new approach to edge detection on different

Computing and Informatics, Vol. 38, 2019, 1067–1090, doi: 10.31577/cai 2019 5 1067

NEW APPROACH TO EDGE DETECTIONON DIFFERENT LEVEL OF WAVELETDECOMPOSITION

Vladimir Maksimovic, Branimir Jaksic, Mile PetrovicPetar Spalevic, Stefan Panic

Faculty of Technical ScienceUniversity of PristinaKneza Milosa 738220 Kosovska Mitrovica, Serbiae-mail: {vladimir.maksimovic, branimir.jaksic, mile.petrovic,

petar.spalevic}@pr.ac.rs, [email protected]

Abstract. This paper proposes a new approach to edge detection on the imagesover which the wavelet decomposition was done to the third level and consistingof different levels of detail (small, medium and high level of detail). Images fromthe BSD (Berkeley Segmentation Dataset) database with the corresponding groundtruth were used. Daubechies wavelet was used from second to tenth order. Gradientand Laplacian operators were used for edge detection. The proposed approach isapplied in systems where information is processed in real time, where fast imageprocessing is required and in systems where high compression ratio is used. Thatis, it can find practical application in many systems, especially in television systemswhere the level of details in the image changes. The new approach consists in thefact that when wavelet transform is applied, an edge detection is performed overthe level 1 image to create a filter. The filter will record only those pixels that canbe potential edges. The image is passed through a median filter that filters onlythe recorded pixels and 8 neighbors of pixel. After that, the edge detection withone of the operators is applied onto the filtered image. F measure, FoM (Figure ofMerit) and PR (Performance Ratio) were used as an objective measure. Based onthe obtained results, the application of the proposed approach achieves significantimprovements and these improvements are very good depending on the number ofdetails in the image and the compression ratio. These results and improvements canbe used to improve the quality of edge detection in many systems where compressedimages are processed, that is, where work with images with a high compression ratiois required.

1068 V. Maksimovic, B. Jaksic, M. Petrovic, P. Spalevic, S. Panic

Keywords: Edge detection, wavelet decomposition, compression, F measure, figureof merit, performance ratio

1 INTRODUCTION

In recent years, multimedia systems have recorded tremendous growth and progress,which means that image resolutions got higher increasing the complexity of the sys-tem and the complexity of the image. It is necessary to achieve as much compressionas possible so these images can be streamed, stored and processed more easily. To-day’s trends require more technology to be involved, so in television systems wehave a virtual reality (VR), augmented reality (AR) and a combination of them.Since it is necessary to have lower bitrate and achieve a high compression ratio andto process an image in VR or AR environment, it is necessary to perform certainoperations over images such as segmentation, edge detection, etc. [1].

Edge detection is one of the fundamental processes in image processing. Thisalso means the segmentation of the image where the segmentation of the desiredobject is performed by detecting the edge. Edge detection is based on the fact thatthere are sudden changes in the gray intensity between the objects. Edge detectionsignificantly reduces the image analysis process by using less data and at the sametime storing all the necessary information. Many edge detection techniques havebeen tried, but gradient and Laplacian methods have proved to be the best [2, 3].Gradient methods for edge detection find the maximum and minimum gradient ofthe image intensity, all in the first derivative of the image. Laplacian methods arebased on finding zero crossing in the second derivative of the image [4]. The gradientof the image can be calculated as [4, 5]:

∇f (x, y) =∂f

∂xi+

∂f

∂yj (1)

where f (x, y) represents the image at the location (x, y) where x and y are thecoordinates of the row and column. The gradient ∇f (x, y) contains the informationabout gray change. The gradient of ∇f (x, y) can be calculated [4, 5]:

e (x, y) =√f 2x + f 2

y (2)

where e (x, y) can be used as an edge detector and can also be defined as the sumof the absolute values of the partial derivative fx and fy [4, 5]:

e (x, y) = |fx (x, y)|+ |fy (x, y)| . (3)

Based on these theoretical principles, the gradient and Laplacian methods areproposed. The gradient methods include Sobel, Prewitt, Robert, while the Laplacianinclude LoG (Laplacian of Gaussian). The classic use of the Canny operator is

New Approach to Edge Detection on Different Level of Wavelet Decomposition 1069

a gradient method, but in some parts, it also contains elements of the Laplaceapproach [6, 7, 8].

