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COMPARATIVE PERFORMANCE ANALYSIS OF SEGMENTATION
TECHNIQUES
Amandeep Singh
ECE, Lovely professional university, near
Phagwara Punjab, India
[email protected]
A.P Gursimran singh sandhu
ECE, Punjab Technical University
[email protected]
ABSTRACT
The study presented in this article focuses on comparative analysis of Segmentation techniques.
Segmentation techniques are applied to extract Region of Interest (ROI) from medical images obtained
from different medical scanners such as Ultrasound, CT or MRI. Global thresholding, Adaptive
Thresholding, Region grow and Active contour using level set techniques has been used in the proposed
segmentation analysis. The approach consists of two steps: Apply segmentation technique to extract most
discriminative regions from image and calculate the parameters from the resulting image obtained by the
applied techniques. Parameters are precision, accuracy sensitivity, specificity. Segmentation techniques
have been tested on medical and synthetic data sets and results are compared with each other. Tests
indicate that using level set contour significantly improves the ability of extracting region of interest with
unbroken boundaries and Adaptive thresholding acquires most of the details present in the image. Manual
global thresholding have the highest success rate of extracting the region of interest.
Keywords
Global threshold; Adaptive threshold; Region grow; Level set contour; Binary classification; Hybrid segmentation
I. INTRODUCTION
The research presented in this article is part of an on-going Mtech thesis aimed at developing an
automated hybrid imaging system for segmentation of tumor present in medical images obtained by
Computed Tomography (CT) scans. Farzaneh Keyvanfard et al [1] Segmenting of human organs in CT
scans using gray level information is particularly challenging due to the changing shape of organs in
medical images and the gray level intensity overlap in soft tissues. Medical image segmentation requires
extracting specific features from an image by distinguishing objects from the background. Medical image
segmentation aims to separate known anatomical structures from the background for research, cancer
diagnosis, quantification of tissue volumes, radiotherapy treatment planning and study of anatomical
structures.
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Cancer diagnose can be manually performed by a human expert who simply examines an image,
determines borders between regions, and classifies each region this process is called segmentation in
terms of image processing. This is perhaps the most reliable and accurate method of image segmentation
because the human visual system is immensely complex and well suited to the task. But the limitation
starts in volumetric images due to the quantity of clinical data. Implementation of image processing
increase the rate of similar CT interpretation between different analysers, now its just 20% and to relief
for the analyzers from routine CT analysis.Nader H. Abdel-massieh et al [2] [3], thresholding is
commonly used image segmentation technique, In this method, pixels that are alike in grayscale (or some
other feature) are grouped together. Often a image histogram is used to determine the best setting for the
threshold. After thresholding image is converted into logical image the pixels range above threshold
become 1 or white pixels and pixel range below threshold become 0 or black pixels. Bio medical images
may have multiple modes and multiple thresholds may be helpful. In general multilevel thresholding is
less reliable than single level thresholding. Mostly because it is very difficult to determine thresholds that
adequately separate objects of interest. N. Otsu et al [4] Global Thresholding choose threshold T that
separates object from background global thresholding is a single threshold method of thresholding
technique. When the pixel values of the components and that of background are fairly consistent in their
respective values over the entire image, global thresholding could be used. In adaptive thresholding,
different threshold values T1,T2,T3 etc for different local areas are used. This more sophisticated version
of thresholding can accommodate changing lighting conditions in the image. The fundamental drawback
of histogram-based region detection is that histograms provide no spatial information (only the
distribution of gray levels).
Region-growing approaches exploit the important fact that pixels which are close together have similar
gray values. The first region-growing method was the seeded region growing method. This method takes
a set of seeds as input along with the image. The seeds mark each of the objects to be segmented. The
regions are iteratively grown by comparing all unallocated neighboring pixels to the regions. The
difference between a pixel's intensity value and the region's mean is used as a measure of similarity. The
pixel with the smallest difference measured this way is allocated to the respective region. This process
continues until all pixels are allocated to a region. Seeded region growing requires seeds as additional
input. The segmentation results are dependent on the choice of seeds. Noise in the image can cause the
seeds to be poorly placed. Unseeded region growing is a modified algorithm that doesn't require explicit
seeds. Region Growing offers several advantages over conventional segmentation techniques. Unlike
gradient and Laplacian methods, the borders of regions found by region growing are perfectly thin (since
we only add pixels to the exterior of our Region) and connected. The algorithm is also very stable with
respect to noise. Region will never contain too much of the background, so long as the parameters are
defined correctly. Other techniques that produce connected edges, like boundary tracking, are very
unstable. Most importantly, membership in a region can be based on multiple criteria. We can take
advantage of several image properties, such as low gradient or gray level intensity value, at once.
