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Comparative Study for Color Edge Detection Using Vector Value, YCbCr Color Space and Least Square Numerical Method

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Edge detection plays an important role in image processing, pattern recognition and computer vision applications. Most of edge detection schemes are based on finding maximum in the first derivative of the image function or zero crossings in the second derivative of the image function. Various methods of edge detection for color images, including techniques extended from monochrome edge detection as well as vector space methods are presented. This research presents a comparative study on different methods of edge detection of color images. The methods are based on vector space, color space and numerical methods. Seven different colored images are test in this research. Performance is analyzed depending on Mean Square Error (MSE).The experimental results show that applying vector value (Jacobian method )will create a thick and disconnected edge with all operators Sobel, Prewitt and Log. While the least square method produce edges that are much thicker but continuous. The best performance was found when using YCbCr luminance (Y) and chrominance (Cb and Cr) method, the edges are sharpened, continuous, and not thickness. They are similar with Sobel and Prewitt operators nonetheless with some missing edges while it is better with Log operator.
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CIC-COCOS’17 March 29-30, 2017, Cihan University-Erbil
24
Comparative Study for Color Edge Detection Using
Vector Value, YCbCr Color Space and Least Square
Numerical Method
Sarah Behnam Aziz
College of Sciences,
Computer Science &IT department
Salahaddin University
Erbil, IRAQ-KRG
sarah.aziz@su.edu.krd
Dalya Abdullah Anwer
College of Sciences,
Computer Science & IT department
Salahaddin University
Erbil, IRAQ-KRG
dalya.anwar@su.edu.krd
DOI: 10.24086/cocos17.04
Mardin A. Anwer
College of Engineering
Software and Informatics Department
Salahaddin University
Erbil, IRAQ-KRG
mardin.anwer@su.edu.krd
Abstract Edge detection plays an important role in image
processing, pattern recognition and computer vision applications.
Most of edge detection schemes are based on finding maximum in
the first derivative of the image function or zero crossings in the
second derivative of the image function. Various methods of edge
detection for color images, including techniques extended from
monochrome edge detection as well as vector space methods are
presented. This research presents a comparative study on
different methods of edge detection of color images. The methods
are based on vector space, color space and numerical methods.
Seven different colored images are test in this research.
Performance is analyzed depending on Mean Square Error
(MSE). The experimental results show that applying vector value
(Jacobian method )will create a thick and disconnected edge with
all operators Sobel, Prewitt and Log. While the least square
method produce edges that are much thicker but continuous. The
best performance was found when using YCbCr luminance (Y)
and chrominance (Cb and Cr) method, the edges are sharpened,
continuous, and not thickness. They are similar with Sobel and
Prewitt operators nonetheless with some missing edges while it is
better with Log operator.
Keywords: Edge detection; least square numerical method;
Sobel operator; Prewitt operator; log operator,Jacobian eignvalue.
I. INTRODUCTION
Edge detection is the first manipulated process toward
recognizing objects in a complex scene of image understanding
system [1]. We can define the edge as a boundary between an
object and the background. Lots of approaches have be
discover to obtain edge detection [2]. Yet most of these
methods are categorized into two types. First derivative-based
edge detection operator to detect image edges by computing
the image gradient values, such as Roberts operator, Sobel
operator, Prewitt operator; and the second derivative-based
edge detection operator, by seeking in the second derivative
zero-crossing to edge detection, such as LOG operator, Canny
operator [3,4]. Gradient is a measure of the function changes
and it is the first order derivative of the image corresponds to
two-dimensional function.
Image can be defined as a series of derivative of image
intensity of sampling points group. Gradient is a type of two-
dimensional equivalent of the first derivative. Therefore, it can
be defined as a vector [5]. Edges mostly divide into step shape
and roof shape. Equation number 1 represent digital image’s
first-order partial derivatives such as water droplet image
which has step edge.
    