The analysis of the frequency domain using Fourier transform is very useful forsignal analysis because the frequency domain is very important for the considerationof the nature of the signal and the influence of the noise over it. The disadvantageof this technique is the loss of time domain information. When viewing the Fouriertransform in a frequency domain, it is difficult to say when a certain event occurred,or when some frequencies occurred. To overcome this problem, only a small part(“window”) of the signal is analyzed at a time, and this window slides over the signalapplying the Fourier transform on it. In this way, part of the frequency informationis lost in order to get an information about the time when a certain frequency hasoccurred. Wavelet transformation is used to solve this problem. It allows the useof different window sizes for different frequencies. The basic difference between thewavelet transformation and the short-time Fourier transform is that the windowlength changes at the wavelet transform and in this way the frequency and timeresolution can be changed. The basic idea of each wavelet transform is to present anarbitrary function x(t) as a superposition of a wavelet set or basic functions. Thebasic functions are derived from a prototype called mother wavelet, by scaling ortranslating this function. The wavelet transformation of the x(t) signal is given inEquation (4) [9, 10]:

ψ (τ, s) =1

s

∫ ∞−∞

x (t) ∗ ψ∗(t− τs

)dt (4)

where τ is a translation, and s is a scaling, while ψ is a “mother” wavelet, and ψ∗ isconjugally complex of ψ. When processing images in a spatial domain, the operationis discretized. Discrete wavelet transformation (DWT) is defined as [9, 10]:

DWTψx (τ, s) =1√|s|

∫ ∞−∞

x (t) ∗ ψ∗(t− τs

)dt. (5)

The discrete wavelet transformation (DWT) can be presented as a matrix ψ (c)and DWT coefficients can be obtained by taking an internal product between thesignal and the wavelet matrix [9, 10]:

DWTψx [n, s] =1√|s|

∑n

x [n]ψ∗n,s [n] . (6)

Special family of wavelet functions has been developed for DWT. They aregenerally divided into orthogonal or biorthogonal and are characterized by a high-pass and low-pass filters [11]. Daubechies wavelet belongs to a family of orthogonalfunctions and the main feature is the possibility of the maximum number of vanishingmoments for a predefined supported length. Types of Daubechies (db) wavelets thatare most commonly used in practical applications are dbN, where N represents theorder as well as the number of vanishing moments in the supported interval from 0


to 20. By increasing the order of the Daubechies wavelet, better characteristics areobtained, but the complexity of the implementation, the price of the system anderrors in the calculations rise. In practical applications, orders 2 to 10 are mostcommonly used [10, 12, 13].

A very important advantage of the wavelet transform is that it uses a mul-tiresolution analysis that allows analysis of different signal frequencies at differentfrequency resolutions. For high-frequency parts, shorter windows are used, whichensures good time domain resolution, while longer parts of the lower frequencies havelonger windows, thus giving good information about the frequencies. If the signalis passed through a set of two filters, low-pass and high-pass, its frequency contentwill be split into two equal-width ranges. The output from these filters contains halfthe frequency of the original signal and the same number of samples as the originalsignal. By decimating, or by passing the input signal through the low-pass filter, thenumber of samples is halved so that the time resolution is also halved while the fre-quency resolution increases. The high-pass filter transmits high-frequency content,i.e. signal details. The low-pass signal transmits low-frequency content, or signal ap-proximation. This approximation signal can be further fed through two filters andthe process can be repeated until the desired decomposition level is reached. Thecomplete information on the original signal is contained in the last approximationsignal and all the detail signals [14, 15].

Higher compression ratio disrupts the quality of the image, resulting in a largeloss of information, and hence makes it difficult to process them, for example, todo an edge detection or facial recognition [16, 17]. The decomposition significantlydegrades the image quality, but besides this degradation there are various types ofnoise that further impair the image quality. To solve this problem or to control it,the various types of filters have been developed [18, 19].

In this paper we used the characteristics of wavelet transform in order to imagecompression, or as a method on which some algorithms for image compression isbased, such as JPEG2000 and SPIHT. Images from the BSD database are com-pressed to the third decomposition level which resulted in a high degree of compres-sion.

