Segmentation Techniques -I

COMPUTER GRAPHICS & IMAGE PROCESSING
COM2304
Segmentation Techniques -I
K.A.S.H.Kulathilake
B.Sc. (Hons) IT (SLIIT), MCS (UCSC)
Rajarata University of Sri Lanka
Faculty of Applied Sciences
Department of Physical Sciences

Learning Outcomes
COM 2304 - Computer Graphics & Image
Processing
• At the end of this lecture, you should be
able to;
– define segmentation.
– Describe edge based in segmentation.
– describe thresholding and its properties.
– apply edge detection and thresholding as
segmentation techniques.
2

What is Segmentation?
• Segmentation subdivides an image into its
constituent regions or objects.
• The level of detail to which the subdivision is
carried depends on the problem being solved.
• In other terms, segmentation should stop
when the objects or region of interest (ROI) in
an application have been detected.
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What is Segmentation? (Cont…)
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• Segmentation accuracy determines the
eventual success or failure of computerized
analysis procedures.
• For this reason, considerable care should be
taken to improve the probability of accurate
segmentation.
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• Let R represent the entire spatial region
occupied by an image.
• we may view image segmentation as a process
that partitions R into n sub regions,
R1,R2,R3,……………..Rn, such that;
– Segmentation must be complete; i.e. every pixel
must be in a region.
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– Ri is a connected set, i=1,2,…………….,n.
– Ri∩Rj = φ for all i and j, i≠j.
• Regions must be disjoint
– Q(Ri) = TRUE for i=1,2,…….,n.
• Properties that must be satisfied by the pixels in a
segmented regions – ex. Q(Ri) = TRUE if all pixels in Ri
have the same intensity level.
– Q(RiURj) = FALSE for any adjacent regions Ri and
Rj.
• Indicates that two adjacent regions Ri and Rj must be
different in the sense of predicate Q.
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Points, Lines and Edge Detection
• The focus of this topic is on segmentation methods that are
based on detecting sharp, local changes in intensity.
• Three types of images features in which we are interested
are;
– Edges: edge pixels are pixels at which the intensity of an image
function changes abruptly, and edges are sets of connected
edge pixels.
– Lines: line may be viewed as a edge segment in which the
intensity of the background on either side of the line is either
much higher or much lower than the intensity of the line pixels.
– Isolated point: It can be viewed as a line whose length and
width are equal to one pixel.
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Background of Points, Lines and Edge
Detection
• Local changes in intensity can be detected
using derivatives.
• Derivatives of a digital function are defined in
terms of differences.
• First order derivatives:
– Must be zero in the areas of constant intensity.
– Must be nonzero at the onset of an intensity step or ramp.
– Must be nonzero along the ramp.
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Detection (Cont…)Image Strip
0
1
2
3
4
5
6
7
8
1st Derivative
-8
-6
-4
-2
0
2
4
6
8
5 5 4 3 2 1 0 0 0 6 0 0 0 0 1 3 1 0 0 0 0 7 7 7 7
-1 -1 -1 -1 -1 0 0 6 -6 0 0 0 1 2 -2 -1 0 0 0 7 0 0 0
10
Processing
Ramp
Isolated point
Line Step
Flat segment

Detection (Cont…)
• Second order derivatives:
– Must be zero in the areas of constant intensity.
– Must be nonzero at the onset and end of an intensity
step or ramp.
– Must be zero along the ramp of constant slope.
• First order derivatives provides thick edges and second
order derivatives provides much finer ones (including
noise).
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Detection (Cont…)
Image Strip
0
1
2
3
4
5
6
7
8
5 5 4 3 2 1 0 0 0 6 0 0 0 0 1 3 1 0 0 0 0 7 7 7 7
2nd Derivative
-15
-10
-5
0
5
10
-1 0 0 0 0 1 0 6 -12 6 0 0 1 1 -4 1 1 0 0 7 -7 0 0
Zero crossing
Zero crossing
property is
quite useful
for locating
edges
12
Processing
Ramp
Isolated point
Line Step
Flat segment

