Principles of 2D Image Analysis
Part 2
Notes prepared by Dr. Bartek Rajwa, Prof. John Turek & Prof. J. Paul Robinson
These slides are intended for use in a lecture series. Copies of the graphics are distributed and students encouraged to take their notes on
these graphics. The intent is to have the student NOT try to reproduce the figures, but to LISTEN and UNDERSTAND the material. All
material copyright J. Paul Robinson unless otherwise stated, however, the material may be freely used for lectures, tutorials and
workshops. It may not be used for any commercial purpose. It is illegal to upload this lecture to CourseHero or any other site.
www.cyto.purdue.edu
UPDATED Feb 2016
19:17
© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Image Processing in the Spatial Domain
• Arithmetic and logic operations
• Basic gray level transformations on
histograms
• Spatial filtering
• Overview of analytical techniques
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Modifying image contrast and brightness
• The easiest and most frequent method is histogram
manipulation
• An 8 bit gray scale image will display 28 =256 different
brightness levels ranging from 0 (black) to 255 (white)
(210=1024, 212=4096). An image that has pixel values
throughout the entire range has a large dynamic range,
and may or may not display the appropriate contrast for
the features of interest. 16 bit would be 216 (or 65,536)
• (Non-linear enhancements - e.g. Equalization see later)
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Histogram Sliding
• It is not uncommon for the histogram to display most of
the pixel values clustered to one side of the histogram or
distributed around a narrow range in the middle. This is
where the power of digital imaging to modify contrast
exceeds the capabilities of traditional photographic optical
methods.
• Images that are overly dark or bright may be modified by
histogram sliding.
•In this procedure, a constant brightness is added or
subtracted from all of the pixels in the image or just to a
pixel falling within a certain gray scale level ( i.e. 64 to
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128).
© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Histogram Operations
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
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Sliding
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Sliding
Histogram Stretching
• A somewhat similar operation is histogram stretching in
which all or a range of pixel values in the image are
multiplied or divided by a constant value. The result of
this operation is to have the pixels occupy a greater
portion of the dynamic range between 0 and 255 and
thereby increase or decrease image contrast.
• It is important to emphasize that these operations do not
improve the resolution in the image, but may have the
appearance of enhanced resolution due to improved
image contrast.
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Histogram operations
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
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Stretching
Stretching
Color images (RGB)
19:17
© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Actin - Rhodamine-phalloidin
Antibody to T.cruzi - FITC
DNA - Dapi
© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Imaged using an MRC 1000
Confocal Microscope, 40 x 1.3 NA Fluor
(Image prepared 1994)
Actin - Rhodamine-phalloidin
Antibody to T.cruzi - FITC
DNA
- Dapi
© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson,
Purdue
University
Imaged using an MRC 1000
Confocal Microscope, 40 x 1.3 NA Fluor
(Image prepared 1994)
Imaged using an MRC 1000
© 1997-2016 J. Turek, B. Rajwa &
Actin - Rhodamine-phalloidin Confocal Microscope, 40 x 1.3 NA Fluor
Antibody to T.cruzi - FITC
DNA
- Dapi
J. Paul Robinson,
Purdue
University
Actin - Rhodamine-phalloidin
Antibody to T.cruzi - FITC
DNA - Dapi
© 1994-2016 J. Paul Robinson Purdue University Cytometry Laboratories
Imaged using an MRC 1000
Confocal Microscope, 40 x 1.3 NA Fluor
(Image prepared 1994)
Slide 12 t:/powerpnt/course/BMS524/BMS524-Lecture-10-sample prep-1.ppt
Actin - Rhodamine-phalloidin
Antibody to T.cruzi - FITC
DNA - Dapi
© 1994-2016 J. Paul Robinson Purdue University Cytometry
Laboratories
Imaged using an MRC 1000
Confocal Microscope, 40 x 1.3 NA Fluor
(Image prepared 1994)
Slide 13 t:/powerpnt/course/BMS524/BMS524-Lecture-10-sample prep-1.ppt
© 1994-2016
Actin - Rhodamine-phalloidin
Antibody to T.cruzi - FITC
DNA
- Dapi
J. Paul Robinson Purdue University
Cytometry
Laboratories
Imaged using an MRC 1000
Confocal Microscope, 40 x 1.3 NA Fluor
Slide 14 t:/powerpnt/course/BMS524/BMS524-Lecture-10-sample prep-1.ppt
Sensitivity of the Human Eye to Light of
Different Wavelengths
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Color models
RGB
red
green
blue
HSI
hue
saturation
lightness
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
(intensity)
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
• Hue is a color attribute
associated with the
dominant wavelength in a
mixture of wavelengths
(“red”, “green”, “yellow”)
• Saturation refers to the
relative purity, or the
amount of white light
mixed with a hue.