2 SYSTEM MODEL AND PROPOSED APPROACH

In this paper, the BSD (Berkeley Segmentation Dataset) image database was usedfor analysis, with its corresponding ground truth images [20]. Table 1 lists theselected images from the BSD database meeting the complexity criteria [16], thatis, each image consists of a different level of detail: small, medium, and high levelof detail. The number of details was calculated by making DCT and DWT on thehigh-frequency components (details), which are divided into four quadrants, alongboth directions (x and y). After that, the mean absolute value of the amplitude ofthe components belonging to the quadrants is calculated [16]: DCT in quadrant 1(dctd); DCT in quadrants 2 and 3 (dctm); DWT in quadrant 1 (dwtd); DWT in


quadrants 2 and 3 (dwtm).

Images dctd dctm dwtd dwtm

Criterion L #135 069 1.544 2.517 0.181 0.354

Criterion M #35 010 3.838 6.197 1.199 2.048

Criterion H #8 143 7.868 15.241 3.181 6.336

Table 1. Criteria

Figure 1 gives a flow diagram of the proposed approach. In the proposed ap-proach, firstly, the BSD and the ground truth images are read on which the DWTis applied to the third decomposition level using the Daubechies wavelet (optionallyfrom 2 to 20). Since grayscale images are needed, a conversion is made, and variablesare created for filters and new images. In order to assign input values to a filter, it isnecessary to perform edge detection on level 1 images. Values stored in the filter areinformation about location of pixels pointing at the potential edge. The compressedimage on which the detection is performed is a binary image and passing throughthe loop, each pixel is examined. If it is equal to the 1, that is, there is an edge,the median filter is used on the pixel and 8 neighbors of pixel. In other words,only those pixels that are relevant for the edge detection are passed through thefilter. After that, the detection is applied and the results are compared, as shownin Figure 1. The algorithm is applied to all edge detection operators (Canny, LoG,Sobel, Prewitt, Robert).

The algorithm consists of the following steps:

Step 1 (Read image): Read the original image. If it is a color image, converts itto a grayscale image.

Step 2 (DWT): DWT is applied to the third decomposition level onto a readimage, whereby as a result, three images are obtained: image from level 1,image from level 2 and image from level 3. The next steps in the algorithm areapplied separately for an image from each level.

Step 3 (Edge detection): On level 1 image, an edge detection is used by selectingone of detectors (Canny, LoG, Sobel, Prewitt, Roberts). The image with de-tected edges serves to create a filter that will contain only those pixel coordinateswhere the edges are located.

Step 4 (Filtering image): Every pixel in the image is analyzed and if it is equalto 1, the filter records its coordinates.

Step 5 (Filtering 8-neighbors of pixel): If the condition in step 4 is fulfilled,filtering is done by filtering 8 neighbors of pixel relative to the current pixelusing the median filter (Figure 2). So, only those image pixels that can be edgesare filtered. The neighbors of pixel are extracted using the following formula:


If current pixel P (i, j) is edge then use following neighbor pixels:

f (Pi,j) = f (Pi−1,j−1) , f (Pi−1,j) , f (Pi−1,j+1) , f (Pi,j−1) , f (Pi,j) , f (Pi,j+1) ,

f (Pi+1,j−1) , f (Pi+1,j) , f (Pi+1,j+1) (7)

and use median filter only on those pixels.

Step 6 (Edge detection on filtered image): Edge detection is applied on a fil-tered image.

For filtering level 2 and level 3 images, coordinates from level 1 image areused.

The proposed algorithm has a quadratic complexity and can be represented as:

O (row , col) = 8 (row − 2) (col − 2) + 1. (8)

In Figure 3, the complexity of the algorithm is given, depending on the numberof pixels in the row (row) and the number of pixel in columns (cols).

In order to accurately and precisely present how well the edge detection is done,it is necessary to calculate Precision, Specificity, Sensitivity and Accuracy or F mea-sure [21]. F measure (F1 score) is a harmonic mean of precision and recall and itcombines precision and recall according to the formula [21]:

F =2 ∗ Precision ∗ Recall

Precision + Recall× 100. (9)

F is within the limits of 0 ≤ F ≤ 1, ideally, F is equal to 1. In the results, F ismultiplied by 100 and represents a percentage value.

Figure of Merit (FoM) was proposed by Pratt [22] and is a measure for estimatingthe accuracy of detected edges. In other words, it represents the deviation of theactual (calculated) point of the edge from the ideal point of the edge, and is definedas:

FoM =1

max [Id, Ii]

Id∑k=1

1

1 + δe2 (k)(10)

where Id is the number of points on the detected edge, and Ii is the number ofpoints on the ideal edge, e (k) represents the distance between the detected edgeand the ideal edge, and δ is scaling constant and is usually 1/9. FoM is within0 ≤ FoM ≤ 1. In this case, FoM is multiplied by 100 and represents a percentagevalue. The higher the FoM is, the better the detected edge is [22].

