Characterizing Urban Landscape by
Using Fractal-based Texture Information
Bingqing Liang and Qihao Weng
Abstract
This study examined the potential of integrating fractal tex-
ture with spectral information on urban landscape charac-
terization by the maximum likelihood image classifier. The
fractal texture was first derived from the red band of a Land-
sat ETM+ image by applying the triangular prism algorithm at
different window sizes. The quality of the twenty-five resultant
texture bands were then analyzed by fourteen approaches at
both of the pre- and post-classification stages. Results showed
all evaluations employed at the pre-classification stage are
useful to screen out texture bands more useful than others to
facilitate the later supervised image classification. This tex-
ture information is observed useful only for classifying medi-
um- and low- density residential categories. The window size
leading to the best overall classification accuracy is identified
as 31 × 31, implying this scale should be kept as a guide-
line for future studies if a similar methodology is adopted.
Introduction
A major problem in urban remote sensing is the heterogeneity
of the urban environment. For example, low density residen-
tial areas may be composed of tree crowns, rooftops, lawns,
paved streets, driveways, and parking lots. Such a hetero-
geneous landscape pattern is usually displayed as spatial
variation of spectral responses and structural features such as
texture in remotely sensed images, presenting a challenge for
image interpretation. In this situation, it is necessary to focus
on the overall spatial pattern of variation that characterizes
each urban category. Traditional remote sensing analyses such
as maximum likelihood (
ML
) classification focuses on the
spectral method based upon the assumption that the spectral
data closely correspond to the surface property. Yet the spec-
tral approach ignores spatial information, which is a primary
characteristic of all geographic phenomena and processes,
presented in the relationship among pixels that comprise the
remotely sensed imagery. For this reason, a major theme in
the remote sensing community has been how to obtain infor-
mation from such a spatial relationship and how this informa-
tion can be used to assist image analysis and interpretation.
Many geospatial algorithms have been developed to address
these problems. These methods are established by assuming
a pattern that tends to be with either repeating (e.g., spatial
autocorrelation) or stochastic (e.g., variogram) structures,
considers more of localized discontinuities (e.g., edge detec-
tion by convolution filters) or global properties (e.g., Fourier
transformation, Wavelets, and Gabor transformation), and
exhibits at a single scale so that it is invariant to image trans-
formation like rotation and translation (e.g., co-occurrence
matrix that produces the Haralick features) or at a multi-scale
so that it remains reliable under scale changes (e.g., Gabor
transformation and fractal analysis) (Hassaballah
et al.
,
2016; Kumar and Bhatia, 2014). When these logics are being
implemented, it can rely on features measured by parametric
(e.g., geostatisticas and edge detection) or nonparametric (e.g.,
artificial neural network) statistics, whose local structure cap-
tured by a moving window (e.g., textural and contextual) or
an object (e.g., object-based classification) in image processing
or a patch in ecology (e.g., landscape pattern metrics), and de-
rived from low-level image processing where learning is not
required in the process (e.g., edge detection) or high-level im-
age processing where training and learning are often involved
in the process (e.g., machine learning) (Hassaballah
et al.
,
2016; Kumar and Bhatia, 2014). Among them, fractal analysis
addresses a unique kind of texture that is neither in repeti-
tion nor stochastic or both, which other geospatial algorithms
consider, and is capable of measuring the scale-independence
property of the spatial structure of interest (Batty, 1991; Batty
and Longley, 1989; Clarke, 1986; Emerson
et al.
, 1999, and
2005; Mandelbrot, 1983; Shen, 2002; Zhao, 2001). It thus is
particularly attractive to remote sensing because it helps to
understand the issue of scale and resolution - a central topic
in remote sensing image analysis and interpretation - and
adopted in this research.
Fractals are the fundamental part of fractal geometry, which
concerns irregular shapes and surfaces that cannot be repre-
sented by simple classical geometry (e.g., 1 for a curve, 2 for
a plane, and 3 for a cube). One of the most important proper-
ties of fractals is self-similarity, which represents invariance
with respect to scale. In other words, a self-similar object is
made up of copies of an infinite number of copies of itself in
a reduced scale. In geoscience, the property of self-similarity
is better interpreted as scale-independence (Clarke, 1986).
However, most environmental phenomena are not pure frac-
tals at all scales. Rather, they only exhibit a certain degree of
self-similarity within limited regions and over finite ranges of
scale, which is measurable by using statistics such as spatial
autocovariances. The underlying principle of fractals is to use
strict or statistical self-similarity to determine fractal dimen-
sion (
FD
) - a measure of the degree of irregularity or complex-
ity of objects. As a non-integer value,
FD
ranges from 1.0 and
2.0 for a curve and from 2.0 to 3.0 for a cube and hence better
describes natural and manmade objects that are rarely com-
posed of straight lines or smooth plane. When fractals are ap-
plied to remote sensing, images are viewed as one type of hilly
terrain surface whose “elevation” is proportional to the digital
numbers. Consequently,
FDs
are readily computable and can
be used to denote how complicated an image is. Typically,
FD
values range from 2.0 for a perfectly smooth image to 3.0 for a
very rugged surface that eventually fills a volume. Since such
studies are based upon the hypothesis that spatial complexity
Bingqing Liang is with the University of Northern Iowa, ITTC
205, Geography Department, Cedar Falls, IA 50614
(
).
Qihao Weng is with the Indiana State University, 600 Chestnut
Street, Science Building,Room 159, Terre Haute, IN 47809.
Photogrammetric Engineering & Remote Sensing
Vol. 84, No. 11, November 2018, pp. 695–710.
0099-1112/18/695–710
© 2018 American Society for Photogrammetry
and Remote Sensing
doi: 10.14358/PERS.84.11.695
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
November 2018
695