• Intensity refers to the
relative lightness or
darkness of a color.
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
intensity
Color (HSL, HSV, HIS)
hue
0°
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Image thresholding based on RGB or HSI
© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Look Up Tables (LUT)
• A look up table (LUT) is an operation that uses a
mathematical calculation to change the display
of any pixel in an image
• This usually is the basis for both the visualization
(the main purpose) but also the saved image
• LUTs are integer operations and can significantly
improve output performance and standardize the
image display manipulation
• LUTs allow you to assign colors that relate to
your own imaging situation
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Gamma
• The gamma of a histogram curve is the slope, expressed as a ratio of
the logs of the output to input values. A gamma value of 1.0 equals an
output:input ratio of 1:1 and no correction is applied. In some programs,
a gamma function applies a lookup table function (LUT) to compensate
or correct for the bias which may be built into the video source.
• A camera's light response is often set to a power function (Gamma
function) to mimic the photometric response of the human eye. This
may result in a non-linear response from the video source and cause
errors if you are making densitometric measurements. The camera bias
can be removed by applying an inverse gamma function.
• This function calculates a lookup table to correct for the bias based on
operator provided parameters. The gamma function for decalibrating
the camera can be obtained from the camera manufacturer.
© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
1.0
The straight line at the 45 degree angle in the output
lookup table indicates that no processing has been
performed on the pixels - gamma = 1.0
© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
In this image a gamma factor of 1.8 has been applied
to the histogram of the output LUT histogram
© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
In this image a gamma factor of 2.2 has been applied
to the histogram of the output LUT histogram
© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Inverse function applied to previous image
© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Arbitrary adjustment to the output LUT histogram
© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Image Processing
.... is the procedure of feature enhancement prior to
image analysis. Image processing is performed on
pixels (smallest unit of digital image data). The
various algorithms used in image processing and
morphological analysis perform their operations on
groups of pixels (3 X 3, 5 X 5, etc.) called kernels.
These image processing kernels may also be used
as structuring elements for the various image
morphological analysis operations.
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Basics of Spatial Filtering
• The process of spatial filtering consists of
moving the filter mask from point to point
in an image
• At each point the response of the filter at
that point is calculated using a predefined
relationship
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
A
B
C
The above figure represents a series of 3 pixel x 3 pixel
kernels. Many image processing procedures will perform
operations on the central (black) pixel by using use
information from neighboring pixels. In kernel A, information
from all the neighbors is applied to the central pixel. In
kernel B, only the strong neighbors, those pixels vertically or
horizontally adjacent, are used. In kernel C, only the weak
neighbors, or those diagonally adjacent are used in the
processing. It is various permutations of these kernel
operations that form the basis for digital image processing.
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Low-pass filter
• A spatial low-pass filter has the effect of passing,
or leaving untouched, the low spatial frequency
components of the image.
• High frequency components are attenuated and
are virtually absent in the output image
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
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High-Pass Filter
• The high pass filter has the opposite effect of the
low-pass filter.
• It accentuates high frequency spatial components
while leaving low frequency components
untouched
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
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Edge Detection and Enhancement
• Image edge enhancement reduces an image
to show only its edges.
• Edge enhancements are based on the pixel
brightness slope occurring within a group of
pixel
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Laplacian Edge Enhancement
• Laplacian is an omnidirectional operator that highlights all
edges in a image regardless of their orientation.