   (1)
The following approximate formula is used to simplify the
calculation of gradient:

(2)
Across operator detects the gradient which cross along with
the image coordinate axis 45° and 135°.
The Operator is:

     (3)
Other common operators include Prewitt operator, Sobel
operator, and Laplace operator [6].
A. Vector Value Method
The vector-valued technique is applied on the color images
and isolate individual component of RGB. Whereas in
grayscale images a discontinuity in the grayscale function is
term as an edge. The term “color edge” is not evidently defined
for color images. There are plenty of different definitions are
proposed for color edges. G.S Robison in 1976 said that the
intensity image contains an edge only when the edge exists
precisely in the color image [7]. In addition, the other
definition of G.S Robison of color edge detection is that, if at
CIC-COCOS’17 March 29-30, 2017, Cihan University-Erbil
25
least one of the color components contains an edge only then
edge exist in color image. Yet, when edges are merged in edge
detection then the color components may cause some problems
due to localization inaccuracies of edges in the individual color
channels. The third definition of G.S Robison to detect the
color edges it is based on the sum of absolute values of the
gradients for the three color components (RGB).
The results of the color edge detection by the previously
named definitions depend heavily on the used color spaces. A
color image represents in the terms of vector-valued function; a
discontinuity of chromatic information can also be defined in a
vector-valued way.
Henriques in 2010 suggested a method of edge detection
that depends on vector-valued techniques, in which the direct
formulas for the Jacobian eigenvalues were used, so this
function is vectorized and yields good results without
sacrificing performance [8]. The main steps of Jacobian
method can be explained briefly as following:
1. Determine the standard edge detection operator that
will to be applied.
2. Compute the x-direction derivative (rx, gx, and bx) for
the three color component (RGB) separately.
3. Compute the y-direction derivative (ry, gy, and by) for
the three color component (RGB) separately.
4. Compute the Jacobian matrix for the x-direction
derivatives, y-direction derivatives and their
combination.
  (4)
   (5)
         (6)
5. Compute first (greatest) eigenvalue (e1) of 2x2 matrix
J' *J.
       (7)
   
( 8)
6. Find the edge magnitude.
  (9)
B. YCbCr Color Space Methods
YCbCr color space uses for component digital video. It
scales and offset version of the YUV color space.YUV space
corresponds to the RGB color cube the YCbCr color. Space is
used for constituent digital video. The location of the block of
RGB-represent able colors in the YCbCr space is shown in
Figure 1 [10].
           (10)
           (11)
           (12)
        (13)
       
  (14)
          (15)
It is crucial to convert the RGB color image to YCbCr color
using equations 10-12 when applying edge detection in YCbCr
color space. Then applying the required edge operator on the
result of equation 11 (the luminance Part (Y)) and reconverted
it again to RGB color space.
Figure 1. RGB Colors Cube in the YCbCr Space [10]
C. Least Square Numerical Method
Al-Nifaay in 2005 suggested a method of edge detection that
depends on the algorithm of least square carve fitting. They
took a sliding mask (like 3x3) and took some steps to detection
an edge point in this mask if it's found [11].In the first step,
they rearrange the pixels of this mask in a pair [x, y(x)], where
(x) represents the location (index) of the color levels values
y(x), {x=1, 2, 3… n}, n is the total number of pixels in the
mask.
The relation then modify in the form of a straight-line
relation given in the equation.
Y(x) = a + b x (16)
Where a, b are constant can be obtained in the following:
Compute the summation
 , 

