Available online www.jsaer.com

(1)

Journal of Scientific and Engineering Research

150

Journal of Scientific and Engineering Research, 2019, 6(1):150-157

Research Article

ISSN: 2394-2630 CODEN(USA): JSERBR

A Comparative Study of Digital Image Processing Operators for Segmentation

BAAH Barida

¹

, NANWIN Domaka Nuka

²

, IDOKO Peter Samson

³

1Department of Computer Science, Ebonyi State University, Abakaliki – Nigeria

2Department of Computer Science, Ignatius Ajuru University of Education, Rumulumini – Nigeria

3Department of Computer Science, Kogi State Polytechnic, Lokoja– Nigeria

Abstract The use of digital image processing operators is an important aspect when it comes to image segmentation as a result there is the need to critically study these various image processing operators to determine its strength and weakness in its application to various segmentation techniques. The major aim of these research work is to compare various digital image processing operators for edge detection like, Robert, Prewitt Sobel, Canny, Robinson, Kirsch and Laplacian since the quality of image segmentation depends on the types of digital image processing operators that is been used.

Keywords Digital Image, Edge Detection, Segmentation, Digital Operator, Noise 1. Introduction

No doubt the application of digital image processing operators in different domain of imaging is growing by the day as there has been different approach with the aim of ensuring that there is significant improvement in the areas of image segmentations. Naturally, every things in life has its strength and weakness so also in the case of these digital image processing operators it also has it strength which is refers to as it advantages and also its weaknesses which is refer to as its disadvantages. The notion is on how to choose a particular digital processing operator above other will solely depend on the type of segmentation that is to be done on images and also improve on the quality of image after segmentation process. In view of this it will ensure that the noise in the images are reduced to almost zero since noise cannot be completely eradicated but it can tend to zero level; that does not mean that there is no more noise in the image been processed but it is not noticed.

1.1. Definition of Image Processing

This is define as method that is used to perform some digital operations on a given image, in order to get a more enhanced image or to extract some useful information from that given set of image. It can also been seen as a type of signal processing in which input is an image and output may be image or characteristics/features that are associated with that image. Nowadays, image processing is among rapidly growing technologies. It forms core research area within engineering and computer science disciplines too.

The various procedures in digital image processing are stated and explained below:

 Importing the image via image acquisition tools;

 Analysing and manipulating the image;

 Output in which the result can be altered image or report that is based on image analysis 2. Methods of Image Processing

Basically, there are two major methods that are used in image processing:

(2)

151 1. Analogue Image Processing: This is an image processing methods that is used to hardcopies like printouts and photographs. An image analysts use this various fundamentals of interpretation while using these visual techniques.

2. Digital Image Processing: This is a technique that is use to manipulate digital images by use of computers. The three general phases that all types of data have to undergo while using digital technique are pre-processing, enhancement, and display of information of extracted.

2.1. Digital Image Processing Operators

There are various kind of digital image processing operators which are used in edge detection, some of these digital image processing operators used during filtering are stated and discussed below:

2.1.1. Roberts Operator: It is an edge detection operator that was proposed by Lawrence Roberts in 1965. It is the first edge detection operator technique. It performance is simple and its own computation is done in no time [1-2].

The operator is a 2D spatial gradient measurement its gray scale image becomes the mode of input and output of the operator. The output operator exhibits the complete magnitude of the input image[3]Fig. 1 below show 2x2 convolution kernel of the operator.

