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5th Intensive Course on Soil Micromorphology

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mathematics using a single pixel with corresponding pixels in one or more images ... Two critical parameters are available - the orientation and M the magnitude of ... – PowerPoint PPT presentation

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Title: 5th Intensive Course on Soil Micromorphology

1
5th Intensive Course on Soil Micromorphology
Naples 2001
12th - 14th September Image Analysis
Lecture 6 Morphological Segmentation Orientation
Analysis
2
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Summary of some key operations of Image
Analysis/Processing
• Operations which rely only on pixel in question
• Threshold
• mathematics using a single pixel and constant
• e.g. add 10 to each pixel - or subtract or
multiply etc.
• mathematics using a single pixel with
corresponding pixels in one or more images
• e.g. multiply pixel (x) in image A by value in
pixel (x) in image B.
• Each pixel is processed in turn

3
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Summary of some key operations of Image
Analysis/Processing
• Operations which rely only on pixel in question
and neighbouring ones (e.g. kernel or convolution
filter)
• each pixel is processed in turn
• Many different types of kernel
• averaging
• hit and miss

4
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Some alternative methods for segmenting images
and related topics
• Orientation Analysis
• Domain Segmentation
• Improved Visualisation of Images.

5
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Segmentation of images without the need for
segmentation
For many images, unambiguous segmentation is not
possible as the resulting image is too complex
even for manual editting to ensure that particles
An alternative approach examines changes in
intensity and not absolute values.
• avoids thresholding/segmentation problems
• can remove subjectivity entirely
• can reduce complex images to a relatively few
parameters which can be related to external
factors such as stress level, water flow etc.

6
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Segmentation of images without the need for
segmentation.
Intensity Gradient Methods were devised primarily
as edge-detectors.
Image 1 and magnitude image from Intensity
Gradient Analysis. Output image is a form of
edge detector.
7
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Simplest form of edge detector considers point 0
and one adjacent pixel. For x-direction - pixel 1
is used i.e. change in intensity is given by
where d is distance between pixels For
y-direction - pixel 2 is used.
An estimate of the orientation is thus available
at each pixel.
8
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Greatest gradient of intensity change will be at
right angles to edges and this can be used to
define an improved edge-dector or to define the
orientation of features at every pixel within an
image.
Two critical parameters are available ? - the
orientation and M the magnitude of the intensity
change
9
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
A better edge detector considers points 0 and 1
- 4. For x-direction change in intensity is
given by
where d is distance between pixels For
y-direction
This filters some noise and is alternatively
known as the 42 formulation as four points are
used in a 2nd order solution.
10
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
A convenient way to process an image is to define
a kernel by which the pixels surrounding the
pixels of interest and multiplied by appropriate
factors.
For the 42 formula, the X - direction kernel
will be defined by- while the Y - direction
kernel is-
11
Best results are obtained using 20 nearest
surrounding pixels. Gives a fourth order
solution for orientation - only 14 points are
required so least squares analysis possible
thereby providing some filtering
12
Kernels for 20,14 Analysis Mehtod of Smart and
Tovey and also Sobel Operator.
Smart and Tovey (1988) kernel for 20,14 method.
This kernel is most accurate in specifying
orientation. Values are multiplied by 1000.
The Sobel Operator uses a 3 x 3 kernel.
13
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
0 270
90
180
Orientation convention follows geological
convention
i.e. 0 degrees is vertically upwards 90 degrees
is horizontal angles go clockwise.
Mathematical convention 0 degrees horizontal 90
degrees vertically upwards angles go
anticlockwise.
14
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Image 1 and angles-coded image
Each pixel has orientation defined by colour
scale. Howver, output image can be difficult to
interpret
15
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Over 250 000 estimates of orientation. Data used
to define a rosette diagram - often approximately
shaped as an ellipse.
16
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Shape of rosette diagram usually approximates to
an ellipse. Use Least Squares to find best
fitting ellipse and length of major and minor
axis. Index of Anistropy Ia may be defined in 4
diffferent ways.
Max and min refer to lengths of major and minor
axes of ellipse.
17
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Sokolov used a different definition Areas of
rosette are divided into 90o segments centred on
major and minor axes.
This is equivalent to definition 3
This is the preferred definition these days as it
is a bounded scale from 0 (random) to 1 as full
orientated. Sokolov uses percentage rather than a
ratio 0 - 1.
18
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
• Index of Anistropy can usually be computed, but
if rosette diagram departs significantly from
ellipse, then problems may arise.
• Alternative
• Mean Resultant Vector (also known as
Consitency Ratio)
• works in all cases.
• Define vector of unit magnitude at each pixel in
angles-coded image having components in X- and Y-
directions
• i.e. at ith pixel - the angle is ?i and
components are
• cos ?i and sin ?i in the two directions
respectively.

19
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
The respective components at all N points in the
image are summed to generate two parameters C and
S
Additionally the Mean Resultant Vector (R) may be
defined as
Also the mean orientation is defined as
20
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
The Mean Resultant Vector can always be computed
even if the rosette diagram is unimodal. The
range is also 0 - 1 as for the Index of
Anisotropy. However, the value will depend on
reference direction set. Curray, (1956), Mardia
(1972), and Tovey (1972) independantly show a
method by which this problem can be
overcome. The range of Mean Resultant Vector
over which most Real Soils exist, is
significantly less than the Index of Anisotropy
and the latter is recommended for most
applications.
21
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Image 2 High degree of general orientation
22
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Image 3 High degree of localised orientation but
random otherwise
23
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Image 4 Near orientation Random orientation
24
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Image 5 High degree of localised orientation but
random otherwise
25
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Image 6 High degree of general orientation
26
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Index of Anisotropy is relatively easy to
determine
but Angles-Coded image can be difficult to
interpret
Domain Segmentation attempts to define regions of
generally consistent orientation.
27
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Each pixel orientation value is replaced by its
general orientation direction. With 4 coded
classes, the replacement values are as in table.
28
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
A large radius Modal filter is passed over image.
At each point, the proportion of each class is
determined, and the dominant class then replaces
the pixel value in question.
In example, there are more pixels coded 4 in mask
area, and so central pixel is replaced by code 4.
If no class is dominant, class 5 (random) is
coded). In examples to be used in this Course,
just 4 classes are used for simpliicty. Usually
8, 12 or 16 classes are used.
29
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Domain Segmentation of Image 1 using a 19 pixel
radius Modal Filter - colour representation
30
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
To help visualisation, boundaries of domains may
be overlain on original image.
31
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Alternatively, just domains of a given general
orientation may be displayed - in this case the
vertical domains.
32
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Image 1
Better approach is to use colour overlay
33
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Image 2
34
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Image 3
35
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Image 4
36
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Image 5
37
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Image 6
38
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
Difficulties with Intensity Gradient Analysis and
Solutions
low contrast, and brightness varies little
between pixels. Solution redefine all pixels
where pixel value in MAGNITUDE image is less than
a given value as undecided - typically less
than 1 in images of clays. Tovey et al.
Recommend that magnitude values lt 2.0 be treated
in this way. Will not all orientation vales be
weighted equally irrespective of contrast in
Index of Anisotropy. YES - and this ensures that
there is no bias just for brighter
features. However, by using selected ranges of
magnitude, various brightness features may be
treated differently.
39
5th Intensive Course on Soil Micromorphology -
Naples 2001 Image Analysis - Lecture 6
Morphological Segmentation
What happens if there are large particles with
little or no contrast? Will this not distort
Index of Anisotropy?. To some extent this may be
true, but intensity values in these regions are
usually below threshold value and are disregarded