search
can affect IDW’s performance signicantly (Yang
and Hodler, 2000). Every effort should be made
to ensure that the estimated values are dependent
upon sample points from all directions and to be
free from the cluster effect. Because the range
of interpolated values cannot exceed the range of
observed values, it is important to position sample
points to include the extremes of the eld. The
choice of the exponent can affect the results sig-
nicantly as it controls how the weighting factors
decline as distance increases. As the exponent
approaches zero, the resultant surface approaches
a horizontal planar surface; as it increases, the
output surface approaches the nearest neighbor
interpolator with polygonal surfaces. Overall,
inverse distance weighting is a fast interpolator

but its output surfaces often display a sort of
‘bull-eye’ or ‘sinkhole-like’ pattern.
131
Spatial Interpolation
kriging
Kriging was developed by Georges Matheron
in 1961 and named in honor of Daniel G. Krige
because of his pioneering work in 1950s. As a
technique that is rmly grounded in geostatistical
theory, Kriging has been highly recommended as
an optimal method of spatial interpolation for geo-
graphic information systems (Oliver and Webster,
1990; Burrough and McDonnell, 1998).
Any estimation made by kriging has three
major components: drift or general trend of the
surface, random but spatially correlated small de-
viations from the trend, and random noise, which
are estimated independently. Drift is estimated
using a mathematical equation that most closely
resembles the overall trend in the surface. The
distance weights for interpolation are determined
using the variogram model that is chosen from
a set of mathematical functions describing the
spatial autocorrelation. The appropriate model is
chosen by matching the shape of the curve of the
experimental variogram to the shape of the curve
of the mathematical function, either spherical,
exponential, linear, Gaussian, hole-effect, qua-
dratic, or rational quadratic. The random noise is
estimated using the nugget variance, a combina-

tion of the error variance and the micro variance
or the variance of the small scale structure.
Kriging can be further classied as ordinary,
universal, simple, disjunctive, indicator, or prob-
ability. Ordinary Kriging assumes that the general
trend is a simple, unknown constant. Trends that
vary, and parameters and covariates are unknown,
form models for Universal Kriging. Whenever the
trend is completely known, whether constant or
not, it forms the model for Simple Kriging. Dis-
junctive Kriging predicts the value at a specic
location by using functions of variables. Indicator
Kriging predicts the probability that the estimated
value is above a predened threshold value.
Probability Kriging is quite similar to Indicator
Kriging, but it uses co-kriging in the prediction.
Co-kriging refers to the models based on more
than one variable.
The use of Kriging as a popular geostatistic
interpolator is generally robust. When it is difcult
to use the points in a neighborhood to estimate
the form of variogram, the variogram model used
is not entirely appropriate, and Kriging may be
inferior to other methods. In addition, Kriging is
quite computationally intensive.
Triangulation
Triangulation is an exact interpolator by which
irregularly distributed sample points are jointed
to form a patchwork of triangles. There are two
major methods that can be used to determine

how points or vertices are connected to triangles:
distance ordering and Delauney triangulation
(Okabe et al., 1992). Almost all systems use the
second method, namely, Delaunay triangulation,
which allows three points to form the corners of a
triangle only when the circle that passes through
them contains no other points. Delaunay triangu-
lation minimizes the longest size of any triangles,
thus producing triangles that are as close to being
equilateral as possible. Each triangle is treated
as a plane surface. The equation for each planar-
triangular facet is determined exactly from the
surface property of interest at the three vertices.
Once the surface is dened in this way, the values
for the interpolated data points can be calculated.
This method works best when sample points are
evenly distributed. Data sets that contain sparse
areas result in distinct triangular facets on the
output surface. Triangulation is a fast interpolator,
particularly suitable for very large data sets.

