Download 1 - University of Oklahoma

Attribute Expression Using Gray Level Co-Occurrence
Sipuikinene Angelo*, Marcilio Matos,Kurt J Marfurt
ConocoPhillips School of Geology & Geophysics, University of Oklahoma
Summary
Theory of Texture(GLCM)
Seismic resolution remains a major limitation in the world of seismic interpretation. The goal of reflection seismology is to analyze seismic amplitude and character to
predict lithologic facies, and rock properties such as porosity and thickness. Seismic attribute analysis is a technique that is commonly used by oil industry to delineate
stratigraphic and structural features of interest. Seismic attributes, are particularly important in allowing the interpreter to extract subtlest at the limits below seismic
resolution. For example, some attributes such as coherence and curvature are particularly good at identifying edges and fractures. Attributes such as spectral components
tend to be more sensitive to stratigraphic thickness. Many commercial seismic interpretation packages contain RMS amplitude and relative impedance which is sensitive to
acoustic impedance. My proposed research focuses upon seismic textural analysis, borrowing upon techniques commonly used in remote sensing to enhance and detect
terrain, vegetation, and land use information. Textures are frequently characterized as different patterns in the underlying data. Seismic texture analysis was first introduced
by Love and Simaan (1984) to extract patterns of common seismic signal character .Recently, several workers (West et al., 2002; Gao,2003; Chopra and Vladimir, 2005)
have extended this technique to seismic through the uses of gray-level co-occurrence matrices(GLCM).The gray level, allows the recognition of patterns significantly more
complex than simple edges. This set of texture attributes, is able to delineate complicated geological features such as mass complex transport and amalgamated channels that
exhibit a distinct lateral pattern.
Texture
Texture is an everyday term relating to touch, that includes such concepts as rough, silky, and
bumpy. When a texture is rough to the touch, the surface exhibits sharp differences in
elevation within the space of your fingertip. In contrast, silky textures exhibit very small
differences in elevation. Seismic textures work in the same way, except, elevation is replaced
by brightness values (also called gray levels ). Instead of probing a finger over the surface, a
"window" or a square box defining the size of the area, a probe is used (Halley, 2007)
GLCM
GLCM, is a tabulation of how often different combinations of Voxel brightness values (gray
levels) occur in a sub-image window. In this research, GLCM compares a series of "second
order" texture calculations, which quantifies and considers the relationship between groups of
two (usually neighboring) pixels in the original image Figure 2b.
Objectives
The objective of this research is to evaluate modern texture analysis as a tool to delineate complex Stratigraphic packages that are easy to identify, but perhaps difficult to
map. This analysis will be based on pattern recognition and will be essential for features that exhibit a distinct lateral patter: mass transport complex ,dewatering features,
and amalgamated channels .
Figure 2a is characterized as a value of 1 corresponding to a trough a
value of 3 to a zero crossing, and of 5 to a peak. A representative, (55)
patch of seismic data using the discretization technique mentioned above.
Figure 2b is the resulting gray-level co-occurrence matrix. Each row i,
column j element of the gray-level co-occurrence matrix, indicates how
many times the pixel lies to the right of the one value being analyzed.
Texture calculations require a symmetrical matrix to account for the
reciprocal nature of neighbor relations. To obtain symmetric matrices
from the above definition, the resulting GLCM matrices are transposed.
For 2D horizon slices, we compute the gray-level co-occurrence matrix in
either 4 or 8 directions and sum the results.
00
Figure 2. (a) A seismic trace scaled and
biased to vary between 1 (a trough) and 5 (a
peak). Zero crossings have a value of 3. (b)
A window of seismic data along a horizon
slice. (c ) Resulting GLCM matrices and
scale bar representing levels of intensity
pixel occurrence.
Normalization
Pi , j 
pi , j
i 0
EQ = (1)
pi , j
50
j 0
y
y
6
30
35
0
0
1
2
3
4
5
7
0
1
2
3
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5
6
15
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30
0
35
x
0
7
0
1
2
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7
40
2
30
0
35
0.8
2
30
4
0.6
4
20
6
10
10
15
20
x
Contrast: 49
Correlation: -1
Energy: 0.5000
Homogeneity: 0.1250
25
1
5
Contrast: 0
Correlation: 1.0000
Energy: 0.5102
Homogeneity: 1
25
Contrast
0
1
2
3
4
5
6
7
0
1
2
3
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7
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10
y
7
x
0.2
5
y
6
2,2
2,3
2,4
3,0
3,1
3,2
3,3
3,4
4,0
4,1
4,2
4,3
4,4
Figure 1. A (5x5) GLCM matrices with its
neighboring and reference pixel
80
60
200
40
20
250
50
100
150
x
200
Random pattern
To extract the key components of the GLCM , workers have formulated some
15 different texture measurements that can be calculated from the input
GLCM. These measurements represent specific image properties such as
contrast, orderliness and statistics. These three measurements are further
subdivided into three groups.
1.Contrast Group: Measures are related to contrast ; it use weights related to
the distance from the GLCM diagonal. Example:
Dissimilarity, Contrast , Homogeneity
2.Orderliness Group: Orderliness means, how orderly the pixel values are
within the window. Example:
Entropy, Energy
3.Statistics Group: This third group of GLCM texture measures, consists of
statistics derived from the GLC matrix. Example,
Correlation, Variance
20
0.4
Second step: Choose the direction, the offset, the size
of the analysis window and calculate the GLCM matrix
5
15
4
6
4
10
0.6
x
3
5
0.8
7
2
y
25
0.2
Gray
level
1
0.2
2
2,1
100
Requirements for Human Interpretation
4
6
Sliding window GLCM
0.4
1
2,0
250
0
Seismic Data
Outcrop
0.8
2
4
0
1,4
1
0.6
20
1,3
Contrast: 32.6667
Correlation: -0.5000
Energy: 0.3333
Homogeneity: 0.4167
The more useful GLCM attributes
0.4
0.8
15
1,2
120
0.6
2
10
1,1
160
100
1
5
1,0
140
Equation one transforms the GLCM matrices into a probability mass function. Equation 1 is an approximation of the
underlying probability density functions;. the true space of the image intensity values is continuous whereas the GLCM is
being calculated using discrete values.
Most texture calculations are weighted averages of the normalized GLCM cell contents. A weighted average multiplies
each value to be used by a factor (a weight) before summing and dividing by the number of values. The weight is intended
to express the relative importance of the value. When calculating a texture image, the result of the image will be a single
value representing the entire window. This value is placed in the center of the window, and then the window is moved one
pixel in the designated direction. This process is repeated and a new texture is calculated such that the entire image is built
up of texture values.
Operational Processes - GLCM
Gray level
0
0,4
Texture
First step: Scale the data
7
0,3
180
150
After making the GLCM symmetrical, there is still one more step to take
before texture measures can be calculated. The measures require that each
GLCM cell contain, not a count of how many times a combination pixel
occurred, but rather a probability or normalization function. This is
achieved by normalizing the matrices such that they each sum to 1.0 (see
Equation 1).
0,2
200
N 1 N 1

0,1
Texture Examples
y
Gray level
05
0,0
25
30
35
0
0.4
6
0.2
5
10
15
20
x
25
30
35
Energy   P
2
ij
i
j
Entropy   Pij log Pij
i
j
Contrast   (i  j ) Pij
2
i
j
0
1
Homogeneit y  
P
2 ij
i
j 1  (i  j )
11/18/2008