Comparative Analysis of Common Edge Detection Algorithms using Pre-processing Technique

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 7, No. 5 October 2017, pp. 2574~2580
ISSN: 2088-8708, DOI: 10.11591/ijece.v7i1.pp2574-2580  2574
Journal homepage: http://iaescore.com/journals/index.php/IJECE
Comparative Analysis of Common Edge Detection Algorithms
using Pre-processing Technique
R.Vijaya Kumar Reddy1
, K. Prudvi Raju2
, M. Jogendra Kumar3
,
L. Ravi Kumar4
, P Ravi Prakash5
, S. Sai Kumar6
Department of Information Technology, PVPSIT, Kanuru, India
Article Info ABSTRACT
Article history:
Received Dec 21, 2016
Revised Apr 21, 2017
Accepted Jun 25, 2017
Edge detection is the process of segmenting an image by detecting
discontinuities in brightness. Several standard segmentation methods have
been widely used for edge detection. However, due to inherent quality of
images, these methods prove ineffective if they are applied without any pre-
processing. In this paper, an image pre-processing approach has been
adopted in order to get certain parameters that are useful to perform better
edge detection with the standard edge detection methods. The proposed pre-
processing approach involves median filtering to reduce the noise in image
and then edge detection technique is carried out. Finally, Standard edge
detection methods can be applied to the resultant pre-processing image and
its Simulation results are show that our pre-processed approach when used
with a standard edge detection method enhances its performance.
Keyword:
Canny technique
Digital image processing
Filtering
Image edge detection
Pre-processing Copyright © 2017 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
R. Vijaya Kumar Reddy
Department of Information Technology,
PVPSIT, Kanuru, AP, India
vijay2.sri@gmail.com
1. INTRODUCTION
Edge detection is basically an image segmentation technique that divides spatial domain, on which
the image is defined into meaningful parts or regions [1]. The discontinuities are abrupt changes in pixel
intensity and the edges that characterize boundaries of objects in an image and object recognition. This is the
fundamental importance of segmentation of image in processing an image. Edges typically occur on the
boundary between two different regions in an image, where there is a more or less abrupt change in pixel
greylevel or texture indicating the end of one region and the begining of another region. Edge detection
allows user to observe those boundaries. Edge detection therefore finds practical applications in medical
imaging, computer-guided surgery, satellite images, face recognition, and finger print recognition, automatic
traffic controlling systems and a study of an atomical structure etc. Several edge detection techniques have
been developed such as Robert, Prewitt, Sobel and Canny. However, this edge detection does not given sharp
edges and which have been highly sensitive and provided poor performance in noisy images [1].
Main aim of performing segmentation on a given image is to extract maximum information from
image. To remove noise from image some filters are used like Gaussian filter, median filter, etc [2]. The edge
detection is also useful for detecting valuable or important changes in the value of the intensity, and can be
explored to hide image distortions introduced in the channel. This kind of detection is mostly achieved using
first order or second order derivative of intensity values. Moreover, one of the reasons that could make this
variation high is the existence of high frequency (noise) at that area. Once data is received at the receiver,
errors are detected and if possible, they are also corrected [3]. An edge detection filter can also be used to
improve the appearance of blurred or anti-aliased image streams [4]. Edges can be detected using various
edge detectors. This considered as the ideal edge detection algorithm for images that are corrupted with
different types of noises [5]. An edge is typically extracted by computing the derivative of the image