Thiessen Polygons (or Voronoi
Polygons)
Thiessen polygons were independently discovered
in several elds including climatology and geog-
raphy. They are named after a climatologist who
used them to perform a transformation from point
climate stations to watersheds. Thiessen polygons
are constructed around a set of points in such a
132

Spatial Interpolation
way that the polygon boundaries are equidistant
from the neighboring points, and they estimate the
values at surrounding points from a single point
observation. In other words, each location within
a polygon is closer to a contained point than to any
other points. Thiessen polygons are not difcult
to construct and particularly suitable for discrete
data, such as rain gauge data. The accuracy of
Thiessen polygons is a function of sample density.
One major limitation with Thiessen polygons is
that they produce polygons with shapes being
unrelated to the phenomena under investigation.
In addition, Thiessen Polygons are not effective
to represent continuous variables.
Radial Basis Functions
The radial basis functions include a diverse group
of interpolation methods. All are exact interpola-
tors, attempting to honor each data point. They
solve the interpolation by constructing a set of
basis functions that dene the optimal set of
weights to apply to the data points (Carlson and
Foley, 1991). Most commonly used basis functions
include: inverse multiquadric equation, multilog
function, multiquadric equation, natural cubic
spline, and thin plate spline (Golden Software,
Inc., 2002). Franke (1982) rated the multiquadric
equation as the most impressive basis function
in terms of tting ability and visual smoothness.
The multiquadric equation method was originally

proposed for topographical mapping by Hardy
(
197
1).
Minimum Curvature
Minimum curvature has been widely used in
geosciences. It is a global interpolator in which
all points available formally participate in the
calculation of values for each estimated point.
This method applies a two-dimensional cubic
spline function to t a surface to the set of input
values. The computation requires a number of
iterations to adjust the surface so that the nal
result has a minimum amount of curvature. The
interpolated surface produced by the minimum
curvature method is analogous to a thin, linearly-
elastic plate passing through each of the data values
so that the displacement at these points is equal
to the observation to be satised (Briggs, 1974).
The minimum curvature method is not an exact
interpolator. It is quite fast, and tends to produce
smooth surfaces (Yang and Hodler, 2000).
Trend Surface
Trend surface solves the interpolation by using one
or more polynomial functions, depending upon
global or local perspective. Global polynomial
ts a single function to the entire sample points,
and creates a slowly varying surface, which may
help capture some coarse-scale physical processes
such as air pollution or wind direction. It is a

quick deterministic interpolator. Local polyno-
mial interpolation uses many polynomials, each
within specied overlapping neighborhoods. The
shape, number of points to use, and the search
kernel conguration can affect the interpolation
performance. While global polynomial interpola-
tion is useful for identifying long-range trends,
local polynomial can capture the short-range
variation in the dataset.
cr Iter IA for se Lect Ing An
Interpo LAt or
Although the pool of spatial interpolation methods
is rich and some general guidelines are available,
it is often difcult to select an appropriate one
for a specic application. For many applications,
users will have to do at least some minimum ex-
periments before a nal selection can be made.
The following ve criteria are recommended to
guide this selection: (1) global accuracy, (2) local
accuracy, (3) visual pleasantness and faithfulness,
(4) sensitivity, and (5) computational intensity.
133
Spatial Interpolation
Global Accuracy
There are two well-established methods for mea-
suring global accuracy: validation and cross-vali-
dation. Validation can use all data points or just a
subset. Assuming that sampling process is without
error, all data points can be used to measure the
degree at which an interpolator honors the control

data. But this way does not necessarily guarantee
the accuracy for unsampled points. Instead of
using all data points, the entire samples can be
split into two subsets, one for interpolation (called
test subset) and the other for validation (training
subset). This way can provide an insight into the
accuracy for unsampled sites. However, splitting
samples may not be realistic for small datasets
because interpolation may suffer from insufcient
training points. The actual tools used for valida-
tion include statistical measures, such as residual
and root mean square error, and/or graphical
summaries, such as scatterplot and Quantile-
Quantile (QQ) plot. Residual is the difference
between the known and estimated point values.
Root mean square error (RMSE) is determined
by calculating the deviations of estimated points
from their known true position, summing up the
measurements, and then taking the square root
of the sum. A scatter plot gives a graphical sum-
mary of predicted values versus true values, and
a QQ plot shows the quantiles of the difference
between the predicted and measured values and
the corresponding quantiles from a standard
normal distribution. Cross-validation removes
each observation point, one at a time, estimates
the value for this point using the remaining data,
and then computes the residual; this procedure
is repeated for a second point, and so on. Cross-
validation outputs various summary statistics of