An important class of segmentation methods is model based methods. Caselles, R. Kimmel [5] [6] Active
Contours, also known as Evolving Fronts . Active contour is an interface usually used to separate
structures and background on the image. There are two principal approaches to build an active contour:
explicit or Lagrangian approach, and resulting interfaces called snakes, implicit or Eulerian approach, and
resulting interfaces called level sets. These methods are used in the domain of image processing to locate
the contour of an object. Trying to locate an object contour purely by running a low level image
processing task such as canny edge detection is not particularly successful. Often the edge is not
continues, i.e. there might be holes along the edge, and spurious edges can be present because of noise.
The level set method makes it very easy to follow shapes that change topology, for example when a shape
splits in two, develops holes, or the reverse of these operations. An active contour tries to improve on this
by imposing desirable properties such as continuity and smoothness to the contour of the object. This
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means that the active contour approach adds a certain degree of prior knowledge for dealing with the
problem of finding the object contour. An active contour is modeled as parametric curve, this curve aims
to minimize its internal energy by moving into a local minimum. In this paper we use level set contour
method along with other methods for analysis.
This paper introduces the use wide range of data set and presents a comprehensive analysis determining
the optimal segmentation technique for the applied to CT scans. This paper is focusing on a robust
implementation technique for segmenting medical volumes and performing binary analysis methodology
on images obtained from a CT scanner. The rest of this paper is organized as follow: The following
section illustrates the proposed medical image segmentation system analysis methodology have been
explained in section 2. The results and analysis of the implemented of segmentation techniques for
medical image segmentation is illustrated in section 3. Finally, section 4 includes the conclusions and
future scope.
II. METHODOLOGY
Binary classification problems often result in a predicted probability surface, which is then translated into
a presence–absence classification map in more generalize way it is act of discriminating an item into one
of two groups based on specified measures or variables. This paper consists of four main binary
classification methods sensitivity, specificity, accuracy and precision. Sensitivity and specificity are
statistical measures of the performance of a binary classification test, also known in statistics as
classification function. Sensitivity (also called recall rate in some fields) measures the proportion of actual
positives which are correctly identified as such (e.g. the percentage of sick people who are correctly
identified as having the condition). Specificity measures the proportion of negatives which are correctly
identified (e.g. the percentage of healthy people who are correctly identified as not having the condition).
The accuracy of a measurement system is the degree of closeness of measurements of a quantity to that
quantity's actual(true) value.
Figure 1. Process Diagram
The precision of a measurement system, also called reproducibility or repeatability, is the degree to which
repeated measurements under unchanged conditions show the same results. Image is first converted in to
gray scale because resulting images of biomedical scans are gray in nature .Salt and paper noise is used in
noise addition process, different segmentation techniques are applied on the resulting image of noise
addition process. Every applied segmentation technique produces a segmented image which is in logical
scale. Binary classification methodology is used to statistically represent the performance of each segment
IMAGE NOISE ADDITION SEGMENTATION
TECHNIQUES
BINARY
CLASSIFICATION
COMPARISION
CHART
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technique and comparison is done on basis values obtained by binary classification methods. These
methods of classification simply work on existence of desired and undesired objects, edges in the image.
Binary classifier use terms to indicate presence of a edges and objects. Some of the images have the
objects, clear edges and our test says they are positive. They are called true positives (TP). Some have the
objects, but the test claims they don't. They are called false negatives (FN). Some don't have the objects,
and the test says they don't - true negatives (TN). Finally, we might have image with no clear edges that
have a positive test result - false positives (FP). Thus, the number of true positives, false negatives, true
negatives, and false positives add up to 100% of the set. Specificity (TNR) is the proportion of objects
that tested negative (TN) of all the objects that actually are negative (TN+FP). As with sensitivity, it can
be looked at as the probability that the test result is negative given that the image is not having object.
With higher specificity, fewer will be the undesired objects which r not present in original image.
Sensitivity (TPR) is the proportion of objects that tested positive (TP) of all the objects that actually are
positive (TP+FN). It can be seen as the probability that the test is positive given that the presence of
object in image.
The accuracy is the proportion of true results (both true positives and true negatives) in the population. Precision or
positive predictive value is defined as the proportion of the true positives against all the positive results (both true
positives and false positives). An accuracy of 100% means that the measured values are exactly the same as the
given values. In the medical domain, the most important performance measures are both specificity and sensitivity.
