SPATIAL PROXIMITY OF STRUCTURAL ATTRIBUTES IN MINING
REMOTELY SENSED IMAGERY
M.P.Canton
Computer Science Department
North Dakota State University
Fargo, NN, 58105, USA
mcanton@skipanon.com
W.Perrrizo
ComputerScienceDepartment
North Dakota State University
Fargo, ND, 58105, USA
william.perrizo@ndsu.edu
Abstract
Spatial domain operations, used in mining
remotely sensed imagery, take into account the
pixels’ structural attributes as well as
neighborhood conditions. These operations can
be classified as pixel-point and pixel-group. In
this paper, we look at pixel-group operations and
focus on spatial proximity of structural
attributes, namely, location and reflectance
values.
INTRODUCTION
This paper is organized as follows: first we
briefly describe the differences between pixelpoint and pixel-group operations, followed by a
discussion of spatial proximity of attributes in
terms of point-, line-, and edge-detection;
Laplace methods and formula, based on vector
analysis techniques, are used.
Figure 1 – Neighborhood Patterns
Some of the most used kernel dimensions are
those that form a square with an odd number of
neighbors on each side, such as the 8-, 20neighbors and 24-neighbors shown. In these
cases, we speak of 3-by-3 and 5-by-5 kernels,
respectively.
In pixel-point operations the output value is
determined by applying a mapping function to
the corresponding input value, with only one
input value used to determine each output value;
both input and output must be at the same
coordinates. The pixel-to-pixel mode of
operation, and the constraint that both pixels
must be at the same spatial location, simplify the
problem. However, pixel-point operations cannot
be used to alter spatial details within the image.
Pixel-group operations take into consideration
the pixel values in an area adjacent to the point
under consideration. Usually, we assume that the
target pixel is at the center and that the adjoining
pixels, the neighborhood, form some kind of
pattern around the target. The target and its
associated neighborhood pixels are sometimes
called a kernel. Here are some typical
neighborhood patterns used in spatial proximity
operations:
Figure 2 – Spatial Proximity Neighborhood
Patterns
1.1 Point Detection
Some spatial proximity operations used in
mining remotely sensed imagery are based on the
detection of variations and discontinuities within
the image. These variations can refer to image
points, lines, and edges, based on structural
attributes of reflectance values and location. The
detection of image discontinuities, or of patterns
of image continuity, plays an important role in
the location and identification of specific objects.
For example, astronomical software can look for
patterns of brightness change to detect particular
types of celestial objects. Here is a made-up
example of how differences in the brightness
patterns of stars and planets can be used to
identify them in an image[4].
In an image, there are significant differences in
local pixel intensity changes that occur within
stars when compared to those that occur within
planets, as shown in the brightness charts in this
illustration. Many different algorithms have been
devised to detect brightness changes at the point,
line, and edge levels[1].
Figure 4 – Star Object Discontinuity Pattern
One method is based on running a special
convolution mask through the image in order to
notice structural attribute variations between a
pixel and its neighbors. For example, a variation
of the high-pass filter mask can be used to detect
individual pixels that vary in relation to a
uniform background. In this case, we are looking
for a center pixel whose absolute value, derived
from its reflectance structural attribute, is
considerably different from that of the average of
its eight neighbors. The following convolution
mask is used for this:
-1
-1
-1
Figure 3 – Object Detection (Planet)
-1 -1
8 -1
-1 -1
The convolution mask is an array of convolution
coefficients, implemented by means of spatial
convolution or finite impulse response (FIR)
filtering. In this case, a two-dimensional pixel
kernel, based on the spatial proximity of the
structural attributes, is moved across the image,
pixel by pixel. The result of a mathematical
operation on the elements in the kernel is placed
in the output set. The calculation is defined as a
linear process since each of the elements in the
kernel is multiplied by a constant factor called
the convolution coefficient. The convolution
coefficient can be expressed as:
cc = f / e
where f is a multiplier and e is the number of
elements in the kernel. Note that the factor f can
vary for different elements in the kernel, while
the number of elements (e) remains the same[1].
For a 3-by-3 kernel, the convolution
coefficients are labeled as follows:
a b c
d e f
g h i
This array of convolution coefficients is the
convolution mask. Once the convolution
coefficient has been determined for every kernel
element, then the calculation of the output value
consists of multiplying each input value by the
convolution coefficient and adding all of them.
The result is used as the value of the output
pixel. Figures 5 and 6 show a convolution mask
applied to an input pixel[4].
1.2 Line Detection
Line detection implies a higher level of
complexity. A simple case would be a straight
line on the vertical plane. In this case, the
convolution mask must be such that it detects
vertically adjacent pixels whose reflectance
structural attributes contrast with those of the
background. This illustration shows the mask
used to detect a vertical line of contrasting
pixels: the grayscale values are shown before
the mask[4].
Figure 5 – Grayscale Values of the Convolution
Mask
Figure 7–Grayscale Values of Convolution Mask
in Line Detection Using Spatial Proximity
Figure 6 – Convolution Mask Applied to the
Input Pixel
Figure 10 – Two Diagonal Detector Masks
1.3 Edge Detection
Figure 8 – Line Detection Using Convolution
Mask shown in Figure 7
A different convolution mask is necessary to
detect horizontal and diagonal lines[5]. Here
again, the mask is designed so that a large output
value indicates the presence of a particular line
type in the input data set. The following figures
show three convolution masks used in detecting
horizontal and diagonal lines; the first one is a
horizontal detector mask. The last two are
diagonal detector masks.
Figure 9 – Horizontal Detector Mask
Using spatial proximity of structural attributes,
irregular edges can be detected. This is the most
complex case of discontinuity detection, (and
also the most useful one). The reason is that
points and straight lines do not occur frequently
in natural image data. Several spatial filters have
been designed specifically for edge detection.
The ones by Sobel, Robinson, and Kirsch are
well known and can be implemented in software
rather easily. Most of these methods are based on
detecting gray level discontinuities by
calculating a local derivative operator. We
discuss this in greater detail in the following
section.
1.4 Vector Analysis Techniques
Laplace methods of edge enhancement are based
on vector analysis techniques. This approach is
founded on the notion of a pixel brightness slope
and of a gradient vector that points in the
direction of the maximum rate of change, based
on the structural attribute values of the pixels
within the target spatial proximity[1]. In one
case, the first derivative is obtained using the
magnitude of the gradient, and the second
derivative by means of the Laplace formula[2].
The principle is that the magnitude of the first
derivative of a dark or light stripe on a relatively
uniform background can be used to detect an
edge, while the sign of the second derivative
indicates whether a pixel is on the dark or the
bright side of the edge. The following figures
illustrate the mechanism of edge detection by
means of derivative operators[4].
.
Figure 11a – Vector Analysis in Spatial
Proximity for Edge Detection
Figure 11b – Vector Analysis
in Special Proximity for Edge
Detection
CONCLUSION
We have looked at different tools for mining
remotely sensed imagery using pixel-group
operations. However, these datasets are massive,
often in the range of billions of pixels. By
defining spatial proximities of the target pixels,
based on their structural attribute values of
reflectance and location, the spatial domain
mining operations become more manageable.
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Programming the 387, 486, and Pentium,
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[5] N.M. Short, The Remote Sensing Tutorial,
NASA, 1997.