Figure 1: Vertical and Horizontal Robert Operator 2x2 Masks

The gradient component of each orientation (Gx and Gy) is calculated by applying the convolution matrices to the input image [4]. The calculation of gradient magnitude is as follows:

|G| = |Gx| + |Gy| or |G|= 𝐺𝑥²+ 𝐺𝑦²

2.1.2. Prewitt Operator: The Prewitt edge detector is considered to be the relevant way to calculate the magnitude and orientation of an image [5]. Prewitt is comparably similar to Sobel operator and is widely used to detect the vertical and horizontal edges of an image [6]. The basic idea behind edge detection is to find places in an image where the intensity changes rapidly. The Prewitt operator consists of pair of 3 x 3 convolution kernels that are given Fig 2 below:

Figure 2: Vertical and Horizontal Prewitt Operator 3x3 Masks

The maximum response of all 8 kernels for a pixel location is used to calculate the local edge gradient magnitude:

|G| = max (|Gi|: i=1 to n)

Here, Gi-The response of the kernel i at the appropriate pixel position n -The number of convolution kernels.

The local edge orientation is estimated with the orientation of the kernel that yields the maximum response (Mahmood A.M. et al., 2014). Fig. 3 shows the process of Prewitt edge detection operator.

Figure 3: Operation of Prewitt Operator [9]

2.1.3. Sobel Operator: Sobel operator locates the edges containing highest gradient. It is used to locate the approximate absolute gradient magnitude at each point of the input image[7][10]. The Sobel operator consists of a pair of 3 × 3 convolution kernels as shown in Fig. 4. One kernel is simply the other rotated by 90°. These kernels are designed in such a way that to respond the edges which are running vertically and horizontally

1 0

0 −1 0 1

−1 0

−1 0 1

1 1 1 0 0 0

−1 −1 −1

(3)

152 relative to the pixel grid [11]. The kernels are applied individually to the input image in-order to generate measurements of the gradient components in the respective orientation Gx and Gy [12].

Figure 4: Vertical and Horizontal Sobel Operator 3x3 Masks The gradient magnitude is represented as follows: 𝐺 = 𝐺𝑥²+ 𝐺𝑦²

An approximate magnitude is computed as below: 𝐺 = 𝐺𝑥 + 𝐺𝑦

Here, computation is done faster. The angle of gradient vector is derived from 𝜕 = 𝑎𝑟𝑐𝑡𝑎𝑛 ^𝐺𝑦

𝐺𝑥

2.1.4. Canny Operator: It is an edge detection operator that uses a multi-stage algorithm to detect a wide range of edges in images. Canny operator is a technique that is used to extract useful structural information from different vision objects and dramatically reduce the amount of data to be processed. It is use to produced a computational theory for edge detection [13].

To be able to smooth the images with a Gaussian filter to reduce noise and unwanted details and texture we apply the algorithm from step1 to step 6:

Step1: g(m,n) = G𝜎:(m,n) * f (m,n) Where

𝐺𝜎 = 1

2𝜋𝜎²exp⁡(−𝑚²+ 𝑛² 2𝜎² )

Step 2: To determine the gradient of g(m,n) using any of the gradient operators (Robert, Sobel, Prewitt, etc) we get:

Step 3: 𝑚 𝑛, 𝑛 = 𝑔_𝑚² 𝑚, 𝑛 + 𝑔_𝑛² 𝑚, 𝑛 and

𝜃 𝑚, 𝑛 = 𝑡𝑎𝑛⁻¹ 𝑔𝑛(𝑚, 𝑛)

𝑔_𝑚(𝑚, 𝑛

Where T is chosen that all edge elements are kept while most of the noise is suppressed

Step 4: To suppress most maxima pixels as the edges in MT obtained above to thin the edge ridges (as the edges might have been broadened as Step 1 above. To do so, we check to see whether each non-zero M_T(m,n) is greater than its two neighbors along the gradient direction 𝜃 𝑚, 𝑛 . 𝐼𝑓 𝑠𝑜, 𝑘𝑒𝑒𝑝 𝑀𝑇 𝑚, 𝑛 unchanged, otherwise, set it to 0

Step 5: setup the threshold of the previous result by two different thresholds T₁ and T₂ (Where T₁<T₂) to obtain two binary images T₁ and T₂. Note that T₂ with gradient T₂ has less noise and fewer false edges but greater gap between edges separate when compared to T₁ with smaller T₁ Step 6: Finally, link the edge segment in T₂ to form continuous edges.