IJECE ISSN: 2088-8708 
Comparative Analysis of Common Edge Detection Algorithms using Pre-processing Technique (R.Vijaya
Kumar Reddy)
2575
function. Some of the edges that normally encountered in image processing are step edge, ramp edge, spike
edge, roof edge.
Step edge is an abrupt intensity change. Ramp edge represents a gradual change in intensity. Spike
edge represents a quick change and immediately returns to original intensity level. Roof edge is not
instantaneous over a short distance [6]. Canny’s aim is to identify optimal edge detection algorithm which
reduces the probability of detecting false edges, and gives sharp edges. Finally, in this method the image is
processed and the resulting one is applied to standard edge detection method for to enhance the final edge
detection method performance. The main aim of an edge detection method is to investigation edges of an
image for detection and localization [7]. In our work, we presents a pre-processing approach is used to
enhance the performance of standard edge detection methods. In our approach the image is pre-processed
with median filtering and then, a standard edge detection method is applied to the resultant segmented image.
The proposed pre-processing involves computation of median filtering of image and then image
segmentation is carried out.
The rest of the paper is organized as follows: In Section 2, a review of edge detection methods is
described; advantage and disadvantage of these methods are summarized. In Section 3. the Problem
Formukation for edge detection is introduced. Section 4, presents experiment results and shows a quantitative
comparison between pre-processed and standard methods with and without the pre-processing. We draw the
conclusion in Section 5.
2. A REVIEW ON EDGE DETECTION METHODS
Edge detection is the process of determining where edges of objects fall within an image. Figure 1
shows schematic diagram for the standard edge detection method. To indentify and detect abrupt change at
edges, several operators have been constructed based on different ideas. In the following section, a brief
review on Edge dectection methods.
Figure 1. Standard edge detector.
Explaining research chronological, including research design, research procedure (in the form of
algorithms, Pseudocode or other), how to test and data acquisition [1-3]. The description of the course of
research should be supported references, so the explanation can be accepted scientifically [2], [4].
2.1. First Order Edge Detector
The gradient method is used to detect the edges by looking for the maximum and minimum in the
first derivative of the image. Thus, consider the two dimensional function f (x, y) to represent the input image
then image gradient is given by the following Equation 1. The magnitude of the gradient computed by
Equation 2 gives edge strength. The gradient direction is always perpendicular to the direction of the edge.
Robert, Sobel, and Prewitt operators are classified as standard first order derivative operators which are easy
to operate but highly sensitive to noise [1].
𝛻𝑓 = 𝐺[𝑓(𝑥, 𝑦)] = [
fx
fy
] = [
𝜕𝑓(𝑥,𝑦)
𝜕𝑥
𝜕𝑓(𝑥,𝑦)
𝜕𝑦
] (1)
The gradient magnitude can be computed by the Equation 2:
|∇f| = √fx2 + 𝑓𝑦2 = √(
𝜕𝑓
𝜕𝑥
)
2
+ (
𝜕𝑓
𝜕𝑦
)
2
≃ |𝑓𝑥| + |𝑓𝑦| (2)
The gradient direction can be computed by the Equation 3:
θ = tan−1
(
fy
fx
) (3)
Edge detection methodInput image Output image

 ISSN: 2088-8708
IJECE Vol. 7, No. 5, October 2017 : 2574 – 2580
2576
2.1.1. Robert edge detector
The Roberts operator performs a simple, quick to compute, Two-Dimension spatial gradient
measurement on an image. It thus highlights regions of high spatial gradient which often correspond to edges.
In its most common usage, the input to the operator is a grayscale image, as is the output. Pixel values at each
point in the output represent the estimated absolute magnitude of the spatial gradient of the input image at
that point. It uses the following 2 × 2 two kernels [8]:
Gx = [
+1 0
0 −1
] 𝑎𝑛𝑑 Gy = [
0 +1
−1 0
] (4)
The plus factor of this operator is its simplicity but having small kernel it is highly sensitive to noise
and not compatible with today’s technology [8].
2.1.2. Sobel Edge Detector
The Sobel operator performs a two-dimension spatial gradient measurement on an image and so
emphasizes regions of high spatial gradient that correspond to edges. Hence, it is used to find the
approximate absolute gradient magnitude at each point in an input grayscale image. It uses the following 3 ×
3 two kernels:
Gx = [
−1 0 +1
−1 0 +1
−1 0 +1
] and Gy = [
+1 +1 +1
0 0 0
−1 −1 −1
] (5)
As compared to Robert operator, Sobel operator has slow computation. When compared to Robert
operator it is less sensitive to noise.
2.1.3. Prewitt Edge Detector
Prewitt edge operator gives better performance than that of Sobel operator. The function of Prewitt
edge detector is almost the same as Sobel detector but have different kernels:
Gx = [
−1 0 +1
−1 0 +1
−1 0 +1
] and Gy = [
+1 +1 +1
0 0 0
−1 −1 −1
] (6)
2.2. Second Order Edge Detector
Let f(x, y) be a continuous two-dimensional scalar field with (x, y) being a point in the image. To
determine the derivatives an operator is applied to the intensity function f(x, y). Any definition of a second
order derivate must be zero in flat areas and must be nonzero at the onset and end of a gray level step and
ramp; and must be zero along ramps of constant slope [9]. The Laplacian operator ∇2
for a 2D image f(x, y) is
defined by the following Equation 7 [8]:
𝛻2
𝑓(𝑥, 𝑦) =
𝜕2
𝜕𝑥2 𝑓(𝑥, 𝑦) +
𝜕2
𝜕𝑦2 𝑓(𝑥, 𝑦) (7)
There are several ways to define digital Laplacian using neighborhoods. In Any definition, it has to
satisfy the properties of a second derivate stated in Equation (11). The following notation is used for second
order derivative in the x and y directions [9].
𝜕2 𝑓
𝜕2 𝑥2 = 𝑓(𝑥 + 1, 𝑦) + 𝑓(𝑥 − 1, 𝑦) − 2𝑓(𝑥, 𝑦) (8)
𝜕2 𝑓
𝜕2 𝑦2 = 𝑓(𝑥, 𝑦 + 1) + 𝑓(𝑥, 𝑦 − 1) − 2𝑓(𝑥, 𝑦) (9)
𝛻2
𝑓 = [𝑓(𝑥 + 1, 𝑦) + 𝑓(𝑥 − 1, 𝑦) + 𝑓(𝑥, 𝑦 + 1) + 𝑓(𝑥, 𝑦 − 1) − 4𝑓(𝑥, 𝑦) (10)
Furthermore, when the first derivative is at a maximum, the second derivative is zero [8].