As an objective measure of the edge detection credibility, Performance Ratio(PR) was used too. The PR is ideally equal to infinity. The PR is calculated as theratio of the true edges to false ones [23, 24]:


PR =True Edge(Edge pixels identified as Edges)

False Edges(Non Edge pixels identified as Edges)+(Edge pixels identified as Non Edge pixels)× 100.

(11)

3 RESULTS

3.1 F Measure

Tables 2, 3 and 4 show the F values before and after the application of the pro-posed approach on image with a small, medium and high number of details, re-spectively, over which db (from 2nd to 10th order) wavelet transform to the thirddecomposition level was applied. These tables show the values obtained for the fiveoperators.

From Table 2 it can be seen that based on the obtained results, in the firstdecomposition level, using the proposed approach, improvements were achieved withthe Canny operator in almost all cases, except for db4. A similar situation occurswhen a LoG operator is used, with the exception that improvements have not beenachieved in the case of db6. Using the proposed approach and image with lowdetails, significant improvements have been achieved at the second level, where alloperators record improvements in F values, except in the case of db8 with Prewittand Sobel operators. In the third level, only Canny and LoG record improvementsin F values using the proposed approach.

In the image with a medium number of details, very small improvements havebeen achieved in some operators at the first level, or the values are generally similar,without major deviations, as can be seen in Table 3. The situation is differentwith the second and third decomposition levels, where improvements are achievedby all operators, with the difference that improvements are higher in the thirdlevel.

In the case where the image consists of a high number of details, using theproposed approach, a similar or slightly better F value is obtained. At the secondlevel, improvements are generally achieved with gradient operators, while at thethird level, using the proposed approach, better values are obtained for all opera-tors.


Read image

DWT

(up to Level 3)

Edge detection

i = 2:row-1

j = 2:col-1

Filtering only

8-neighbors of Pixel

with median filter

Edge detection on

filtered image

Filtering level 1 image

if edge (i,j) == 1

Figure 1. Proposed approach


Pi,j

Pi-1,j-1

Pi-1,j

Pi-1,j+1

Pi,j+1

Pi+1,j+1

Pi+1,j

Pi+1,j-1

Pi,j-1

Figure 2. Extraction neighbors of pixel

Figure 3. Complexity of proposed algorithm

1076 V. Maksimovic, B. Jaksic, M. Petrovic, P. Spalevic, S. PanicW

avelet

db2

db4

db6

db8

db10

Opera

tor

Old

New

Old

New

Old

New

Old

New

Old

New

Level1

Canny

0.36

50.378

0.37

90.

364

0.36

80.380

0.36

30.365

0.37

10.375

LoG

0.31

10.314

0.31

30.317

0.31

10.

299

0.30

00.303

0.31

10.315

Pre

witt

0.36

20.

342

0.35

50.

346

0.36

60.364

0.32

20.345

0.38

00.3

62

Sobel

0.36

50.

336

0.35

60.

349

0.37

10.

363

0.32

50.346

0.37

70.3

62

Roberts

0.53

60.563

0.50

30.579

0.51

90.576

0.55

10.566

0.51

40.582

Level2

Canny

0.27

80.305

0.24

60.269

0.20

30.225

0.18

90.194

0.19

40.211

LoG

0.25

60.274

0.23

50.256

0.19

10.211

0.20

50.207

0.18

60.202

Pre

witt

0.26

90.302

0.28

50.339

0.28

50.321

0.33

80.

301

0.27

90.351

Sobel

0.26

40.306

0.28

40.320

0.28

10.314

0.33

30.

303

0.27

80.333

Roberts

0.29

90.416

0.35

00.453

0.39

70.456

0.44

80.486

0.43

30.495

Level3

Canny

0.10

80.160

0.11

30.169

0.09

60.170

0.10

00.158

0.10

60.172

LoG

0.12

80.173

0.14

80.190

0.13

20.187

0.14

80.174

0.14

40.176

Pre

witt

0.14

70.

203

0.18

90.

241

0.18

40.

247

0.18

00.

251

0.19

40.2

56

Sobel

0.14

60.

201

0.18

70.

229

0.18

20.

