Ijmet 09 11_013

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International Journal of Mechanical Engineering and Technology (IJMET)
Volume 9, Issue 11, November 2018, pp. 106–113, Article ID: IJMET_09_11_013
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=9&IType=11
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication Scopus Indexed
PERFORMANCE ANALYSIS OF PSO - EM
HYBRID EDGE DETECTION IN ULTRASOUND
IMAGES
Harikumar Rajaguru and Sunil kumar Prabhakar
Department of ECE, Bannari Amman Institute of Technology, Sathyamangalam, India
ABSTRACT
Ultrasound medical images are very important component of the diagnostics process.
As a part of image analysis, edge detection is often considered for further segmentation
or more precise measurements of patterns in the picture. Unfortunately, ultrasound
images are subject to degradations, especially speckle noise which is also a high
frequency component. Conventional edge detector can detect edges in image with additive
noise effectively but not ultrasound image that are corrupted by multiplicative speckle
noise which alleviates image resolution resulting in inaccurate characterization of object
features. In this paper, anisotropic diffusion and PSO-EM based edge detectors are
analyzed and compared for the suppression of the multiplicative noise effectively while
preserving the edge of the object in ultrasound image. The result shows that the proposed
methods provided better result than conventional method.
Key words: ultrasound, speckle noise, anisotropic diffusion, PSO-EM
Cite this Article Harikumar Rajaguru and Sunilkumar Prabhakar, Performance Analysis
of Pso - Em Hybrid Edge Detection in Ultrasound Images, International Journal of
Mechanical Engineering and Technology, 9(11), 2018, pp. 106–113.
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=9&IType=11
1. INTRODUCTION
The use of ultrasound imaging in medical diagnosis is well established because of its non invasive
nature, low cost, capability of forming real time imaging and continuing improvement in image
quality. However, it suffers from a number of shortcomings and these include: acquisition noise
from the equipment, ambient noise from the environment, the presence of background tissue,
other organs and anatomical influences such as body fat, and breathing motion. Therefore, noise
reduction is very important, as various types of noise generated limits the effectiveness of medical
image diagnosis.
Ultrasound is a sound wave with a frequency that exceeds 20 kHz. It transports energy and
propagates through several means as a pulsating pressure wave [1]. It is described by a number
of wave parameters such as pressure density, propagation direction, and particle displace‐ ment.
If the particle displacement is parallel to the propagation direction, then the wave is called a
longitudinal or compression wave. If the particle displacement is perpendicular to the propagation

direction, it is a shear or transverse wave. The interaction of ultrasound waves with tissue is
subject to the laws of geometrical optics. It includes reflection, refraction, scattering, diffraction,
interference, and absorption. Except from interference, all other interactions reduce the intensity
of the ultrasound beam.
Ultrasound technique is mainly based on measuring the echoes transmitted back from a
medium when sending an ultrasound wave to it. In the echo impulse ultrasound technique, the
ultrasound wave interacts with tissue and some of the transmitted energy returns to the transducer
to be detected by the instrument [2]. Further, the reflected waves are picked up by the transducer
probe and relayed to the machine. The machine calculates the distance from the transducer probe
to the tissue or organ (boundaries) using the speed of sound in tissue (1,540 m/s) and the time of
the each echo's return ( millionths of a second). The machine displays the distances and intensities
of the echoes on the screen, forming a two dimensional image. Superficial structures such as
muscles, tendons, testes, breast and the neonatal brain are imaged at a higher frequency (7- 18
MHz), which provides better axial and lateral resolution. Deeper structures such as liver and
kidney are imaged at a lower frequency 1-6 MHz with lower axial and lateral resolution but
greater penetration.
The usefulness of ultrasound imaging is degraded by the presence of signal dependent noise
known as speckle. Speckle noise is multiplicative in nature. This type of noise is an inherent
property of medical ultrasound imaging and because of this noise the image resolution and
contrast become reduced, which affects the diagnostic value of this imaging modality [3]. So,
speckle noise reduction is an essential pre processing step, whenever ultrasound imaging is used
for medical imaging. Therefore, image de speckling is a very important task, and should be
filtered out [4,5], without affecting important features of the image. Figure 1 shows the flow of
the paper, which includes that the ultra sound images are segmented and the Region of Interest
(ROI) is found through the threshold method. Then the edges in the ROI are analyzed through
various edge detects like, mean, median, Lee, SRAD and PSO-EM algorithm. The performance
of various edge detectors are analyzed by the PSNR metric. The organization of the paper as
follows, section I introduces the basics of ultra sonic imaging techniques and in section II various
edge detectors are explained. In the section III PSO-EM based edge detection algorithm is
discussed. The results are analyzed in the section IV and the paper is concluded in the section V.