 , 
 (17)
From the least square approximation method, we calculate
a and b:
b=





 (18)
a=
 

(19)
The best of derived data can be obtained from equation (19)
depends on the values of (a) and (b) [11].
The paper is organized as follows: An introduction of edge
detection is given in Section 1. Previous related works are
presented in Section 2. Section 3, introduce the experiments
and results of the comparing the three methods: vector Value
(Jacobian), YCbCr Color Space and Least Square Numerical
Method.
CIC-COCOS’17 March 29-30, 2017, Cihan University-Erbil
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II. RELATED WORKS
It is noteworthy that currently there is no research that
undertaken vector value, YCbCr color space and least square
numerical methods in comparing color edge detection.
However, most of researches are done on comparing the
traditional methods on edge detection. Therefore, in our related
work we will refer to some papers that focused on edge
detection in general. Amer in 2005 detected the edge for many
real color image that represented the type of digital image by
using a new operator in least square approximation method
which is a type of the numerical method [11].
Bhadauria in 2008 presented a brief study of the
fundamental concepts of the edge detection operation, theories
behind different edge detectors and compares different image
edge detection algorithms including Roberts, Sobel, Prewitt,
and Canny with MATLAB tool in his paper [12].
While (Hassan,2013) presented an edge detection method
applicable to grey level images based on Approximation
Theory. He compared the performance of his proposed method
with other methods such as Sobel and Prewitt edge detector by
using various tested images. The experimental results in the
research reveal that the proposed method exhibits better
performance and may efficiently for the detection of edges in
image[13].
Ahmed in 2013 proposed a new algorithm for detection the
edge in biomedical images depends on least square
approximation method, which considered one of the types of
the numerical methods. They focused on edge detection task in
biomedical images, which is a key problem. They showed how
the proposed method cans detection on the edge in images with
high efficiency compare with standard methods [14].
Rupinder Singh and Jarnail Singh in 2011 proposed
algorithm that designed for integrating edges and regions. The
edge map of image is obtained by using canny edge operator
[15]. In the same year, Nagabhushana Rao illustrated the
comparative analysis of various image edge detection
techniques on finger print images [16]. While in 2010 Jagadish
H. Pujar, proposed a novel algorithm for medical image
segmentation according to vigorous smoothening by
recognizing the type of noise and edge detection ideology
which seems to be a boom in medical image diagnosis [17].
In 2009, Andres described a new line segment detection
and extraction algorithm for computer vision, image
segmentation, and shape recognition applications [18].
Maik and Kumar (2016) applied Canny’s edge detection
technique on color and grey scale images. They observed that
the Canny’s edge detection algorithm performs better than all
other methods under almost all scenarios it gives better result
in gray scale images and color [19].
III. RESULT AND DISCUSSION
In this paper, various color edge detection methods namely
vector Value, YCbCr color space and least square numerical
method are applied on seven different colored shapes. For
implementation, Matlab R2013 is used on a computer that has
Intel(R) Pentium (R) CPU with 4GB RAM. The results of
these methods are shown in figure 2-8 respectively. In the other
hand the algorithm used in this paper are shown below.
Start
For i=1 to 7 do the following
Begin
Select colored image
X= detect edge using Least Square Method
Y1= detect edge using YCbCr Method using Sobel
Y2= detect edge using YCbCr Method using Prewitt
Y3= detect edge using YCbCr Method using log operator
Z1= detect edge using Jacobian Method using Sobel
Z2= detect edge using Jacobian Method using Prewitt
Z3= detect edge using Jacobian Method using log operator
Evaluate MSE for X, Y1, Y2, Y3, Z1, Z2, Z3
End
End
Figure 2. The algorithm used in implementing the program