the errors that measure the global accuracy.
Local Accuracy
While global accuracy provides a bulk measure,
it provides no information on how accuracy var-
ies across the surface. Yang and Hodler (2000)
argued that in many cases, the relative variation of
errors can be more useful than the absolute error
measures. When the global errors are identical, an
interpolated model with evenly distributed errors
is much reliable than one with highly concentrated
errors. Local accuracy can be characterized with
a method proposed by Yang and Hodler (2000),
which involves a sequence of steps: computation
of residual for all data points, interpolation of
the residual data using an exact method (such as
Kriging or Radial Basis Functions), drawing a
2D or 3D map, and analyzing the visual pattern
of local errors.
Visual Pleasantness and
Faithfulness
Models generated by different interpolators
vary not only in statistical accuracy but also in
their visual appearance (Figure 1). Models with
identical statistical accuracy can still vary in their
visual appearance (e.g., Franke, 1982; Yang and
Hodler, 2000). How attractive a surface model
looks is dened as the visual pleasantness (Yang
and Hodler, 2000). Some operational criteria
recommended to measure the visual pleasantness
include: Is the model visually attractive? Is this

model smooth? Is there any “bull-eye” or “sink-
hole” appearance? Is there any other less pleasant
appearance? Obviously, visual pleasantness is by
nature a subjective measure.
Visual faithfulness is dened as the closeness
of an interpolated surface to the reality (Yang and
Hodler, 2000). In some applications, particularly
in the domain of scientic visualization, an analyst
may appreciate much more on the visual appear-
ance of the output surface than on their statistical
accuracy. With the increasing role of scientic
visualization in geographic information systems,
the measure of visual faithfulness has gained its
practical signicance. To evaluate the level of vi-
sual faithfulness, surface reality is needed to serve
as reference. While locating a reference for the
134
Spatial Interpolation
continuous surface can be difcult or impossible
for some variables (such as temperature or noise),
analysts can focus on some specic aspects such
as surface discontinuities or extremes that can be
inferred from direct or indirect sources.
Sensitivity
Interpolation methods are based on different
theoretical assumptions. Once certain parameters
or conditions are altered, these interpolators
can demonstrate different statistical behavior
and visual appearance. The sensitivity of an
interpolator with respect to these alterations is

critical in assessing the suitability of a method
as, preferably, the interpolator should be rather
stable with respect to changes in the parameters
(Franke, 1982). It is impossible to incorporate
each combination of parameters in an evaluation.
Based on a comprehensive literature review, the
sensitivity of a method with respect to the vary-
ing sample size and/or search conditions for some
local interpolators should be targeted (Yang and
Hodler, 2000).
Computational Intensity
Computational intensity is measured as the
amount of processing time needed in gridding
or triangulation. Different interpolation methods
Figure 1. Three-dimensional perspectives of the models generated from the same data set with different
algorithms. The original surface model (i.e., USGS 7.5’ Digital Elevation Model) is shown as the basic
for further comparison. (Source: Yang and Hodler, 2000)
135
Spatial Interpolation
have different levels of complexity due to their
algorithm designs that can lead to quite a varia-
tion in their computational intensity. This differ-
ence can be polarized when working with large
sample sets that normally take much longer time
to process. Triangulation is always a fast method.
Global interpolators are generally faster than local
methods. Smooth methods are normally faster
than exact methods. Deterministic interpolators
are generally faster than stochastic methods (e.g.,
different types of Kriging).

conc Lus Ion And future
rese Arch
Over the past several decades, a rich pool of spa-
tial interpolation methods have been developed
in several different elds, and some have been
implemented in major geographic information
system (GIS), spatial statistics or geostatistics
software packages. While software developers
tend to implement more interpolators and offer
a full range of options for each method included,
practitioners often struggle to nd an appropriate
method for their specic applications due to the
lack of practical guidelines. The criteria discussed
in this article should be useful to guide this selec-
tion. Nevertheless, there are some challenges in
this eld, and perhaps the biggest one is that there
are some arbitrary decisions involved, particularly
for Kriging and other local methods, which may
ultimately affect the performance. Therefore,
further research is needed to develop guidance
that helps identify the circumstances under which
particular methods should be adopted and how to
optimize the parameters that control them. For
this purpose, more empirical, inter-model com-
parisons and rigorous assessment of interpolation
performance with different variables, sample sizes
and internal parameters are needed.
references
Bailey, T. C., & Gatrell, A. C. (1995). Interactive
Spatial Data Analysis. Longmans.