Detection (Cont…)
• Double Edge Effect in Second Order Derivatives:
– In both the ramp and step edges that the second
derivatives has opposite signs ( -ve to +ve or vise-
versa) as it transitions into and out of an edge.
– This is known as double edge effect and it is important
to locate edges.
• The sign of the second derivative is used also to
determine whether an edge is a transition from
light to dark (-ve  +ve second derivative) or
from dark to light (+ve  -ve second derivative),
where the sign is observed as we move into the
edge.
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Edge Models
• Edge detection is the approach used most
frequently for segmenting images based on
abrupt(local) changes in intensity.
• Edge models are classified according to their
intensity profiles as follows:
– Step edges
– Ramp edges
– Roof edges
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Edge Models (Cont…)
• Step Edges:
– A step edge involves a transition between two
intensity levels occurring ideally over the distance
of 1 pixel.
– Canny edge detection algorithm was derived using
a step edge model.
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• Ramp Edges:
– In practice, digital images have edges that are blurred and
noisy.
– Blurring determined by limitations in the focusing
mechanism and the noise level determined principally by
the electronic components of the imaging system.
– In such situations, edges are more closely modeled as
having an intensity ramp profile.
– The slope of the ramp is inversely proportional to the
degree of blurring in the edge.
– It does not contains a thin path.
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• Roof Edges:
– Roof edge being
determined by the
thickness and
sharpness of the line.
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• 1st derivative tells us
where an edge is
• 2nd derivative can
be used to show
edge direction
• Zero crossings can be
used for locating the
canters of thick
edges.
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Zero Crossing

• Derivative based edge detectors are extremely sensitive to noise ( 2nd
derivatives are more sensitive).
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Images are with Gaussian
Noise

Detection of Isolated Points
• Point detection is based on second
derivatives.
• Point detection can be achieved simply using
the Laplacian mask given below:
• Points are detected at those pixels in the
subsequent filtered image that are above a set
threshold
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Detection of Isolated Points (Cont…)
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X-ray image of a
turbine blade
Result of point
detection
Result of
thresholding

Line Detection
• We can use Laplacian mask for line detection.
• It is assumed that the lines are thin with respect to
the size of the detector.
• The masks below will extract lines that are one pixel
thick and running in a particular direction.
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Line Detection (Cont…)
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Binary image of a wire bond mask
Horizontal +45° Verticle -45°

Edge Detection with Image Gradient
• Given a 3*3 region of an image the following edge detection
filters can be used under the 1st order derivatives.
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Thresholding
• Objective is to partitioning images directly into regions based
on intensity values and/or properties of these values.
• Single value thresholding can be given mathematically as
follows:
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





Tyxfif
Tyxfif
yxg
),(0
),(1
),(
T
Histogram
Modes

Thresholding (Cont…)
Original Image Thresholded Image

• If you get the threshold wrong the results can
be disastrous
Threshold Too Low Threshold Too High

The Role of Noise in Image
Thresholding
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Original image without
noise
Gaussian noise of 0 mean
and standard deviation of
10 intensity levels
50 intensity levels

The Role of Illumination &
Reflectance in Image Thresholding
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10 intensity levels
Multiply the noise image with this variable intensity
function to obtain the non-uniformly illuminated
image.

The Role of Illumination &
Reflectance in Image Thresholding
(Cont…)
• Similar results would be obtained when
illumination was uniform and reflectance was not
in situations like natural reflectivity variations in
the surface of object and/ or background.
• The key idea of these experiments is that the
reflectance and the illumination play central role
in the success of image segmentation using
thresholding or other segmentation technique.
• Therefore, controlling these factors should be the
first step considered in the solution of
segmentation problem.
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Basic Global Thresholding
• It is possible when the intensity distribution of
objects and background pixels are sufficiently
distinct.
• The basic global threshold, T, is calculated as
follows:
1. Select an initial estimate for T (typically the
average grey level in the image)
2. Segment the image using T to produce two groups
of pixels: G1 consisting of pixels with grey levels >T
and G2 consisting pixels with grey levels ≤ T
3. Compute the average grey levels of pixels in G1 to
give μ1 and G2 to give μ2
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Basic Global Thresholding (Cont…)
4. Compute a new threshold value:
5. Repeat steps 2 – 4 until the difference in T in
successive iterations is less than a predefined
limit T∞
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2
21  
T
T∞ is used to control the number of iterations in
situations where speed is an important issue. In
general, the larger T∞ is, the fewer iterations the
algorithm will perform.

Basic Global Thresholding (Cont…)
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Single value
thresholding only
works for bimodal
histograms
Images with other
kinds of histograms
need more than a
single threshold
This algorithm works very
well for finding thresholds
when the histogram has a
clear valley between the
two modes