Figure 3. Edge detection results of image 1, a: original image , b: least
square, c: YCbCr Sobel, d:YCbCr Prewitt, e: YCbCr log, f:Jacobian Sobel, g:
Jacobian Prewitt , h: Jacobian Log.
CIC-COCOS’17 March 29-30, 2017, Cihan University-Erbil
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Figure 4. Edge detection results of image 2, a: original image , b: least
square, c: YCbCr Sobel, d:YCbCr Prewitt, e: YCbCr log, f:Jacobian Sobel, g:
Jacobian Prewitt , h: Jacobian Log.
.
Figure 5. Edge detection results of image 3, a: original image , b: least
square, c: YCbCr Sobel, d:YCbCr Prewitt, e: YCbCr log, f:Jacobian Sobel, g:
Jacobian Prewitt , h: Jacobian Log.
Figure 6. Edge detection results of image 4, a: original image , b: least
square, c: YCbCr Sobel, d:YCbCr Prewitt, e: YCbCr log, f:Jacobian Sobel, g:
Jacobian Prewitt , h: Jacobian Log.
Figure 7. Edge detection results of image 5, a: original image , b: least
square, c: YCbCr Sobel, d:YCbCr Prewitt, e: YCbCr log, f:Jacobian Sobel, g:
Jacobian Prewitt , h: Jacobian Log.
CIC-COCOS’17 March 29-30, 2017, Cihan University-Erbil
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Figure 8. Edge detection results of image 6, a: original image , b: least
square, c: YCbCr Sobel, d:YCbCr Prewitt, e: YCbCr log, f:Jacobian Sobel, g:
Jacobian Prewitt , h: Jacobian Log.
Figure 9. Edge detection results of image 7, a: original image , b: least
square, c: YCbCr Sobel, d:YCbCr Prewitt, e: YCbCr log, f:Jacobian Sobel, g:
Jacobian Prewitt , h: Jacobian Log.
Table 1 represent the result of MSE for images 1,2, 3,4,5,6
and 7. MSE is The Mean Square Error (MSE). It is used to
compare image edge detection quality. The MSE value gives
the average difference of the pixels throughout the original
image with edge detected image. The higher MSE indicates a
greater difference between the input image and resultant
image [20].
TABLE 1 MSE RESULTS
Image
Numerical
Method
YCbCr Method Jacobian Method
Least Square Sobel Prewitt Log Sobel Prewitt Log
1 0.2895 0.2769 0.2769 0.2689 0.2869 0.2821 0.2786
2 0.2156 0.0974 0.0957 0.1222 0.1720 0.1341 0.1903
3 0.6244 0.3487 0.3480 0.3392 0.5473 0.5028 0.5361
4 0.4170 0.4090 0.4091 0.3791 0.4089 0.4055 0.4194
5 0.5728 0.5115 0.5114 0.5001 0.5651 0.5569 0.5396
6 0.5584 0.5729 0.5729 0.5561 0.5610 0.5677 0.5686
7 0.3247 0.1604 0.1608 0.1751 0.3171 0.2725 0.1971
IV. CONCLUSSION
In our research edge detection methods that are explain
previously are applied on seven different images in order to
analyze the performance of these methods and discover the
best one. The images were selected so they contain areas of
fine details as well as areas of consistent colors. The 7 images
and their results can be seen in figures 3 to 9. We conclude that
the Jacobian method produce a thick and disconnected edge
with all operators Sobel, Prewitt and Log. While the least
square method produce edges that are much thicker but
continuous. The good performance was found when using
YCbCr method, the edges are sharpen, continuous, and not
thickness. They are similar with Sobel and Prewitt operators
but with some missing edges while it is better with Log
operator.
Table two summaries the performances of the different
methods according to the computation complexity, noises
immunity, and lines, corners, and curve detected.
TABLE 2 COMPERISM RESULTS
Edge Detection
Method
Computation
Complexity
Noises
Immunity
Lines, Corners,
and Curves
Detected
Least Square Complex Very
Sensitive
Thickness lines,
corners, and
curves.
YCbCr-Sobel Less Complex Low
Sensitive
Detect outlines
(continuous
Boundaries) but
missing the inners
ones.
YCbCr-Prewitt Less Complex Low
Sensitive
Detect outlines
(continuous
Boundaries) but
missing the inners
ones.
YCbCr-Log More Less
Complex
Low
Sensitive
Detected inner and
outlines.
Jacobian-Sobel Much More
Complex Sensitive Thick lines and
some breakouts.
Jacobian-Prewitt Much More
Complex Sensitive Thick lines and
some breakouts.
CIC-COCOS’17 March 29-30, 2017, Cihan University-Erbil
29
Jacobian-Log More
Complex
Less
Sensitive
Thick lines, lot of
breakouts and
missing corners.
ACKNOWLEDGMENT
We would like to thank all who help us in preparing this
research. Their help is highly appreciated.
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