IJECE ISSN: 2088-8708 
Kumar Reddy)
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2.2.1. Laplacian
Laplacian of an image f (x, y) is defined by:
𝐿[𝑓(𝑥, 𝑦)] = 𝛻2
𝑓 = [𝑓(𝑥 + 1, 𝑦) + 𝑓(𝑥 − 1, 𝑦) + 𝑓(𝑥, 𝑦 + 1) + 𝑓(𝑥, 𝑦 − 1) − 4𝑓(𝑥, 𝑦) (11)
In this case, Laplacian kernel given by the following equation is adopted.
𝐺𝑥𝑦 = [
0 1 0
1 −4 1
0 1 0
] (12)
2.2.2 Laplacian of gaussian (Marr-Hildreth Edge Detector)
It follows the following four steps [11]:
1) Smoothing the image using Gaussian filter. Gaussian smoothing helps eliminate noise. The
larger the sigma, the greater the smoothing.
𝐺(𝑥, 𝑦) =
1
√2𝜋𝜎2
𝑒
−(
𝑥2+𝑦2
2𝜎2 )
(13)
2) Enhancing the edges using Laplacian operator.
𝐿𝑜𝐺(𝑥, 𝑦) = −
1
𝜋𝜎4 [1 −
𝑥2+𝑦2
2𝜎2 ] 𝑒
−(
𝑥2+𝑦2
2𝜎2 )
(14)
3) Estimate the zero crossings denote the edge location.
4) Sub-pixel location of the edge is determined by using linear interpolation.
Too much smoothing may make the detection of edges difficult to indentify.
2.2.3. Difference of Gaussian
To reduce the computational requirements, the Laplacian of Gaussian (LoG) is be similar to the The
difference of Gaussian (DoG). The width of the edge can be changed by adjusted σ1 and σ2 values. DoG
operator of an image f (x, y) is defined by:
𝐷𝑜𝐺(𝑥, 𝑦) =
𝑒
−(
𝑥2+𝑦2
2𝜋𝜎1
2)
2𝜋𝜎1
2 −
𝑒
−(
𝑥2+𝑦2
2𝜋𝜎2
2)
2𝜋𝜎2
2 (15)
LoG requires large computation time for a large edge detector mask. Second Order Derivative
Methods Properties. The following are the most important properties to consider when using the second order
derivate:
1) Laplacian is very sensitive to noise
2) False and missing edges remains
3) Localization is better than gradient operators
2.3. Canny edge detector
The Canny edge detection algorithm is known to be the optimal edge detector algorthim for
detection of edge in segmentation of a image. In this paper, we followed a list of criteria to improve current
methods of edge detection. The first and most obvious is low error rate. The frist criterion, it is important that
edges occurring in an image should not be missed. The second criterion is that the edge points be well
localized. In other words, the distance between the edge pixels as found by the detector and the actual edge is
to be at a minimum [12]. A third criterion is to have single edge to only one response of a edge. This was
implemented because the first two criteriors were not substantial enough to completely eliminating the
possibility of multiple responses to edges. The algorithm then tracks along the top of these ridges and sets to
zero all pixels that are not actually on the ridge top so as to give a thin line in the output, a process known as
nonmaximal suppression. The tracking process exhibits hysteresis controlled by two thresholds values: T1
and T2 with T1 > T2. Tracking can only begin at a point on a ridge higher than T1 threshold. Tracking then
continues in both directions out from that point until the height of the ridge falls below T2 thershold. This
hysteresis helps to ensure that noisy edges are not broken up into multiple edges. In order to implement the
canny edge detector algorithm the steps must be followed [10].