Briggs, I. C. (1974). Machine contouring using
minimum curvature. Geophysics, 39(1), 39-48.
Burrough, P. A., & McDonnell, R. A. (1998).
Principles of Geographical Information Systems,
333. Oxford University Press.
Carlson, R. E., & Foley, T.A. (1991). Radial Basis
Interpolation Methods on Track Data. Lawrence
Livermore National Laboratory, UCRL-JC-
1074238.
Franke, R. (1982). Scattered data interpolation:
tests of some methods. Mathematics of Computa-
tion, 38(157), 181-200.
Golden Software, Inc. (2002). Surfer 8: User’s
Guide, 640. Golden, Colorado.
Goodchild, M. F., & Lam, N. (1980). Areal in-
terpolation: A variant of the traditional spatial
problem. Geo- Processing, 1, 297-312.
Hardy, R. L. (1971). Multivariate equations of
topography and other irregular surfaces. Journal
of Geophysical Research, 71, 1905-1915.
Hutchinson, M. F. (1989). A new procedure for
gridding elevation and stream line data with
automatic removal of spurious pits. Journal of
Hydrology, 106, 211-232.
Isaaks, E. H., & Srivastava, R. M. (1989). An In-
troduction to Applied Geostatistics, 592. Oxford
University Press.
Krige, D. G. (1951). A statistical approach to some
basic mine valuation problems on the Witwa-
tersrand. Journal of Chemistry, Metallurgy, and

Mining Society of South Africa, 52(6), 119-139.
Lancaster, P., & Salkauskas, K. (1986) Curve and
Surface Fitting: An Introduction, 280. Academic
Press.
136
Spatial Interpolation
Matheron, G. (1962). Traité de Géostatistique
appliquée, tome 1 (1962), tome 2 (1963). Paris:
Editions Technip.
Okabe, A., Boots, B., & Sugihara, K. (1992).
Spatial Tessellations, 532. New York: John Wiley
& Sons.
Oliver, M. A., & Webster, R. (1990). Kriging: A
method of interpolation for geographic informa-
tion systems. International Journal of Geographi-
cal Information Systems, 4(3), 313-332.
Tobler, W. R. (1970). A computer movie simulat-
ing urban growth in the Detroit region. Economic
Geography, 46, 234–40.
Tobler, W.R. (1979). Smooth pycnophylactic inter-
polation for geographical regions. Journal of the
American Statistical Association, 74, 519-30.
Yang, X., & Hodler, T. (2000). Visual and statisti-
cal comparisons of surface modeling techniques
for point-based environmental data. Cartography
and Geographic Information Science, 17(2),
165-175.
key ter Ms
Cross Validation: A validation method in
which observations are dropped one at a time,

the value for the dropped point is estimated us-
ing the remaining data, and then the residual is
computed; this procedure is repeated for a second
point, and so on. Cross-validation outputs various
summary statistics of the errors that measure the
global accuracy.
Geostatistics: A branch of statistical esti-
mation concentrating on the application of the
theory of random functions for estimating natural
phenomena.
Sampling: The technique of acquiring suf-
cient observations that can be used to obtain a
satisfactory representation of the phenomenon
being studies.
Search: A procedure to nd sample points
that will be actually used in a value estimation
for a local interpolator.
Semivariogram (or Variogram): A traditional
semivariogram plots one-half of the square of the
differences between samples versus their distance
from one another; it measures the degree of spatial
autocorrelation that is used to assign weights in
Kriging interpolation. A semivariogram model
is one of a series of mathematical functions that
are permitted for tting the points on an experi-
mental variogram.
Spatial Autocorrelation: The degree of cor-
relation between a variable value and the values
of its neighbors; it can be measured with a few
different methods including the use of semivar-