235

0.17

90.

240

0.19

50.2

44

Roberts

0.18

30.

276

0.20

80.

255

0.21

80.

297

0.25

60.

335

0.26

80.3

48

Tab

le2.

Fva

lues

for

anim

age

wit

ha

low

num

ber

ofdet

ails

(LD

)

New Approach to Edge Detection on Different Level of Wavelet Decomposition 1077W

avelet

db2

db4

db6

db8

db10

Opera

tor

Old

New

Old

New

Old

New

Old

New

Old

New

Level1

Canny

0.31

80.

316

0.32

20.

318

0.32

10.

317

0.32

10.

319

0.32

10.3

20

LoG

0.23

40.

234

0.23

50.236

0.23

50.236

0.23

60.

236

0.23

70.2

36

Pre

witt

0.29

90.

222

0.21

90.220

0.22

50.

225

0.21

80.219

0.22

60.2

26

Sobel

0.22

90.

223

0.22

00.

219

0.22

60.

226

0.21

70.219

0.22

70.2

25

Roberts

0.25

00.

249

0.26

70.268

0.26

80.

258

0.27

40.

267

0.28

20.2

70

Level2

Canny

0.29

50.302

0.29

90.312

0.29

70.312

0.29

80.312

0.30

00.309

LoG

0.21

30.

211

0.20

70.213

0.21

10.213

0.20

90.214

0.20

70.212

Pre

witt

0.20

50.209

0.17

00.182

0.16

00.184

0.15

80.182

0.16

40.185

Sobel

0.20

50.209

0.16

90.180

0.16

10.182

0.15

80.178

0.16

30.183

Roberts

0.15

30.154

0.15

71.196

0.15

80.183

0.15

50.177

0.16

20.179

Level3

Canny

0.18

60.238

0.19

90.246

0.21

50.252

0.20

30.250

0.20

40.250

LoG

0.13

40.153

0.11

10.135

0.08

80.111

0.08

10.104

0.07

60.100

Pre

witt

0.11

80.138

0.09

20.118

0.07

80.115

0.07

20.110

0.07

50.110

Sobel

0.11

80.135

0.09

20.114

0.07

80.109

0.07

20.104

0.07

50.105

Roberts

0.07

80.081

0.06

50.088

0.04

20.054

0.03

40.046

0.03

50.047

Tab

le3.

Fva

lues

for

anim

age

wit

ha

med

ium

num

ber

ofdet

ails

(MD

)


avelet

db2

db4

db6

db8

db10

Opera

tor

Old

New

Old

New

Old

New

Old

New

Old

New

Level1

Canny

0.22

20.

219

0.21

90.220

0.22

00.

219

0.21

90.220

0.22

00.221

LoG

0.19

20.

192

0.19

00.

189

0.19

20.

192

0.19

20.193

0.19

20.1

91

Pre

witt

0.17

10.

167

0.16

40.166

0.17

80.

175

0.16

50.166

0.17

20.1

69

Sobel

0.17

00.

165

0.16

40.165

0.17

70.

174

0.16

30.165

0.17

00.1

68

Roberts

0.16

10.

152

0.16

60.

163

0.16

30.

157

0.17

00.

162

0.16

40.1

57

Level2

Canny

0207

0.207

0.21

60.224

0.20

50.215

0.21

50.220

0.21

40.220

LoG

0.17

70.

176

0.18

20.

183

0.17

20.176

0.17

40.175

0.17

90.182

Pre

witt

0.15

90.166

0.13

90.145

0.12

70.143

0.13

50.141

0.13

30.150

Sobel

0.15

70.166

0.13

90.144

0.12

70.142

0.13

30.140

0.13

30.147

Roberts

0.12

30.

123

0.12

90.167

0.12

50.143

0.13

50.149

0.14

20.1

59

Level3

Canny

0.14

50.184

0.15

40.175

0.15

40.197

0.16

10.190

0.16

20.190

LoG

0.12

10.148

0.10

40.133

0.09

40.114

0.08

40.108

0.07

70.102

Pre

witt

0.11

00.136

0.07

70.102

0.07

80.114

0.07

30.103

0.07

70.111

Sobel

0.10

90.133

0.07

70.098

0.07

80.112

0.07

30.100

0.07

80.110

Roberts

0.08

70.089

0.06

40.088

0.06

70.084

0.06

40.079

0.07

00.087

Tab

le4.