Performance Analysis of Pso - Em Hybrid Edge Detection in Ultrasound Images
Figure 1 Block Diagram of the Edge Detection Method
2. MATERIALS AND METHODS
Various noise models and edge detectors are discussed in this section of the paper.
A.SPECKLE NOISE MODEL
Effective speckle reduction techniques require an accurate statistical model of ultrasound signals.
A generalized model of the speckle imaging [6] can be written as
g(x,y)=f(x,y).n(x,y)+a(x,y) (1)
where g(x, y) represents the noisy pixel; f(x, y) represents the noise-free pixel; n(x, y) and a(x,
y) represent the multiplicative and additive noise, respectively; and (x, y) are the indices of the
spatial locations in the two-dimensional (2D) image. In this section of the paper, we have outlined
a partial differential equation (PDE) approach to speckle removal that we call speckle reducing
anisotropic diffusion (SRAD) and compared with various other filtering techniques. SRAD not
only preserves edges but also enhances edges by inhibiting diffusion across edges and allowing
diffusion on either side of the edge.
B.FILTERIG METHODS
Filter has very important role in image de-noising process. Using filter technique, in order to
decide particular value of pixel in output image the neighbour pixels also participate. The values
in filter are known as coefficient rather than pixels. The filter which we use for denoising is also
called as mask.
Mean filter
The mean filter also called averaging filter [7] replaces the value of every pixel in an image by
the average of the gray levels in the neighbourhood. It has the effect of smoothing and blurring

the image and it is optimal filter for Gaussian noise. Since the speckle noise is multiplicative, the
simple mean filter is not effective.
Median filter
Median filtering is a nonlinear filtering method, which is used to remove the speckle noise from
an Ultrasound image. It replaces the original gray level of a pixel by the median of gray values
of pixels in a specific neighbourhood [12]. This filter is popular for reducing the noise without
blurring the edges of the image. The median filter is also called the order specific filter because
it is based on statistics derived from ordering the elements of a set rather than taking the mean.
Lee filter
Lee filter is based on the multiplicative speckle model and it can use local statistics to effectively
preserve edges and features. Lee filter is based on the approach that if the variance over an area
is low, then the smoothing will be performed. Otherwise, if the variance is high (e.g. near edges),
smoothing will not be performed. Lee filter can be described by [7]
W(X,Y) = 1 – (C2
B / (C2
I + C2
B)) (2)
where W(X,Y) is the adaptive filter coefficient. CI is the coefficient of variation of the noised
image and CB is the coefficient of variation of the noise.
Anisotropic Diffusion
Perona and Malik proposed the following nonlinear PDE for smoothing image on a continuous
domain:[5],
= [ ∇ . ∇ ]
= 0 =
(3)
where is ∇ the gradient operator, the divergence operator, denotes the magnitude, c(x) the
diffusion coefficient, and I0a the initial image. They suggested two diffusion coefficients
c(x)= /
(4)
and
c(x)=exp[-(x/k)2
] (5)
Where k is an edge magnitude parameter.
In the anisotropic diffusion method, the gradient magnitude is used to detect an image edge
or boundary as a step discontinuity in intensity. If |∇I| >> k, then c(|∇I|) trends to 0 and we have
an all-pass filter; if |∇I| << k, then c(|∇I|) trends to 1 and we achieve isotropic diffusion (Gaussian
filtering).
A discrete form of PDE is given by
∆
= +
∆
| |
∑ c ∇ ,# ∇ ,##∈ (6)
Where is the discretely sampled image, s denotes the pixel position in a discrete two-
dimensional (2-D) grid, and Δt is the time step size & represents the spatial neighbourhood of
pixel , |& | is the number of pixels in the window (usually four, except at the image boundaries),
and ∆
= - # ∀( ∈ & .
The advantages of anisotropic diffusion include intra-region smoothing and edge
preservation. Anisotropic diffusion performs well for images corrupted by additive noise. Several
enhancements and edge detection methods have been described in the literature for images with