Optimally one would want both high specificity and high sensitivity measures. However, theoretically these two
measures should have a negative correlation. Since accuracy reflects both the sensitivity and specificity in relation to
each other, this descriptor was selected to determine the overall correctness of the classifier. To evaluate the
performance of each classifier; specificity, sensitivity, precision, accuracy rates are then calculated from each of the
misclassification matrices.
Table1-Description table of TP, TN, FP, FN
Table 2-Defination of binary classification
True positive (TP) Correctly identified
True negative (TN) Correctly rejected
False positive (FP) Incorrectly identified
False negative(FN) Incorrectly rejected
Sensitivity True Positive / Total Positive
Specificity True Negative / Total Negatives
Accuracy (True Positives + True Negatives) / (True
Positive + True Negative + False Positive +
False Negative)
Precision True Positive / (True Positive + False
Positives)
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III. RESULTS The segmentation algorithms are applied to various formats of images and results are given below. The binary
analysis Parameters has value range from 0 to 1.
(a) (b) (c) (d) (e) (f) Figure 2. Segmentation results for Eye image .(a) Original eye image effected by salt paper noise (b) Global threshold applied on original eye image (c) Result
of Adaptive threshold segmentation applied on eye image.(d) Eye image result of region grow thin segmentation (e) Eye image result of region grow thin
segmentation (c) Result of Level set segmentation applied on eye image.
(a) (b) (c) (d) (e) (f)
Figure 3. Segmentation results for Bone image .(a) Original bone image effected by salt paper noise (b) Global threshold applied on original bone image (c)
Result of Adaptive threshold segmentation applied on bone image.(d) Bone image result of region grow thin segmentation (e) Bone image result of region
grow thin segmentation (c) Result of Level set segmentation applied on Bone image.
(a) (b) (c) (d) (e) (f)
Figure. 4. Segmentation results for Lena image .(a) Original lena image effected by salt paper noise (b) Global threshold applied on original lena image (c)
Result of Adaptive threshold segmentation applied on lena image.(d) Lena image result of region grow thin segmentation (e) Lena image result of region
grow thin segmentation (f) Result of Level set segmentation applied on lena image.
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(a) (b) (c) (d) (e) (f) Figure 5. Segmentation results for Hex shapes image .(a) Original hex shapes image effected by salt paper noise (b) Global threshold applied on original hex
shapes image (c) Result of Adaptive threshold segmentation applied on hex shapes image.(d) Hex shapes image result of region grow thin segmentation (e)
Hex shapes image result of region grow thin segmentation (f) Result of Level set segmentation applied on hex shapes image.
(a) (b) (c) (d) (e) (f)
Figure 6. Segmentation results for Frog image .(a) Original frog image effected by salt paper noise (b) Global threshold applied on original frog image (c)
Result of Adaptive threshold segmentation applied on frog image.(d) Frog image result of region grow thin segmentation (e) Frog image result of region
grow thin segmentation (f) Result of Level set segmentation applied on frog image.
(a) (b) (c) (d) (e) (f)
Fig. 7. Segmentation results for Frog image.(a) Original frog image effected by salt paper noise (b) Global threshold applied on original frog image (c) Result
of Adaptive threshold segmentation applied on frog image.(d) Frog image result of region grow thin segmentation (e) Frog image result of region grow thin
segmentation (f) Result of Level set segmentation applied on frog image.
Table 3. Results of Sensitivity applied on segmentation methods
Images Eye Bone Lena Frog Hex shapes Two cell
Techniques Sensitivity Sensitivity Sensitivity Sensitivity Sensitivity Sensitivity
Result of segmentation
after Global thresholding 0.75 1 1 1 0.25 1
Result of segmentation
after Adaptive thresholding 0.75 0.66 0.25 0.8 0.25 1
Result of segmentation after
region grow-thick 0.75 0 1 0.4 0.5 0
Result of segmentation after
region grow-thin 0.75 0 1 0.4 0.5 0
Result of segmentation after
level set 0 1 0 1 1 0
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Table 4. Results of Specificity applied on segmentation methods.
Images EYE Bone Lena Frog Hex Two cell
Techniques Specificity Specificity Specificity Specificity Specificity Specificity
Result of
segmentation
after Global thresholding
0.5 1 0.5 1 0.66 0.5
Result of segmentation
after Adaptive
thresholding
0.5 0 0.25 0.66 0 0.5
Result of segmentation
after region grow-thick
0.5 1 0.5 1 1 1
Result of segmentation
after region grow-thin 0.5 1 0.5 1 1 1
Result of segmentation
after level set 0.5 0.66 0 0.33 1 0
Table 5. Results of Accuracy applied on segmentation methods.