Fva

lues

for

anim

age

wit

ha

hig

hnum

ber

ofdet

ails

(HD

)


3.2 Figure of Merit

Tables 5, 6 and 7 show the FoM values before and after the application of theproposed approach on image with a small, medium and high number of details,respectively, over which db (from 2nd to 10th order) wavelet transform to the thirddecomposition level was applied. These tables show the values obtained for the fiveoperators.

From Table 5 it can be seen that in the first decomposition level, the best valuesare obtained for the Canny operator, where in almost all cases it gives better values,except in the case of db4. By comparing Table 5 with Table 2, it can be seen thatusing FoM objective measurements, improvements have been made in the same orsimilar cases. By increasing the compression, that is, in Levels 2 and Levels 3, usingthe proposed approach, better FoM values were obtained, and greater improvementswere achieved, especially in the third level.

In the case of an image with a medium number of details, in the first level, Cannygave the best results, in other words, better values were achieved. In the second level,in the case of db2, improvements were achieved only with the Canny operator, whileother operators gave similar, but lower values. In other cases, the proposed algorithmrecords substantially better FoM values. For images with a medium number ofdetails, the best edge detection enhancements have been achieved in the third levelusing the proposed algorithm.

Since the compression ratio is higher in the image with a high number of details,based on this fact, it can be concluded that the detection will be much worse. Also,in the case of images with a high number of details, the best improvements areachieved with the Canny operator at all levels. Based on the results obtained, itcan be seen that the best improvements are achieved in the third level.

3.3 Performance Ratio

Tables 8, 9 and 10 show PR values before and after applying the proposed approachusing five edge detection operators and three wavelet decomposition levels. Table 8shows the values for an image with a low number of details. Based on the resultsobtained, it appears that improvements have been made with certain operators.However, based on the values obtained in Table 8, it can be seen that the oldPR values and new PR values obtained using the proposed approach have greatestdifference when using the Robert operator.

Table 9 contains the PR values obtained for an image with medium number ofdetails. From Table 9 can be seen that the new values obtained are best in thesecond and third decomposition levels. In other words, the best improvements areachieved in the second and third levels, depending on the operator used and theorder of the db wavelet.

Table 10 contains PR values obtained for an image with a high number of details.Based on these results, it can be seen that improvements have been achieved usingthe proposed approach, especially in the third decomposition level.


avelet

db2

db4

db6

db8

db10

Opera

tor

Old

New

Old

New

Old

New

Old

New

Old

New

Level1

Canny

88.9

5591.928

89.4

6189

.272

85.9

8291.960

86.0

2586.914

88.7

67

89.626

LoG

89.1

6389

.024

90.2

0990.514

86.9

1585

.582

83.6

0585.108

89.7

79

88.5

56Pre

witt

91.7

8491.937

92.3

4192

.327

92.3

5892.572

92.6

6492

.632

92.8

68

92.5

40Sobel

91.8

9191

.712

92.6

7892.695

92.4

2392.466

93.0

3192

.934

92.8

91

92.7

42Roberts

95.1

5095.387

89.4

1995.816

86.6

8095.561

93.8

3795

.613

83.2

59

95.653

Level2

Canny

61.7

2766.006

51.3

0852.452

40.2

0741.320

31.9

7434.924

36.0

49

37.174

LoG

75.0

0679.220

60.4

7266.126

47.1

8751.753

45.9

5550.186

44.3

79

49.053

Pre

witt

82.1

8276

.052

88.8

2492.094

88.6

5491.490

89.0

7491.115

88.6

76

91.615

Sobel

82.7

8577

.091

88.8

1891.599

88.5

8191.498

88.9

7990.786

88.7

16

91.575

Roberts

82.4

9485.980

89.8

3288

.389

91.0

1688

.300

91.2

8191.386

91.8

77

92.731

Level3

Canny

6.04

59.491

34.3

1638.640

27.0

3534.575

25.1

5833.672

26.9

26

33.476

LoG

42.3

8548.432

49.2

0153.907

47.3

1250.844

48.1

3251.458

48.6

46

52.246

Pre

witt

52.0

3655.246

78.6

7571.700

78.1

3685.231

76.1

9685.186

75.8

41

84.392

Sobel

52.1

1355.991

78.6

0673.264

78.0

8886.561

76.1

9084.761

75.8

37

84.193

Roberts

57.3

8474.222

78.8

2181.909

77.9

5181.587

78.8

3982.599

78.9

01

82.152

Tab

le5.