Otsu Thresholding
• Otsu's thresholding method involves iterating
through all the possible threshold values and
calculating a measure of spread for the pixel
levels each side of the threshold, i.e. the pixels
that either fall in foreground or background.
• The aim is to find the threshold value where
the sum of foreground and background
spreads is at its minimum.
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Otsu Thresholding (Cont…)
• The algorithm will be demonstrated using the simple
6x6 image shown above.
• The calculations for finding the foreground and
background variances (the measure of spread) for a
single threshold are explained next.
• In this case the threshold value is 3.
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• The next step is to calculate the 'Within-Class
Variance'.
• This is simply the sum of the two variances
multiplied by their associated weights.
• This final value is the 'sum of weighted variances'
for the threshold value 3.
• This same calculation needs to be performed for
all the possible threshold values 0 to 5.
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• It can be seen that for the threshold equal to 3, as well as being used for
the example, also has the lowest sum of weighted variances.
• Therefore, this is the final selected threshold.
• All pixels with a level less than 3 are background, all those with a level
equal to or greater than 3 are foreground.
• This approach for calculating Otsu's threshold is useful for explaining the
theory, but it is computationally intensive, especially if you have a full 8-bit
greyscale.
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• Making Otsu faster using Between
class variance:
– A faster method of performing the calculations
which is much more appropriate for
implementations.
– So it can also be used for finding the best
threshold and therefore due to being simpler is a
much better approach to use.
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– The table below shows the different variances for
each threshold value.
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Global
Thresholding
T=169
Otsu
Thresholding
T= 181

Effect of Image Smoothing for
Thresholding
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Noise image Histogram Otsu Thresholding
Smoothed Image
(5 by 5, Mean)
Histogram Otsu Thresholding
Boundary Distortion occurred

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Noise image Histogram Otsu Thresholding
Smoothed Image
(5 by 5, Mean)
Histogram Otsu Thresholding
Segmentation failed

• Reason for above matter:
– Region is so small that its contribution to the
histogram is insignificant compared to the
intensity spread caused by noise.
– To overcome this problem from global
thresholding we can use edges.
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Using Edges for Improving Global
Thresholding
• We can use pixels that lie on or near the edges
between objects and the background for
improving the shape of the histogram.
• Using pixels that satisfy some simple measures
based on Gradient and Laplacian operators has a
tendency to deepen the valley between
histogram peaks.
• In this approach, we assume that the edges
between the objects and background are known.
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• Algorithm: f(x, y) is the input image
1. Compute the edge image ( use either gradient
magnitude or Laplacian method).
2. Specify a threshold value, T.
3. Threshold the image from step 1 using the threshold
from step 2 to produce a binary image, gT(x, y). Use this
image as a mask image to select pixels from f(x, y)
corresponding to “strong” edge pixels.
4. Compute a histogram using only the pixels in f(x, y) that
correspond to the locations of the 1-valued pixels in
gT(x,y).
5. Use the histogram from step 4 to segment f(x, y) globally
using, for example Otsu’s method.
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Image of Yeast cells (only white patches ) Histogram Otsu Thresholding
Smoothed Image using Laplacian. T=115 Histogram Otsu Thresholding . Segmentation is
successful

Multiple Thresholds
• Objective of the multiple thresholding is to
separate the original image into multiple
classes.
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Dark background
Illuminated area
Shadow

Variable Thresholding
• Image Partitioning
– One of the simplest approach to variable
thresholding is to subdivide an image into non-
overlapping rectangles.
– This approach is used to compensate for non-
uniformities in illumination and/or reflectance.
– The rectangles are chosen small enough to that
the illumination of each is approximately uniform.
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Variable Thresholding (Cont…)
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Noisy shaded image Histogram Otsu Thresholding
Image sub divide into six sub images Result of applying Otsu method to each sub
image individually
Errors in
segmentation

– Six histograms of six sub images have produced
bimodel histograms as the result of this thresholding
approach.
– Hence, it leads to effective global thresholding.
– Image subdivision generally works well when the
object of interest and the background occupy regions
of reasonably comparable size.
– When this is not the case, the method typically fails
because of the likelihood of subdivisions containing
only object or background pixels.
•
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• Adaptive Thresholding:
– It is a modified threshold technique in which the
threshold level is itself variable.
– It is useful when there are strong illumination or
reflectance gradients that you need to threshold
relative to the general intensity gradients.
– Adaptive thresholding set on a pixel by pixel basis
by computing a weighted average of the b-by-b
region around each pixel location minus a
constant where b is given by block size.
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Reference
• Chapter 10, of Gonzalez, R.C., Woods, R.E.,
Digital Image Processing, 3rd ed. Addison-
Wesley Pub.
• Threshold, Learning OpenCV, pp 135-141
• Lecture 07
• http://www.labbookpages.co.uk/software/im
gProc/otsuThreshold.html
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Learning Outcomes Revisit
• Now, you should be able to;
– define segmentation.
– Describe edge based in segmentation.
– describe thresholding and its properties.
– apply edge detection and thresholding as
segmentation techniques.
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QUESTIONS ?
Next Lecture – Segmentation Techniques - II
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57

Segmentation Techniques -I

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