• Laplacian is based on the second-order derivative of the
image:
f
 f ( x  1)  f ( x )
x
2
2

f

f
2 f  2  2
x
y
2 f
 f ( x  1)  f ( x  1)  2 f ( x )
2
x
 2 f  [ f ( x  1), y )  f ( x  1, y )  f ( x , y  1)  f ( x , y  1)]  4 f ( x , y )
• Useful for finding directional organelles, structural
components, ETC
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Laplacian (cont.)
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Sobel Edge
Enhancement
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• The Sobel filter extracts all of the edges in an image,
regardless of direction
• It is implemented as the sum of two directional edge
enhancement operators
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Unsharp Masking
• The unsharp masking enhancement operation sharpens an image by
subtracting a brightness-scaled, low-pass-filtered image from its
original.
• A further generalization of unsharp masking is called high-boost
filtering:
f hb  A f ( x , y )  f ( x , y )
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Shape analysis
• Shape measurements are physical dimensional measures
that characterize the appearance of an object.
• The goal is to use the fewest necessary measures to
characterize an object adequately so that it may be
unambiguously classified.
• The shape may not be entirely reconstructable from the
descriptors, but the descriptors for different shapes should
be different enough that the shapes can be discriminated.
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Area
original image
net area
filled area
convex area
• The area is the number of pixels in a shape.
• The convex area of an object is the area of the
convex hull that encloses the object.
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Perimeter
perimeter
external perimeter
convex perimeter
• The perimeter [length] is the number of pixels in
the boundary of the object.
• The convex perimeter of an object is the perimeter
of the convex hull that encloses the object.
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Major and minor axes
• The major axis is the (x,y) endpoints
of the longest line that can be drawn
through the object. The major axis
endpoints (x1,y1) and (x2,y2) are by
computing the pixel distance between
every combination of border pixels in
the object boundary and finding the
pair with the maximum length.
• The minor axis is the (x,y) endpoints
of the longest line that can be drawn
through the object whilst remaining
perpendicular with the major-axis. The
minor axis endpoints (x1,y1) and (x2,y2)
are found by computing the pixel
distance between the two border pixel
endpoints.
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Aspect ratio
•
•
•
The major-axis length of an object is
the pixel distance between the majoraxis endpoints.
The minor-axis length of an object is
the pixel distance between the minoraxis endpoints
The aspect ratio measures the ratio
of the objects height to its width:
height
aspect ratio 
width
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Compactness (formfactor)
• Compactness is defined as the ratio of the area of
an object to the area of a circle with the same
perimeter:
4    area
compactnes s 
perimeter 2
• A circle is used as it is the object with the most
compact shape: the measure takes a maximum
value of 1 for a circle
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Compactness (cont.)
1
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Circularity or roundness
• A measure of roundness or circularity (area-toperimeter ratio) which excludes local irregularities
can be obtained as the ratio of the area of an
object to the area of a circle with the same convex
perimeter:
4    area
roundness 
2
perimeter convex
• Roundness equals 1 for a circular object and less than 1
for an object that departs from circularity, except that it is
relatively insensitive to irregular boundaries.
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Roundness (cont.)
1
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Convexity
• Convexity is the relative amount that an object differs from a
convex object. A measure of convexity can be obtained by
forming the ratio of the perimeter of an object’s convex hull
to the perimeter of the object itself:
convexity 
perimeter convex
perimeter external
• This will take the value of 1 for a convex object, and will
be less than 1 if the object is not convex, such as one
having an irregular boundary.
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Convexity (cont.)
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Solidity
• Solidity measures the density of an object. A
measure of solidity can be obtained as the ratio
of the area of an object to the area of a convex
hull of the object:
area net
solidity 
area convex
• A value of 1 signifies a solid object, and a value
less than 1 will signify an object having an
irregular boundary (or containing holes).
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Solidity (cont.)
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Moments of shape
• The evaluation of moments represents a
systematic method of shape analysis.
• The most commonly used region attributes are
calculated from the three low-order moments.
• Knowledge of the low-order moments allows the
calculation of the central moments, normalized
central moments, and moment invariants.
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Centroid
• The first-order moments in x (m10) and y (m01) normalized
by the area can be used to specify the location of the
centre of gravity, or centroid of an object.