FoM

valu

esfo

ran

imag

ew

ith

alo

wnum

ber

ofdet

ails

(LD

)


avelet

db2

db4

db6

db8

db10

Opera

tor

Old

New

Old

New

Old

New

Old

New

Old

New

Level1

Canny

83.3

3482.917

83.5

9383.835

83.6

3383.926

83.5

9683.773

83.7

15

84.068

LoG

76.3

5876

.351

76.9

8476

.892

77.0

0376

.875

77.2

1676

.957

77.2

30

77.0

50Pre

witt

65.0

9664

.526

63.4

0363

.351

63.6

9463

.564

63.0

5862

.834

63.6

96

63.3

35Sobel

65.0

6164

.397

65.5

5363

.420

63.9

4863

.449

63.0

7662

.941

63.7

05

63.4

44Roberts

58.4

8458.800

60.4

7758

.903

56.1

6055

.423

58.0

4656

.431

57.5

63

56.5

11

Level2

Canny

80.2

7380.650

80.2

6080.889

80.9

6381.348

80.9

2181.384

81.2

00

81.295

LoG

73.4

3373

.272

73.3

0073.418

73.4

7473.511

73.2

6173

.002

73.5

19

73.5

04Pre

witt

60.8

3060

.702

55.9

9156.815

55.3

1756.128

54.3

4655.447

55.1

18

56.2

28Sobel

60.8

4360

.732

56.0

5756.975

55.3

5456.375

54.4

6355.598

55.1

77

56.389

Roberts

54.3

2750

.858

50.2

6551.582

46.0

3346.891

43.3

0043.996

43.9

72

44.406

Level3

Canny

70.6

2875.211

68.8

3573.034

68.8

4773.556

66.7

9471.193

66.9

68

71.698

LoG

61.5

0361.749

51.3

2353.911

44.3

1647.050

41.3

1043.968

39.2

84

41.870

Pre

witt

49.6

8050.908

40.5

0944.000

36.6

6740.527

34.8

4028

.934

35.0

81

38.936

Sobel

49.6

1851.109

40.5

4343.917

36.6

5440.182

34.9

1038

.611

35.0

98

38.686

Roberts

42.2

9838

.790

31.9

9034.236

19.1

4320.251

15.9

7916.983

16.2

16

17.198

Tab

le6.

FoM

valu

esfo

ran

imag

ew

ith

am

ediu

mnum

ber

ofdet

ails

(MD

)


avelet

db2

db4

db6

db8

db10

Opera

tor

Old

New

Old

New

Old

New

Old

New

Old

New

Level1

Canny

70.1

1171.230

69.1

2771.555

67.7

8770.466

68.0

5769.417

68.4

20

70.459

LoG

80.6

1280

.029

80.7

1380

.131

81.0

1680

.593

80.8

9480

.399

81.0

20

80.5

43Pre

witt

64.3

3863

.895

58.0

6358.180

62.1

6561

.852

59.8

0459.969

60.5

13

60.4

54Sobel

64.2

5963

.817

58.4

3558.711

62.3

4062

.180

59.9

9260.167

60.9

24

60.6

59Roberts

52.6

9252

.351

56.1

2153

.588

49.4

4647

.979

53.2

0451

.154

49.3

77

47.7

62

Level2

Canny

79.2

4179.417

80.7

6680.868

79.8

1179.977

80.1

9580.628

79.9

64

81.130

LoG

74.0

3473

.853

74.9

8874

.765

74.4

9874

.087

73.8

2673

.502

75.3

16

74.9

86Pre

witt

57.1

6456

.225

51.8

6251

.670

50.1

9851.235

47.0

2047.824

50.5

19

51.654

Sobel

57.1

8656

.503

51.5

9451

.833

50.4

0951.258

47.0

4047.927

50.5

45

51.554

Roberts

48.5

1645

.265

45.5

1146.339

42.0

7541

.858

37.1

9037.934

39.9

90

40.475

Level3

Canny

69.1

4873.049

66.3

0270.065

67.7

0471.391

66.0

9669.790

66.0

69

70.312

LoG

61.9

5463.395

51.6

1954.322

45.8

4048.129

41.8

2444.563

39.6

93

41.655

Pre

witt

48.6

0450.094

36.4

8739.421

32.0

2835.209

29.1

7632.407

29.6

50

33.184

Sobel

48.6

7050.230

36.4

0739.104

32.0

8035.073

29.3

0932.294

29.6

56

32.994

Roberts

41.7

2437

.448

29.3

6831.066

21.0

3821.889

19.9

5120.950

20.8

29

21.832

Tab

le7.