iogram.
137
Chapter XVIII
Spatio-Temporal Object
Modeling
Bo Huang
Chinese University of Hong Kong, China
Magesh Chandramouli
Purdue University, USA
Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited.
Abstr Act
Integrating spatial and temporal dimensions is a fundamental yet challenging issue in modeling geo-
spatial data. This article presents the design of a generic model within the object-oriented paradigm
to represent spatially-varying, temporally-varying, and spatio-temporally-varying information using a
mechanism, called parametric polymorphism. This mechanism allows a conventional data type (e.g.,
string and integer) to be enhanced into a spatial, temporal, and/or spatiotemporal collection type, and
so an ordinary attribute can be extended with spatial and/or temporal dimensions exibly. An associated
object query language has also been provided to support the manipulation of spatio-temporal informa-
tion. The design of the model as well as the query language has given rise to a uniform representation of
spatial and temporal dimensions, thereby offering a new option for the development of a spatio-temporal
GIS to facilitate urban/environmental change tracking and analysis.
over vIew
Spatio-temporal databases are a subject of
increasing interest and the research community
is dedicating considerable effort in this direc-
tion. Natural as well as man-made entities can
be referenced with respect to both space and
time. The integration of the spatial and temporal
components to create a seamless spatio-tempo-
ral data model is a key issue that can improve

spatio-temporal data management and analysis
immensely (Langran, 1992).
Numerous spatio-temporal models have been
developed. Notable among these are the snapshot
138
Spatio-Temporal Object Modeling
model (time-stamping layers, Armstrong 1988),
the space-time composite (time-stamping at-
tributes, Langran and Chrisman 1988), the spa-
tio-temporal object model (ST-objects, Worboys
1994), the event-based spatio-temporal data model
(ESTDM, Peuquet and Duan 1995) and the three-
domain model (Yuan 1999). The snapshot model
incorporates temporal information with spatial
data by timestamping layers that are considered
as tables or relations. The space-time composite
incorporates temporal information by timestamp-
ing attributes, and usually only one aspatial
attribute is chosen in this process. In contrast
to the snapshot and the space-time composite
models, Worboys’s (1994) spatio-temporal ob-
ject model includes persistent object identiers
by stacking changed spatiotemporal objects on
top of existing ones. Yuan (1999) argues that
temporal Geographic Information Systems (GIS)
lack a means to handle spatio-temporal identity
through semantic links between spatial and tem-
poral information. Consequently, three views of
the spatio-temporal information, namely spatial,
temporal, and semantic, are provided and linked

to each other. Peuquet and Duan’s ESTDM (1995)
employs the event as the basic notion of change in
raster geometric maps. Changes are recorded using
an event list in the form of sets of changed raster
grid cells. In fact, event-oriented perspectives that
capture the dynamic aspects of spatial domains
are shown to be as relevant for data modeling
as object-oriented perspectives (Worboys and
Hornsby 2004; Worboys, 2005).
Despite these signicant efforts in spatio-tem-
poral data modeling, challenges still exist:
a
. Ob
ject attributes (e.g., lane closure on a
road) can change spatially, temporally, or
both spatially and temporally, and so fa-
cilities should be provided to model all of
these cases, i.e., spatial changes, temporal
changes, and spatio-temporal changes;
b
. Ob
ject attributes may change asynchro-
nously at the same, or different, locations.
As an additional modeling challenge, object
attributes can be of different types (e.g., speed
limit is of the integer type and pavement mate-
rial is of the string type). To overcome these
challenges, a spatio-temporal object model that
exploits a special mechanism, parametric poly-
morphism, seems to provide an ideal solution

(Huang, 2003).
pAr AMetr Ic po LyMorph IsM
for spAt Io-te Mpor AL
eXtens Ions
Parametric polymorphism has been extensively
studied in programming languages (PL), espe-
cially in functional PLs (e.g. Metalanguage, ML).
In general, using parametric polymorphism, it
is possible to create classes that operate on data
without having to specify the data’s type. In other
words, a generic type can be formulated by lift-
ing any existing type. A simple parametric class
(type) can be expressed as follows:
class CP<parameter>{
p
ara
meter a;
…
};
where parameter is a type variable. The type
variable can be of any built-in type, which may
be used in the CP-declaration
The notion of parametric polymorphism is
not totally new, as it has been introduced in ob-
ject-oriented databases (OODBs) (Bertino et
al., 1998). This form of polymorphism allows a
function to work uniformly on a range of types
that exhibit some common structure (Cardelli
and Wegner, 1985). Consequently, in addition
to the basic spatial and temporal types shown in