additive noise. In cases where images contain speckle, anisotropic diffusion will actually enhance
the speckle, instead of eliminating the corruption.
3. PSO-EM BASED EDGE DETECTOR
Now days the use of heuristics and learning algorithms are very useful in the edge detection and
preservation one such a type of learning method is PSO-EM edge detector which is discussed in
the following section of the paper. This hybrid algorithm combines the usefulness of PSO and
EM methods which in turn bestowed with better results than the traditional models.
A.PSO Algorithm
PSO uses a number of agents (particles) that constitute a swarm moving around in the search
space looking for the best solution. Each one particle is treated as a point in a N-dimensional
space which adjusts its “flying” according to position and velocity. Every particle's movement is
influenced by its local best known position and is also guided toward the best known positions in
the search-space, which are updated as better positions are found by other particles and this is
expected to move the swarm toward the best solutions[8]. It makes few or no assumptions about
the problem being optimized and can search very large spaces of candidate solutions. To be more
specific, PSO does not use the gradient of the problem being optimized, which means PSO does
not require that the optimization problem be differentiable as is required by classic optimization
methods such as Quasi Newton methods and Gradient Descent. PSO can therefore also be used
on optimization problems that are partially noisy, irregular, change over time, etc.
Consider a swarm of p particles or birds. For each particle, indexed by i, the position Xi is
adjusted by a stochastic velocity vi which depends on the distance that the particles are from its
own best solution and that of its neighborhood. The position Xi is updated in the following
manner[10]
1 1
i i i
k k kX X v+ += + (7)
where velocity vi (k) is calculated as follows:
1 1 1 2 2( ) ( )i i i i g i
k k k k k kv v c r p X c r p X+ = + − + − (8)
where i
kv is the current velocity of the particle Xi , k denotes the time step, c1 and c2 are
acceleration coefficients, r1, r2 ~ U(0, 1) represents uniform random numbers, i
kp is the personal
best solution of particle i at time k, and g
kp is the best position found by the neighborhood of
particle i at time k.
In equation (8), the velocity of a particle is determined by three factors:
i) i
kv serves as a momentum term to prevent excessive oscillations in search direction,
ii) 1 1( )i i
k kc r p X− is referred as the cognitive component, which represents the distance that a
particle is from the best solution, i
kp found by itself. The cognitive component represents the
natural tendency of individuals to return to the environments where they experienced their best
Performance
iii) 2 2 ( )g i
k kc r p X− is referred as the social component, which represents the distance that a
particle is from the best position, g
kp found by its neighbourhood. This represents the tendency
of individuals to follow the success of other individuals.
PSO Procedure
PSO algorithm can be implemented by using the following procedure[10].