• Centroid It has two components, denoting the row and
column positions of the point of balance of the object:
 m10 m 01 

centroid  (x , y)  
,
 m 00 m 00 
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Moments of shape
L. monocytogenes
ATCC19113
L. innocua F4248
L. ivanovii ATCC19119
L. seeligeri LA 15
L. welshimeri ATCC35897
L. grayi LM37
L. welshimeri ATCC35897
L. innocua V58
L. ivanovi ATCC19119
L. ivanovi SE98
L. monocytogenes ATCC19113
L. monocytogenes V7
Graphical representation of radial Zernike polynomials
Zn,m in 2D (image size 128 x 128 pixels), and their
magnitudes: A – real part Z10,6; B – imaginary part Z10,6; C
– magnitude Z10,6; D – real part Z13,5; E – imaginary part
Z13,5; F – magnitude Z13,5. The larger the n-|m|
difference, the more oscillations are present in the
shape. Features used in this study are the magnitudes of
Zernike polynomials. One may note that the values of
the magnitudes do not change when arbitrary rotations
are applied.
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Reference: Bayraktar, B et al, J. Biomed. Opt. 11:34006, 2006
Extension
Extension is a measure of how much the
shape differs from the circle. It takes value of
zero if the shape is circular and increases
without limit as the shape become less
compact
E  log 2  1  c ln  1  ln  1
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Dispersion
• Dispersion is the minimum extension that can be
attained by compressing the shape uniformly.
There is a unique axis, the long axis of the shape,
along which the shape must be compressed in
order to minimize its extension.
• Dispersion is invariant to stretching, compressing
or shearing the shape in any direction
D  log 2
1
1
1 2  c ln 1 2  ln 1 2
2
2
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Elongation
• Elongation is the measure how much the shape
must be compressed along its long axis in order to
minimize the extension
• Elongation never take a value of less than zero or
greater than extension
L  log 2
1 1
1 1 1
 c ln
 ln
2 2
2 2 2
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Cell shape
No
1
2
3
4
5
6
7
8
9
10
11
12
Extension
0.1197
0.3998
0.7575
0.8725
0.0920
0.3784
0.7411
0.8591
0.0816
0.3617
0.7243
0.8350
Dispersion
0.0542
0.0524
0.0550
0.1740
0.0262
0.0277
0.0313
0.1434
0.0138
0.0160
0.0199
0.1029
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Elongation
0.0655
0.3474
0.7025
0.6985
0.0659
0.3506
0.7099
0.7157
0.0679
0.3457
0.7044
0.7321
Fiber length
perimeter  perimeter 2  16  area
thread length 
4
• This gives an estimate as to the true length of a
threadlike object.
• Note that this is an estimate only. The estimate is
fairly accurate on threadlike objects with a
formfactor that is less than 0.25 and gets worse as
the formfactor increases.
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Fiber width
perimeter - perimeter 2  16  area
thread width 
4
• This gives an estimate as to the true width of a
threadlike object.
• Note that this is an estimate only. The estimate is
fairly accurate on threadlike objects with a
formfactor that is less than 0.25 and gets worse as
the formfactor increases.
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Average fiber length
Picture size =
3.56 in x 3.56 in
Skeletonization
Total length = 29.05 in
Number of
end-points = 14
• The number of skeleton end-points estimates the
number of fibers (half the number of ends)
• Average length: average fiber length 
total length
0.5  number of end points
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Length=4.15 in
Euclidean distance mapping
• Euclidean Distance Map (EDM) converts a binary image to
a grey scale image in which pixel value gives the straightline distance from each originally black pixel within the
features to the nearest background (white) pixel.
• EDM image can be thresholded to produce erosion, which is
both more isotropic and faster than iterative neighbor-based
morphological erosion.
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Watershed
• The limitation of the watershed approach is that it
applies only to features that are slightly overlapped,
and which have fundamentally convex shape.
• The local maxima in the distance map are the values
of inscribed radii of circles that subdivide the image
into features.
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Distance… (cont.)
50
Relative frequency
40
30
20
10
0
0
40
80
120
160
Distance [A.U.]
© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
200
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Thresholding
• Image thresholding is a segmentation
technique which classifies pixels into two
categories:
– Those to which some property measured from
the image falls below a threshold,
– and those at which the property equals or
exceeds a threshold.