Figure 1, three parametric classes, Spatial<T>,
Temporal<T>, and ST<T> are dened in Huang
and Yao (2003). Here, T is dened as a spatial type
that contains the distribution of all sections of T
139
Spatio-Temporal Object Modeling
(e.g., all locations of sections of pavement material
of type String), a temporal type that contains the
history of all episodes of T, and a spatial-temporal
type that contains both the distribution and his-
tory of an object (e.g., pavement material along
a road during the past six months), respectively.
The parameter type T can be any built-in type
such as Integer, String, or Struct. Corresponding
operations inside the parameterized types are also
provided to traverse the distribution of attributes.
Thus polymorphism allows users to dene the type
of any attribute as spatially varying, temporally
varying or spatial-temporally varying, thereby
supporting spatio-temporal modeling. The three
parameterized types form a valuable extension
to an object model that meets modeling require-
ments and queries with respect to spatio-temporal
data. Some details about these three types are
provided below.
t he Spatial<T> Type
As the value of an attribute (e.g., speed, pavement
quality and number of lanes) can change over
Parametric typesParametric types
space (e.g., along a linear route), a parameterized

type called Spatial<T> is dened to represent the
distribution of this attribute (Huang, 2003).
The distribution of an attribute of type T is
expressed as a list of value-location pairs:
{(val
1
, loc
1
), (val
2
, loc
2
), …, (val
n
, loc
n
)}
where val
1
, …, val
n
are legal values of type T, and
loc
1
, … loc
n
are locations associated with the at-
tribute values. This way, a Spatial<T> type adds
a spatial dimension to T.
t he Temporal<T> Type

Just as Spatial<T> can maintain the change of
attributes over space, Temporal<T> represents
attribute changes over time (Huang and Clara-
munt, 2005).
A Temporal object is a temporally ordered
collection of value-time interval pairs:
{(val
1
, tm
1
), (val
2
, tm
2
), …, (val
n
, tm
n
)}
Figure 1. Extended spatio-temporal object types
Time-interval
Temporal<T> Spatial<T>

Geometric types
ST<T>
Parametric types

Geometric types
Geometry

Collection

Geometry


Point
LineString

Polygon


Points

LineStrings
Polygons


Extended object types

140
Spatio-Temporal Object Modeling
where val
1
, …, val
n
are legal values of type T, and
tm
1
, … tm
n

are time intervals such that tm
i
∩ tm
j

= ∅, and i ≠ j and 1 ≤ i, j ≤ n. The parameter type
T can be any built-in type, and hence this type is
raised to a temporal type.
t he ST<T> Type
ST<T> represents the change of attributes over
both space and time. An ST object is modeled as
a collection of value-location-time triplets:

{(val
1
, loc
1,
tm
1
), (val
2
, loc
2,
tm
2
), …, (val
n
, loc
n,

tm
n
}
where val
1
, …, val
n
are legal values of type T,
loc
1
, … loc
n
are line intervals; also, loc
i
∩ loc
j

= ∅, i ≠ j and 1 ≤ i, j ≤ n, tm
1
, … tm
n
are time
intervals such that tm
i
∩ tm
j
= ∅, i ≠ j and 1 ≤ i,
j ≤ n. Each pair, i.e., (val
i
, loc

i,
tm
i
), represents a
state which associates location and time with an
object value.
An example utilizing parameterized
Types
Using the Spatial<T>, Temporal <T> and ST
<T> types, a spatio-temporal class, e.g., route,
is dened as follows.
class route
(extent routes key ID)
{
attribute String ID;
attribute String category;
attribute Spatial<String> pvmt_quality;
//user-dened space-varying attr
attribute Spatial<Integer> max_speed;
//user-dened space-varying attr
attribute Temporal<Integer> trafc_light;
//user-dened time-varying attr
attribute ST<Integer> lane_closure;
//user-dened space-time-varying attr
attribute ST<Integer> accident; //
user-dened space-time-varying attr
attribute Linestring shape;
};
The types of attributes pvmt_quality and
max_speed are represented as Spatial<String>