2.1.5. Robinson Operators: This is another type of derivative mask which is used for edge detection. This operator is also known as direction mask. In this operator we take one mask and rotate it in all the 8 compass major directions that are as follows:

1. North 2. North West 3. West 4. South West 5. South 6. South East 7. East 8. North East

−1 0 1

−2 0 2

−1 0 1

1 2 1 0 0 0

−1 −2 −1

(4)

153 There is no fixed mask. You can take any mask and you have to rotate it to find edges in all the above mentioned direction. All the masks are rotated on the bases of direction of zero columns. For examples let see the following masks from Fig. 5 to Fig. 12.

Figure 5: North Direction Mask o 3X3

Figure 6: North-West Direction Mask o 3X3

Figure 7: West Direction Mask o 3X3

Figure 8: South-West Direction Mask o 3X3

Figure 9: South Direction Mask o 3X3

Figure 10: South- East Direction Mask o 3X3

Figure 11: East Direction Mask o 3X3

Figure 12: North-East Direction Mask o 3X3

Algorithms for Robinson Operator

In order to detect edges in any given digital imagery, the following steps are apply using the Robinson operators introduced by Robinson in 1977:

Step 1: Read the value of the value of the pixels of RGB image converted into a grayscale image

Step 2: Apply the convolution between every pixel in the image to eight mask of Robinson operator already determined as Fig. 5 to Fig. 12

Step 3: Note, in image not all pixels can do convolution of rows and columns which is located on the edge of the image have a neighbor is not complete. In such a case, we create additional rows and columns at edge is filled with a value of 0 so that the process convolution can be implemented

Step 4: In convolution, there are two possibilities if found, solved in the following manner, namely:

a. If the value result of convolution is negative, the value is made 0.

−1 0 1

−2 0 2

−1 0 1

0 1 2

−1 0 1

−2 −1 0

1 2 1

0 0 0

−1 −2 −1

2 1 0

1 0 −1

0 −1 −2

1 0 −1 2 0 −2 1 0 −1

0 −1 2 1 0 −1

2 1 0

−1 −2 −1

0 0 0

1 2 1

−2 −1 0

−1 0 1

0 1 2

(5)

154 b. If the value result of convolution is bigger than maximum grayscale degree(>255), the value is

converted to the maximum grayscale degree Step 5: Take the maximum value from eight convolution result.

Step 6: The display image is the result of the convolution value

2.1.6 Kirsch Operators: It is an operator that takes a single kernel mask and then rotates it in 45⁰ increments through all 8 compass directions: North (N),NorthWest(NW),West(W),SouthWest(SW), South(S), SouthEast(SE), East(E) and NorthEast(NE). The edge magnitude of the Kirsch operator is calculated as the maximum magnitude across all directions [14]:

ℎ𝑛,𝑚 = 𝑚𝑎𝑥

𝑧=1,…8

𝑔_𝑖,𝑗^(𝑧). 𝑓𝑛+1, 𝑚 + 𝑗

1

𝑗 =−1 1

𝑖=−1

Where z enumerates the compass direction of kernel g in fig 13 below:

Figure 12: Kirsch Compass Direction of Kernel g The edge direction is defined by the mask that produces the maximum edge magnitude

2.1.7. Laplace operator: It is an isotropic operator, second order differential operator. It is more appropriate when it is only concerned with the position of the edge regardless of the pixel gray scale difference around it [15].