• Thesholding creates a binary image
(binarisation).
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Texture segmentation
• Texture is a feature used to partition images
into regions of interest and to classify those
regions.
• Texture provides information about the
spatial arrangement of colors or intensities
in an image.
• Texture is characterized by the spatial
distribution of intensity levels in a
neighborhood.
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Texture segmentation – an example
thresholding
Texture
filters
range
variance
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Haralick entropy
Texture segmentation
variance
range
Original
image
Texture
operator
Gaussian
Blur
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Haralick entropy
Threshold
EDM
Open,
Fill holes
Image math
• Image arithmetic on grayscale images
(addition, subtraction, division, multiplication,
minimum, maximum)
• Image Boolean arithmetic (AND, OR, Ex-OR,
NOT)
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
AND
The pixel at location (x,y) is 1 if is 1 in both
images f1(x,y) and f2(x,y):
g ( x , y )  f1 ( x , y ) AND f 2 ( x , y )  1
if f1 ( x , y )  f 2 ( x , y )  1
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
AND (cont.)
AND
=
So it’s on both…..
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
OR
The pixel at location (x,y) is 1 if it is 1 in either
of the images f1(x,y) or f2(x,y):
g ( x , y )  f1 ( x , y ) OR f 2 ( x , y )  1
if f1 ( x , y )  1 OR f 2 ( x , y )  1
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
OR (cont.)
OR
=
So it’s on either…..
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
XOR
• Exclusive OR
• The pixel at location (x,y) is 1 if it is 1 in
either of the images f1(x,y) or f2(x,y), but not
if it is 1 in both:
g ( x , y )  f1 ( x , y ) XOR f 2 ( x , y )  1
if f1 ( x , y )  1 AND f 2 ( x , y )  0
or f1 ( x , y )  0 AND f 2 ( x , y )  1
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
XOR (cont.)
XOR
=
So it’s on not on both…..
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
NOT
• Not requires only a single image
• The pixel at location (x,y) becomes 1 if it was
0 and becomes 0 if it was 1:
g ( x , y )  NOT ( f1 ( x , y ))  1 if f1 ( x , y )  0
g ( x , y )  NOT ( f1 ( x , y ))  0 if f1 ( x , y )  1
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
NOT (cont.)
NOT
=
So it’s just itself…..
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Non-linear filters
• Non-linear filters are known collectively as
order statistic filters or rank filters
• How does it work? Let’s combine a list of
intensity values in the neighborhood of a
given pixel, sort the list into ascending order,
then select a value from a particular position
in the list to use as the new value for the
pixel.
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Median filter
Selects the middle-ranked value from a
neighborhood. For a n x n neighborhood
(kernel), with n odd, the middle value is at
position:
n
median  
 2
2
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University

  1

Median filter (cont.)
+
Median filter
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Periodic Noise
Periodic noise in an image may be removed
by editing a 2-dimensional Fourier transform
(FFT). A forward FFT of the image below,
will allow you to view the periodic noise
(center panel) in an image. This noise, as
indicated by the white box, may be edited
from the image and then an inverse Fourier
transform performed to restore the image
without the noise (right panel next slide).
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Remove periodic noise with fast
fourier transforms
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Pseudocolor image based upon
gray scale or luminance
Human vision more sensitive to color. Pseudocoloring makes it
is possible to see slight variations in gray scales
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Manipulating Images for
publication
• …we teach you how to manipulate images
• ….But we also know how to determine if you
did cheat!!....
• To be expanded in a separate lecture!
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© 1997-2016 J. Turek, B. Rajwa & J. Paul Robinson, Purdue University
Conclusion & Summary
• Image Collection
– resolution and physical determinants of collection instrument – collect
only what you actually need
• Image Processing
–
thresholding, noise reduction, filtering, histogram manipulation, etc
• Image Analysis
– feature identification, segmentation, value of data, representation of
image, extract arithmetic information
• Must not exceed an acceptable scientific standard in
modification of images
• If you cheat and publish, its there for everyone to see…someone
smarter than you may dig into your data and expose you!!
© 1997-2016 J. Turek , B. Rajwa & J. Paul Robinson, Purdue University