collected by the ETM+, ASTER, and IKONOS sensors, it was shown that, when the
spatial resolution increased from 30 to 15 m and then to 4 m, all resultant FD values
were different, illustrating the scale effect on fractal measurement resulted from the
sensor’s spatial resolution. Overall, it was found that the shapes of the image texture
of individual spectral bands do not always grow more complex with data acquired by
sensors having finer spatial resolution. Only the NIR bands of the three sensors can
characterize rougher texture in images collected with smaller pixel size and thus are
superior to others (G and R in particular) for this purpose. A similar trend was also
noticed when the LULC images derived from the same image types were employed.
Using the traditional ISODATA unsupervised algorithm, the classified images
derived from the data sets with higher spatial resolution (e.g., IKONOS) grew
smoother instead rougher as compared to those from images with coarser spatial
resolution, such as ETM+. Obviously, there exists a discrepancy between the more
detailed spatial information recorded in images with better spatial resolution and the
less fragmented image surface as suggested by lower FD values. This can be attributed
to a major drawback of fractal measurement in describing the spatial complexity.
It only considers the shape of a feature, which is just one of the many properties
of image texture. Other factors such as the form, size, and distribution of a given
spatial object can all potentially help or hinder the separation of one image texture
from another. A possible solution that has been suggested is to use the Lacunarity
analysis, which considers multiple textural characteristics for a single fractal object
(Mandelbrot, 1983).
The efficiency of fractal measurement for detecting the scaling properties of remote
sensing images due to the resampling process was also evaluated with the resampled
images. For a single image, their FD values changed with different pixel aggregation
levels, implying real remotely sensed images are not true fractals. Overall, it was found
that the resampling process tended to complicate the image texture with increasing pixel
size. At some pixel aggregation levels, the resampling process also appeared to have
stronger impact than other levels on changing image spatial properties. Specifically, for
the images collected by the MSS, ETM+, and ASTER sensors, the textural complexity
of the original images was less dissimilar to each other once they were resampled by the
480 m pixel size. When only the resampled images were considered, the resampling
process could generate more distinct images at 480 m than other aggregation levels for
the three image types. The results from image subscenes acquired by the ETM+,
ASTER, and IKONOS sensors show that the textural complexity of both of the
residential and downtown landscapes recorded in the original images was more
comparable after being resampled to the 120 m aggregation level than other scales.
Besides, the resampling process could produce image texture that is most different from
other resampled images at 120 m for the ETM+ images regardless of the dominant
landscape, 60 m for both ASTER and IKONOS residential images, and 30 m for both
ASTER and IKONOS residential images. Overall, these pixel aggregation levels may
suggest critical scale ranges where the intricacy of the underlying urban landscape
recorded in the original image would reach a threshold that may be due to the
interoperation of various natural (e.g., geological and ecological) and anthropogenic
processes involved in urbanization. These aggregation scales may potentially link to
250
MULTISCALE FRACTAL CHARACTERISTICS OF URBAN
spatial resolution increased from 30 to 15 m and then to 4 m, all resultant FD values
were different, illustrating the scale effect on fractal measurement resulted from the
sensor’s spatial resolution. Overall, it was found that the shapes of the image texture
of individual spectral bands do not always grow more complex with data acquired by
sensors having finer spatial resolution. Only the NIR bands of the three sensors can
characterize rougher texture in images collected with smaller pixel size and thus are
superior to others (G and R in particular) for this purpose. A similar trend was also
noticed when the LULC images derived from the same image types were employed.
Using the traditional ISODATA unsupervised algorithm, the classified images
derived from the data sets with higher spatial resolution (e.g., IKONOS) grew
smoother instead rougher as compared to those from images with coarser spatial
resolution, such as ETM+. Obviously, there exists a discrepancy between the more
detailed spatial information recorded in images with better spatial resolution and the
less fragmented image surface as suggested by lower FD values. This can be attributed
to a major drawback of fractal measurement in describing the spatial complexity.
It only considers the shape of a feature, which is just one of the many properties
of image texture. Other factors such as the form, size, and distribution of a given
spatial object can all potentially help or hinder the separation of one image texture
from another. A possible solution that has been suggested is to use the Lacunarity
analysis, which considers multiple textural characteristics for a single fractal object
(Mandelbrot, 1983).
The efficiency of fractal measurement for detecting the scaling properties of remote
sensing images due to the resampling process was also evaluated with the resampled
images. For a single image, their FD values changed with different pixel aggregation
levels, implying real remotely sensed images are not true fractals. Overall, it was found
that the resampling process tended to complicate the image texture with increasing pixel
size. At some pixel aggregation levels, the resampling process also appeared to have
stronger impact than other levels on changing image spatial properties. Specifically, for
the images collected by the MSS, ETM+, and ASTER sensors, the textural complexity
of the original images was less dissimilar to each other once they were resampled by the
480 m pixel size. When only the resampled images were considered, the resampling
process could generate more distinct images at 480 m than other aggregation levels for
the three image types. The results from image subscenes acquired by the ETM+,
ASTER, and IKONOS sensors show that the textural complexity of both of the
residential and downtown landscapes recorded in the original images was more
comparable after being resampled to the 120 m aggregation level than other scales.
Besides, the resampling process could produce image texture that is most different from
other resampled images at 120 m for the ETM+ images regardless of the dominant
landscape, 60 m for both ASTER and IKONOS residential images, and 30 m for both
ASTER and IKONOS residential images. Overall, these pixel aggregation levels may
suggest critical scale ranges where the intricacy of the underlying urban landscape
recorded in the original image would reach a threshold that may be due to the
interoperation of various natural (e.g., geological and ecological) and anthropogenic
processes involved in urbanization. These aggregation scales may potentially link to
250
MULTISCALE FRACTAL CHARACTERISTICS OF URBAN