and Spatial<Integer>. These attributes are capable
of representing the distribution of sections along
a route by associating locations with their value
changes. The attribute trafc_light is raised to Tem-
poral <Integer>, which indicates some lanes may
be closed at some time. The attribute lane_closure
is raised to ST<Integer>, which associates both
location and time with a lane_closure event. The
same is true for the attribute accident. However,
the other three attributes (i.e., ID, category, and
shape) remain intact. Therefore, the Spatial<T>
type, Temporal<T> type and ST<T> types allow
users to choose the attributes to raise.
spAt Io-te Mpor AL Quer y
LAngu Age
A query language provides an advanced interface
for users to interact with the data stored in a da-
tabase. A formal interface similar to ODMG’s
Object Query Language (OQL) (Cattell, 2000),
i.e., Spatio-temporal OQL (STOQL) is designed
to support the retrieval of spatio-temporal infor-
mation.
STOQL extends OQL facilities to retrieve
spatial, temporal and spatial-temporal informa-
tion. The states in a distribution or a history are
extracted through iteration in the OQL from-
clause. Constraints in the where-clause can then
be applied to the value, timestamp or location of a
state through corresponding operations. Finally,
the result is obtained by means of the projection

operation in the select-clause.
Given the above standards, STOQL provides
some syntactical extensions to OQL to manipulate
space-varying, time-varying and space-time-
varying information represented by Spatial<T>,
Temporal<T>, and ST<T>, respectively.
141
Spatio-Temporal Object Modeling
In Table 1, time1 and time2 are expressions
of type Timestamp, location1 and location2 are
expressions of type Point. e is an expression of type
Temporal<T>, and es is an expression denoting a
chronological state, a state within a distribution,
or a state within a distribution history.
The following examples illustrate how spatio-
temporal queries related to the route class are
expressed using STOQL.
Example 1 (spatial selection). Find the speed
limit from mile 2 to mile 4.
select r_speed.val
from routes as route, route.pvmt_quality! as
r_qlty,
route.max_speed! as r_speed
where r_qlty.loc.overlaps([2,4])
In this query, variable r_qlty, ranging over the
distribution of route.pvmt_quality, represents a
pavement quality segment. r_qlty.loc returns
the location of a pavement quality segment. The
overlaps operator in the where-clause species
the condition on a pavement quality segment’s

location.
Example 2 (spatial projection). Display the loca-
tion of accidents on route 1 where the maximum
speed is 60 mph and pavement quality is poor.
select r_acdt.loc
from routes as route, route.acdt! as r_acdt,
route.pvmt_quality! as r_qlty, route.
max_speed! as r_speed
where route.ID=”1” and r_speed.val =60 and
r_qlty.val =”poor” and
(r_speed.loc.intersection(r_quality.loc)).
contains(r_acdt.loc)
The intersection operation in the where-clause
obtains the common part of r_speed.loc and
r_quality.loc.
Example 3 (temporal projection). Show the time
of all accidents on Route 1.
select r_acdt.tm
from routes as route, route.acdt! as r_acdt
where route.ID=”1”
In this query, variable r_acdt, ranging over
the distribution of route.acdt, represents an ac-
cident. r_acdt.tm returns the time of a selected
accident.
Table 1. Syntactical constructs in STOQL
STOQL Spatial<T> Temporal<T> ST<T> Result Type
[location1,
location2]
struct(start:
location1, end:

location2)
struct(start:
location1, end:location2)
Segment: Linestring
[time1,
time2]
struct(start:time1,
end:time2)
struct(start:time1,end:
time2)
TimeInterval
e! e.distribution e.history e.distribution_history List
es.val es.val es.val es.val T (any ODMG type)
es.vt es.vt es.vt TimeInterval
es.loc es.loc es.loc Geometric type
142
Spatio-Temporal Object Modeling
Example 4 (spatial and temporal join). Find the
accidents which occurred between 8:00-8:30am
on route 1 where the pavement quality is poor.
select r_acdt.loc
from routes as route, route.pvmt_quality! as
r_qlty,
route.accident! as r_acdt
where Route.ID=”1” and r_acdt.tm.overlaps([8am,
8:30am]) and r_qlty.val = “poor” and
r_quality.loc.contains(r_acdt.loc)
This query joins two events through the con-
tains operator.
conc Lus Ion And future work