The Laplace operator's response to isolated pixels is stronger than the edge or line, and therefore applies only to noise-free images. In the presence of noise, the Laplacian operator needs to perform low-pass filtering before detecting the edge. Therefore, the usual segmentation algorithm combines the Laplacian operator with the

+5 +5 +5

−3 0 −3

−3 −3 −3 g

^{1)

=

+5 +5 −3 +5 0 −3

−3 −3 −3 g

^{2)

=

+5 −3 −3 +5 0 −3 +5 −3 −3 g

^{3)

=

−3 −3 −3 +5 0 −3 +5 +5 −3 g

^{4)

=

−3 −3 −3

−3 0 −3 +5 +5 +5 g

^{5)

=

−3 −3 −3

−3 0 +5

−3 +5 +5 g

^{6)

=

−3 −3 +5

−3 0 +5

−3 −3 +5 g

^{7)

=

−3 +5 +5

−3 0 +5

−3 −3 −3

g

^{8)

=

(6)

155 smoothing operator to generate a new template. Laplacian operator is also the simplest isotropic differential operator with rotational invariance. The Laplace transform of a two-dimensional image function is an isotropic second derivative, which is more suitable for digital image processing, and the pull operator is expressed as a discrete form:

In addition, the Laplace operator can also be expressed in the form of a template.

Figure 14: Positive Discrete Laplacian garlic template

Figure 15: Extended template

Furthermore, the laplacian operator can be classified into two which are the Positive laplacian Operator and the Negative laplacian Operator.

Positive Laplacian Operator

The positive laplacian have a standard mask in which the centre element of the mask should be negative and corner elements of the mask are all zero as shown in Fig. 13 above. This is use to take the outward edges found in any given image.

Negative Laplacian Operator

This is an operator that also has a standard mask in which the centre element should be positive. All the elements in the corner should be zero and the rest of all the other elements in the mask should be -1 as shown in the Fig. 16 below. This is an operator that is use to take inward edges in any given image.

Figure 16: Negative Laplacian Operator template

The Laplacian operator is used to improve the blurring effect due to the blurring effect, since it conforms to the descent model. Diffusion effect is often occurring in the imaging process. The Laplacian operator is used to improve the blurring effect due to the blurring effect, since it conforms to the descent model. Diffusion effect is often occurring in the imaging process.

Proposed Improved Laplacian Operator

In order to improve on better approximation perform on images we will create a matrix of 5 x 5 kernel that has 24 bits at the centre and everything else – 1 as shown in Fig. 16 or create a 5 x 5 kernel with 12 bits Negative laplacian operators as shown in Fig. 18. Note either of them cannot used both at the same time.

Figure 17: An Improved Laplacian Operator of 5x5 Mask Or

Figure 18: An Improved Negative Laplacian Operator of 5x5 Mask

0 −1 0

−1 4 −1 0 −1 0

−1

−1 −1

−1

−1 −1

−1 −1 −1 −1

−1 −1

24 −1

−1 −1 −1 −1 −1 −1

−1 −1

−1

0 0

−1 0 0

0 −1 −1 −1 0

−1 −1

12 −1

−1 0 −1 −1 −1 0

0 0

−1

0

(7)

156 Table 1: Comparism between the different digital operators used digital image processing

SN Operators Name

Strength Weaknesses

1 Roberts Operator

1. It is simple to implement and fast.

2. Detects thicker edges.

1. Localization is not good.

2. It is weak in responding to genuine edge.

2 Prewitt Operator

1. Detection of edges and their orientations are high.

1. It is inaccurate.

2. Size of the coefficient and kernel filter is fixed and cannot be changed to a given image.

3 Sobel Operator

1. It is simple in its implementation 2. It has a better approximation to gradient

magnitude.

1. Sensitivity to Noise.

2. Not accurate in locating edges.

3. Accuracy descends when magnitude of the edges de- creases.

4 Canny Operator

1. It is adaptable to various environments 2. Its parameters permits it to be customized

to recognize the edges with different characteristics

3. It is a well defined method which offers a reliable detection

4. It is the most popular edge detection method because it meets the three criteria for any edge detection and it is also easy to use.