Images Eye Bone Lena Frog Hex shapes Two cell
Techniques Accuracy Accuracy Accuracy Accuracy Accuracy Accuracy
Result of
segmentation
after Global thresholding
0.66 1 0.75 1 0.42 0.75
Result of segmentation
after Adaptive
thresholding
0.66 0.33 0.25 0.75 0.14 0.25
Result of segmentation
after region grow-thick 0.66 0.5 0.75 0.62 0.71 0.5
Result of segmentation
after region grow-thin 0.66 0.5 0.75 0.62 0.71 0.5
Result of segmentation
after level set 0.16 0.83 0 0.75 1 0
Table 6. Results of Precision applied on segmentation methods.
Images Eye Bone Lena Frog Hex Two cell
Techniques Precision Precision Precision Precision Precision Precision
Result of
segmentation
after Global thresholding
0.75 1 0.66 1 0.25 0.66
Result of segmentation
after Adaptive
thresholding
0.75 0.4 0.25 0.8 0.25 0.66
Result of segmentation
after region grow-thick 0.75 0 0.66 1 0.5 0
Result of segmentation
after region grow-thin 0.75 0 0.66 1 0.5 0
Result of segmentation
after level set 0 0.75 0 0.71 1 0
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Table 7. Overall performance results of different segmentation methods.
Average Average
Techniques Sensitivity
Result of segmentation
after Global thresholding 0.83
Result of segmentation
after Adaptive thresholding 0.61
Result of segmentation afte
region grow-thick 0.44
Result of segmentation afte
region grow-thin 0.44
Result of segmentation after
level set 0.5
Figure 8. Graphical representation of performance of segmentation methods.
IV. CONCLUSION
The image segmentation is a relevant technique in image processing. Numerous and varied methods exist
for many applications. Now that we have described the algorithms, we can compare the outputs and check
which type of segmentation technique is better for
classification is best analysis method for biomedical image key factors which allow for the use of a
segmentation algorithm in a Many object detection system:. Accuracy, Sensitivity, Precision, Specifici
On an average parameter set of the edge detection techniques, Global thresholding technique performed
better than all other techniques for all the formats of images, sample of which can be found in results.
Histogram based methods are found to be very
compared to other image segmentation methods. If significant peaks and valleys are identified properly
and proper thresholding is fixed, this technique yields good result. Region
Average
sensitivity
Average
Specificity
Results of segmentation after Global thresholding
Results of segmentation after region grow thick
Results of segmentation after Level set
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Table 7. Overall performance results of different segmentation methods.
Average Average Average Average
Sensitivity Specificity Accuracy Precision
0.83 0.69 0.76 0.72
0.61 0.31 0.39 0.51
0.44 0.83 0.62 0.48
0.44 0.83 0.62 0.48
0.5 0.41 0.45 0.41
Figure 8. Graphical representation of performance of segmentation methods.
The image segmentation is a relevant technique in image processing. Numerous and varied methods exist
for many applications. Now that we have described the algorithms, we can compare the outputs and check
which type of segmentation technique is better for a particular format. It is believed that the binary
classification is best analysis method for biomedical image key factors which allow for the use of a
segmentation algorithm in a Many object detection system:. Accuracy, Sensitivity, Precision, Specifici
On an average parameter set of the edge detection techniques, Global thresholding technique performed
better than all other techniques for all the formats of images, sample of which can be found in results.
Histogram based methods are found to be very efficient in terms of computation complexity when
compared to other image segmentation methods. If significant peaks and valleys are identified properly
and proper thresholding is fixed, this technique yields good result. Region-grow technique operates wel
Average Accuracy Average Precision Overall
Performance
Results of segmentation after Global thresholding Results of segmentation after Adaptive thresholding
Results of segmentation after region grow thick Results of segmentation after region grow thin
Results of segmentation after Level set
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print),
Average Overall
Precision Performance
0.72 0.75
0.51 0.455
0.48 0.5925
0.48 0.5925
0.41 0.4425
The image segmentation is a relevant technique in image processing. Numerous and varied methods exist
for many applications. Now that we have described the algorithms, we can compare the outputs and check
a particular format. It is believed that the binary
classification is best analysis method for biomedical image key factors which allow for the use of a
segmentation algorithm in a Many object detection system:. Accuracy, Sensitivity, Precision, Specificity.