Step 1: Set the swarm size and initialize each particle by generating random candidate
solutions and velocities.
Step 2: Evaluate each particle in the predefined fitness function and update its i
kp only
if the current fitness is better.
Step 3: Find the particle that has the best fitness in the whole swarm and update g
kp only
if the fitness value found is better.
Step 4: If the stopping criterion is satisfied (e.g., stability or number of iterations), then
stop.
Step 5: Update velocity and position of all the particles according to equation (8) and
equation (7), then repeat steps 2 to 5.
B. Expectation-Maximization Algorithm
The EM algorithm is an efficient iterative procedure to compute the Maximum Likelihood (ML)
estimate in the presence of threshold data. In ML estimation, we wish to estimate the model
parameter(s) for which the observed data are the most likely. Each iteration of the EM algorithm
consists of two processes: The E-step, and the M-step. In the expectation, or E-step, the threshold
data are estimated given the observed data and current estimate of the model parameters [9].This
is achieved using the conditional expectation, explaining the choice of terminology.
In the M-step, the likelihood function is maximized under the assumption that the threshold
data are known. The estimate of the missing data from the E-step is used in lieu of the actual
threshold data.
EM Algorithm Procedure
Given a set of samples X={x1, x2,…xk}, the complete data set S=(X, Y) consists of the sample
set X and a set Y of variables indicating from which component of the mixtures the sample came.
We describe, below how to estimate the parameters of the Gaussian mixtures with the EM
algorithm. After classification of the abnormal regions, EM segmentation is adopted to segment
the intracranial area into two clusters. Basically, EM algorithm is a statistical estimation
algorithm used for finding maximum likelihood estimates of parameters in probabilistic models
[11].
i) Find the initial values for the maximum likelihood parameters which are means, co
variances and mixing weights.
ii) In expectation (E) step, use the probability density function for a Gaussian distribution to
compute the cluster probability for every pixel. The multivariate Gaussian conditional density
function is written as:
1 1 1( | ) exp ( ) ( )
/ 2 1/ 2 2(2 ) | |
tf x x xii i i id
i
θ µ µ
π
 −= − − −∑ 
 ∑
(9)
where θi= (μi, ∑i). x is a d- dimensional feature vector. μi is the mean vector and ∑i, |∑i| and
∑i
-1
are the d-by-d covariance matrix, its determinant and inverse respectively.
iii) In maximization (M) step, use the probability values obtained in E-step to re-estimate the
means, co variances and mixing weights.
iv) Repeat E-step in (ii) and M-step in (iii).
The algorithm terminates when the difference between the log likelihood for the previous
iteration and current iteration fulfills the tolerance.
4. IMAGE QUALITY EVALUATION METRICS

The performance of each filter is evaluated quantitatively for ultrasound image with speckle noise
using the quality metrics like Root Mean Square Error(RMSE) and Peak Signal-to – Noise
Ratio(PSNR).Let x and y denote the original and denoised image.
RMSE: The Root Mean square error (RMSE), is given by
RMSE=)
*+
∑ ∑+
,- ./,, − 1/,,
2*
/- (10)
PSNR: PSNR is defined by the mean squared error.
PSNR=10.log10
*345
6*78
(11)
Figure 2 Original Ultrasound Image Figure 3 Edge Detected Ultrasound Image by PSO-EM
Algorithm
Figure 2 shows the original Ultra sound Image and figure 3 depicts the PSO-EM algorithm
based edge detection in the ultra sound Image.
5. RESULTS AND DISCUSSION
To remove speckle noise, detection and preservation of edges from ultrasound images anisotropic
diffusion method, PSO-EM and some other methods are used in this work. Results are shown in
the table 1.
Table 1 Performance of the Filters in Removal of Speckle Noise.
TYPES OF FILTERS RMSE PSNR
MEDIAN 3.5936 31.7539
MEAN 3.1430 30.1534
LEE 3..0651 32.1763
SRAD 2.9424 33.4777
PSO EM EDGE
DETECTOR
2.86 36.5931
It is observed from the table 1 that the PSO-EM based edge detector outperforms all the other
types of edge detectors including SRAD.
6. CONCLUSION
The speckle reduction and detail retention are two key issues in speckle suppression of medical
ultrasound images. Performance of all algorithms is tested with ultrasound image of abdomen.
Speckle Reducing Anisotropic Diffusion filter (SRAD) and PSO-EM are better than several
commonly used filters including Mean, Lee and median in terms of speckle suppression and detail
preservation.
REFERENCES

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