A generic spatio-temporal object model has been
developed using parametric polymorphism. This
mechanism allows any built-in type to be enhanced
into a collection type that assigns a distribution,
history or both to any typed attribute. In addi-
tion, an associated spatio-temporal object query
language has also been provided to manipulate
space-time varying information.
While spatio-temporal data modeling is fun-
damental to spatio-temporal data organization,
spatio-temporal data analysis is critical to time-
based spatial decision making. The integration
of spatio-temporal analysis with spatio-temporal
data modeling is obviously an efcient means to
model spatio-temporal phenomena and capture
the dynamics. In doing so, on the one hand, the
spatio-temporal changes can be tracked; on the
other hand, spatio-temporal data analysis has
a strong database support that facilitates data
management including retrieval of necessary
data for applying spatio-temporal mathematical
analysis models.
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time. In Proc. Twelfth European Conference on
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edited by E. Jul (Brussels), pp. 41-66.
Cardelli, L. and Wegner, P. (1985). On Understand-
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Cattell, R.G. (ed.) (2000). The Object Data Stan-
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Huang, B., & Claramunt, C. (2005). Spatiotem-
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database approach to dynamic segmentation.
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Langran, G. (1992). Time in Geographic Informa-
tion Systems (London: Taylor & Francis).
Langran, G., & Chrisman, N. (1988). A framework
for temporal geographic information. Carto-
graphica, 25, 1-14.
Peuquet, D., & Duan, N. (1995). An event-based
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Worboys, M. (1994). A unied model of spatial
and temporal information. Computer Journal,
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Worboys, M. and Hornsby, K. (2004) From objects
to events: GEM, the geospatial event model. In
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(pp. 327-343).
Yuan, M. (1999). Use of a three-domain repre-
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137-159.
key t er Ms
Distribution: A list of value-location pairs
representing the spatial change.
History: A list of value-time pairs represent-
ing the temporal change.
Parametric Polymorphism: The ability
of writing classes that operate on data without
specifying the data’s type
Parametric Type: The type that has type
parameters
Polymorphism: The ability to take several
forms. In object-oriented programming, it refers

to the ability of an entity to refer at run-time to
instances of various classes; the ability to call
a variety of functions using exactly the same
interface
Spatial Change: The value of an attribute of
certain type (e.g., integer or string) changes at
different locations
Spatio-Temporal Change: The value of an
attribute of certain type (e.g., double or string)
changes at different locations and/or different
times.
Temporal Change: The value of an attribute
of certain type (e.g. integer or string) changes at
different times
144
Chapter XIX
Challenges and Critical Issues
for Temporal GIS Research
and Technologies
May Yuan
University of Oklahoma, USA
Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited.
Abstr Act
Temporal Geographic Information Systems (GIS) technology has been a top research subject since late
the 1980s. Langran’s Time in Geographic Information Systems (Langran, 1992) sets the rst milestone
in research that addresses the integration of temporal information and functions into GIS frameworks.
Since then, numerous monographs, books, edited collections, and conference proceedings have been
devoted to related subjects. There is no shortage of publications in academic journals or trade maga-
zines on new approaches to temporal data handling in GIS, or on conceptual and technical advances
in spatiotemporal representation, reasoning, database management, and modeling. However, there is

not yet a full-scale, comprehensive temporal GIS available. Most temporal GIS technologies developed
so far are either still in the research phase (e.g., TEMPEST developed by Peuquet and colleagues at
Pennsylvania State University in the United States) or with an emphasis on mapping (e.g., STEMgis
developed by Discovery Software in the United Kingdom).