On an average parameter set of the edge detection techniques, Global thresholding technique performed
better than all other techniques for all the formats of images, sample of which can be found in results.
efficient in terms of computation complexity when
compared to other image segmentation methods. If significant peaks and valleys are identified properly
grow technique operates well
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Results of segmentation after Adaptive thresholding
Results of segmentation after region grow thin
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over all formats of images provided proper seed point is selected and range of threshold is properly
defined. This method performs well even when noise is present and it is reflected with a reasonable values
of parameters in table. Adaptive thresholding yield fine results over all but in some type of image it yield
better results than all other segmentation methods, we can observe it by resulting image of segmentation
methods . The level set algorithm is guaranteed to converge but it may not return optimal solution for
details of images. Region grow can enhance salt noise if seeds are not selected properly. As the adaptive
thresholding perform nearly close to global thresholding and adaptive thresholding is an automatic
procedure of segmentation it is a better choice for hybrid segmentation. Region grows and Adaptive
thresholding will be used for creating a hybrid segmentation method to improve the Detection and
segmentation of liver cancer from CT scan.
ACKNOWLEDGMENT
THE AUTHOR IS THANKFUL TO ALL THE STAFF MEMBERS OF THE SCHOOL OF ECE, LOVELY PROFESSIONAL
UNIVERSITY FOR THEIR VALUABLE SUPPORT.
REFERENCES
[1] Farzaneh Keyvanfard” Feature selection and classification of breast MRI image “Artificial
Intelligence and Signal Processing AISP 2011 International Symposium on (2011) pp. 54 – 58
[2] Nader H. Abdel-massieh “Fully Automatic Liver Tumor Segmentation from Abdominal CT Scans” .
[3] Amandeep singh, Jaspinder sidhu “Performance Analysis of Segmentation Techniques”
International Journal of Computer Applications (0975 – 8887) Volume 45– No.23, May 2012
[4] N. Otsu, “A Threshold Selection Method from Gray-Level Histograms”, IEEE Trans.Syst., Man,
Cybern., vol. SMC-9 (1), pp. 62-66, Jan. 1979.
[5] C.M. Li, C.Y. Xu, C.F. Gui, M.D. Fox, Level set evolution without re-initialization: a new
variational formulation, in: IEEE Conference on Computer Vision and Pattern Recognition, San
Diego, 2005, pp. 430–436.
[6] Caselles, R. Kimmel, G. Sapiro, Geodesic active contours, in: Processing of IEEE International
Conference on Computer Vision’95, Boston, MA, 1995, pp. 694–699.
[7] S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces, Springer-Verlag, New
York, 2002.
[8] P. K. Sahoo, S. Soltani and A. K. C. Wong, “A Survey of Thresholding Techniques”, Computer
Vision, Graphics, and Image Processing, vol. 41, 133-260 (1988).
[9] J. S. Weszka, R. N. Nagel, and A. Rosenfeld, “A threshold selection technique”, IEEE Trans.
Comput., vol. C-23, pp. 1322-1326, 1974.
[10] N. R. Pal and S. K. Pal, “A Review on Image Segmentation Techniques”, PatternRecognition, vol.
26, No. 9, pp. 1277-1294, 1993.
[11] N. Lee et al., “Fatty and fibroglandular tissue volumes in the breastsof women 20-83 years old:
Comparison of X-ray mammography andcomputer-assisted MR imaging,” Amer. J. Roentgenol.,
vol. 168, pp.501–506, 1997.
Page 10
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 2, July-September (2012), © IAEME
247
[12] L. Ludemann, P. Wust, and J. Gellermann, “Perfusion measurement using DCE-MRI: Implications
for hyperthermia,” Int. J. Hyperthermia,vol. 24, no. 1, pp. 91–96, 2008.
[13] N. Senthilkumaran et al,” Edge Detection Techniques for Image segmentation – A Survey of Soft
Computing Approaches” nternational Journal of Recent Trends in Engineering, Vol. 1, No. 2, May
2009.
[14] A. Korpel, " Acousto-Optics," in Applied Solid State Science, R. Wolfe, ed.,vol.3, Academic,
New York (1972).
[15] Shudong Wu, Feng Cheng and Francis T.S.YU, “Pattern recognition by OTF method”, J.Optics
(paris), vol.20, 5, pp 201-204, 1989.
[16] Joseph Rosen, “Three-dimensional optical Fourier transform and correlation”, Vol.22, No. 13,
Optics Letters, 964-966, July 1, 1997
[17] Ting-Chung Poon and Taegeum Kum, “Optical image recognition of three dimensional objects”,
Vol.38, No.2, Applied Optics, 370-381, 10 Jan 1999.