5. It gives a good localization, response and us immune to a noisy environment.

1. It consumes a lot of time due to complexity in its computation process

2. It is also difficult to implement due to its real time response 3. It gives a bias towards vertical

and horizontal edges and does not give a good approximation of rotational symmetry,

5 Laplace Operator

1. It is good at finding the fine details in any given images in order to restore fine detail to an image which has been smoothed to remove the noise present. It utilizes the median filter

2. It is computationally faster due this facts it sometimes produces an exceptional results

1. The use of minus(-) is a problem because it is sensitive to noise since it uses the second order derivatives

6 Robinson Operators

1. It uses the eight wind direction of compass to detect edges faster

1. It produces a thin line edge and not assertive and grey line edges 7 Kirsch

Operator

1. It is simple to implement

2. It can detect edges and its respective orientations

1. It is sensitive to noise and inaccurate

Conclusion

In conclusion, in our research we have been able to discussed the various digital image processing operators for edge detection techniques that are used in digital image processing with the view of comparing these operators to determine its various strength and weaknesses in other choose properly an appropriate operators that will be used digital image processing. Robert operator, Prewitt operator, Sobel operator, Canny operator, Robinson operator and Kirsch Operators are all first order derivatives operators but the Laplacian operator is a second order derivative operators that perform computation in a single pass with fast computation time. However some of these operators are geared towards ensuring good quality of images and accurate results in its application in image segmentation process is of great important but the choice of any operators still depend type of images segmentation to applied

References

[1]. Adem K, Orhan U, Hekim M.(2015) Image processing based quality control of the impermeable seams in multilayered aseptic packages. Expert Systems with Applications. 2015 May; 42(7):3785–89.

(8)

157 [2]. Islam S, Ahmed M. A (2013) study on edge detection techniques for natural image segmentation.

International Journal of Innovative Technology and Exploring Engineering (IJITEE). 2(3)80–3.

[3]. Khan AM, Ravi S (2013). Image segmentation methods: A comparative study. International Journal of Soft Computing and Engineering (IJSCE).3(4)84–92.

[4]. Baselice F, Reale D (2013).Edge detection using real and imaginary decomposition of SAR data. IEEE Transactions on Geoscience and Remote Sensing. 52(7):013833–42.

[5]. Funmilola AA, Oke OA, Adedeji TO, Alade OM, Adewusi EA (2012) Fuzzy k-c-means clustering algorithm for medical image segmentation. Journal of Information Engineering and Applications.

2(6):21–32.

[6]. Sharma K, Kaur N. (2013), Comparative analysis of various edge detection techniques, International Journal of Advanced Research in Computer Science and Software Engineering. 2013; 3(12):617–21.

[7]. Mahmood AM, Elbasi E (2014) Measurement of edge detection algorithms in clean and noisy environment. IEEE 8^th International Conference on Application of Information and Communication Technologies (AICT) p. 1–6.

[8]. Vincent OR, Folorunso O. A (2009) descriptive algorithm for Sobel image edge detection. Proceedings of Informing Science & IT Education Conference (InSITE). p. 97–107.

[9]. P. Sujatha and K. K. Sudha (2015), Performance Analysis of Different Edge Detection Techniques for Image Segmentation, Indian Journal of Science and Technology, Vol 8 (14), DOI:

10.17485/ijst/2015/v8 i14/72946

[10]. Boykov Y.Y, Jolly MP (2001). Interactive graph cuts for optimal boundary and region segmentation of objects in N-D images. Proceedings of International Conference on Computer Vision. 1:105–12.

[11]. Matej J. (2014), Determination of forestry machines tilt angle using camera and image processing.

Computers and Electronics in Agriculture. 109:134–40.

[12]. Kumar I, Rawat J, Bhadauria HS (2014). A conventional study of edge detection technique in digital image processing. IJCSMC. 3(4) pp. 328–34.

[13]. Canny, J. F. (1986). A computation approach to edge detectors. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8, 34–43

[14]. Kirsch R. (1971), Computer Determination of the constituent structure of biological images, Computers and Biomedical Research Vol. 4 pp 315-328.

[15]. Haddon J F. (1988), Generalised threshold selection for edge detection [J]. Pattern Recognition, 21(3):

pp. 195-203.