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2578
Step 1: Gaussian filters.
Step 2: Take the gradient of the image.
Step 3: Non-maximum suppression.
Step 4: The edge direction are computed using the gradient values in the x and y directions of an 2D image.
Step 5: Edge direction that can be traced in an image.
Step 6: Hysteresis.
2.4. Merits and demerits of standard edge detection methods
Each edge detection method has its Merits and Demerits. Table 1 summarizes the main Merits and
Demerits of each method [11].
Table 1. Merits and demerits of edge detector ion methods.
Method Merits Demerits
Sobel, Prewitt, Roberts Simplicity in detection of edges and their orientations Sensitivity to noise data and inaccurate
Zero crossing
(Laplacian, 2nd
directional derivative)
Detection of edges and their orientations are having
fixed characteristics in all directions of image
Responding to some of the existing edges, sensitivity
to noise
Laplacian of Gaussian
(LoG)-(Marr-Hildreth)
Finding the correct places of edges, and testing wider
area around the pixel for edges
Malfunctioning at the corners, curves and where the
gray level intensity function varies. Due to Laplacian
filter the orientation of edge are can not be find.
Gaussian (Canny, Shen-
Castan)
Using probability for finding error rate, localization
of response. Improving signal to noise ratio for better
detection. specially in noise conditions.
Complex computations, false zero crossing, time
consuming
3. PROBLEM FORMULATION
Figure 2 shows schematic diagram for the proposed pre-processed edge detection method. In this
method the image is been pre-processed in first step and then in second step the resulted image is applied to
standard edge detection method. The proposed pre-processing involves computation of median filtering of
image and then image segmentation is carried out.
Figure 2. Proposed technique for edge detection
This pre-processing can be implemented in the following two steps.
Step1: pre-processing
1. Convert the original image Figure 3 to grayscale as shown in Figure 4
2. Calculation total edge pixels identified as edges of grayscale image before apply the median filter
3. Filter the grayscale image using a pre-processing technique i.e. median filter
𝑓̂(𝑥, 𝑦) =
𝑚𝑒𝑑𝑖𝑎𝑛
(𝑠, 𝑡)𝜖𝑆 𝑥𝑦
{𝑔(𝑠, 𝑡)} (16)
4. Calculation total edge pixels identified as edges of grayscale image after applying the median filter.
Step2: Edge detection method and comparsion
1. Find the difference between the original grayscale image and median filter grayscale image
2. Using the Noise Reduced Ratio (NRR).calculate the comparison between them
3. Apply the above steps to different edge detection algorithms.
Proposed pre-processing
Edge detection method
Input image
Output image

IJECE ISSN: 2088-8708 
Kumar Reddy)
2579
Figure 3. Original images
Figure 4. Gray images
4. RESULTS
This section presents a comparison between different edge detection models. For this purpose
MATLAB 8.1 (R2013a) program has been adopted to investigate the difference between edge detection
models. This comparison between Roberts, Prewitt, sobel, log and Canny edge detection methods is done
using ground truth of images. The performance parameters used are Edge Pixels Before Pre-processing
(EPB), Edge Pixels After Pre-processing (EPA) and Noise Reduced Ratio (NRR). The original images are
used in simulation and its ground truth and the output of standard and pre-processed methods mentioned in
Table 2.
EPB = (
1
𝑁𝑀
∑ ∑ Bij
M
j=1
N
i=1 ) ∗ 100 (17)
EPA = (
1
𝑁𝑀
∑ ∑ Aij
M
j=1
N
i=1 ) ∗ 100 (18)
Here Bij and Aij is Edge pixel identified before and After pre-processing, N and M are row and
cloumn size.
Noise Reduced Ratio (NRR) = EPA-EPB. (19)
Table 2. Comparison between the proposed pre-processed and standard edge detection methods
Edge detection method Standard Pre-processed Noise reduced ratio (NRR).
Robert
Sample image 98.8998 98.9926 0.0928
Lena 96.6518 96.7584 0.1066
Mandrill 97.8850 97.4209 0.4640
Prewitt
Sample image 98.6603 98.8237 0.1634
Lena 96.4480 97.1218 0.6738
Mandrill 95.8822 96.8462 0.9639
Sobel
Sample image 98.6338 98.7979 0.1640
Lena 96.4231 97.1101 0.6870
Mandrill 95.7845 96.7401 0.9555
Laplacian of gaussian (LoG)
Sample image 96.8322 97.0711 0.2389
Lena 94.1728 94.5448 0.3719
Mandrill 88.7237 90.2029 1.4791
Canny
Sample image 95.2561 95.5833 0.3271
Lena 91.9763 93.1979 1.2216
Mandrill 84.4618 86.9576 2.4958

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5. CONCLUSION
In this paper, we have presented a pre-processing approach in order to enhance the performance of
commonly used edge detection methods. The pre-processing approach consists of computation of the median
filtering to reduce the noise in image and then image segmentation is carried out. Finally, a standard edge
detection method can be applied to the resultant segmented images. The pre-processing approach has been
summarized in steps and demonstrated by an image example. Experimental results have shown that the pre-
processing approach is used with standard edge detection methods to enhance their performance. Results also
shown that edge detection with the pre-processing approach provides the better performance among other
standard methods. The accuracy is increase when we are working with images having more regional
difference in the grey level.
6. ACKNOWLEDGEMENT
Author is thankful to all Assitant Professor, Departmentt. of IT, for giving continues support and
encouragement to carry out this work. Authors are also thankful to the reviewer for critically going through
the manuscript and giving valuable suggestions for the improvement of manuscript.
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