FoM

valu

esfo

ran

imag

ew

ith

ahig

hnum

ber

ofdet

ails

(HD

)


avelet

db2

db4

db6

db8

db10

Opera

tor

Old

New

Old

New

Old

New

Old

New

Old

New

Level1

Canny

28.6

9530.234

30.5

1928

.649

29.1

6430.704

28.5

2628.800

29.5

27

29.945

LoG

22.5

3222.923

22.7

9823.225

22.5

8921

.305

21.4

7321.741

22.5

73

23.038

Pre

witt

28.3

6726

.024

27.5

5326

.478

28.8

5628

.676

23.7

3926.379

30.7

06

28.4

26Sobel

28.7

9525

.315

27.6

6726

.757

29.5

3728

.484

24.1

1326.399

30.2

01

28.3

88Roberts

57.8

1364.519

50.5

4368.677

53.8

5767.983

61.2

4365.303

52.9

37

69.606

Level2

Canny

19.2

2221.983

16.3

2018.378

12.7

4214.538

11.6

6712.021

12.0

19

13.333

LoG

17.1

6518.843

15.3

4517.218

11.8

0313.387

12.8

5513.068

11.4

43

12.642

Pre

witt

18.3

8021.641

19.9

7825.675

19.8

9923.619

25.5

3521

.490

19.3

00

26.996

Sobel

17.9

1422.085

19.8

1123.516

19.5

8722.875

24.9

2221

.730

19.2

24

24.930

Roberts

21.2

2735.587

26.9

4841.347

32.9

2541.833

40.5

6047.205

38.1

56

48.936

Level3

Canny

6.04

59.491

6.35

610.141

5.28

610.217

5.54

99.375

5.9

09

10.356

LoG

7.35

810.470

8.71

711.731

7.60

011.502

8.70

210.541

48.6

46

52.246

Pre

witt

8.61

612.775

11.6

3015.895

11.2

5616.399

11.0

1016.723

12.0

19

17.248

Sobel

8.51

712.598

11.4

8514.844

11.1

3515.399

10.8

7115.795

12.0

77

16.171

Roberts

11.2

2119.060

13.1

0717.118

13.9

7821.112

17.2

1425.186

18.2

70

26.741

Tab

le8.

PR

valu

esfo

ran

imag

ew

ith

alo

wnum

ber

ofdet

ails

(LD

)


avelet

db2

db4

db6

db8

db10

Opera

tor

Old

New

Old

New

Old

New

Old

New

Old

New

Level1

Canny

23.3

5523

.137

23.7

9123

.282

23.6

0923.231

23.6

0323

.428

23.6

12

23.4

80LoG

15.2

4615.296

15.3

9915.421

15.3

5015.459

15.4

2615

.413

15.5

38

15.4

31Pre

witt

14.8

1414

.285

14.0

2414.098

14.4

8514

.477

13.9

2014.028

14.6

34

14.5

95Sobel

14.8

7214

.320

14.1

0814

.003

14.5

5814.568

13.8

8814.006

14.6

51

14.5

36Roberts

16.6

9416

.557

18.2

4518.317

18.3

0617

.373

18.8

8718

.219

19.5

95

18.4

54

Level2

Canny

20.9

0621.648

21.3

7622.659

21.1

6622.678

21.2

4622.690

21.3

87

22.407

LoG

13.5

3913

.402

13.0

2013.546

13.3

6613.549

13.2

3413.610

13.0

59

13.478

Pre

witt

12.8

8313.215

10.2

1711.158

9.52

511.262

9.40

411.097

9.7

81

11.356

Sobel

12.8

6513.208

10.1

7811.005

9.56

811.110

9.39

010.842

9.7

30

11.182

Roberts

9.01

39.132

9.33

712.206

9.36

911.179

9.16

710.777

9.3

62

10.936

Level3

Canny

11.4

2815.604

68.8

3573.034

13.6

6016.821

12.7

4916.686

12.7

76

16.643

LoG

7.45

49.010

6.24

07.788

4.80

66.272

4.41

05.796

4.1

04

5.568

Pre

witt

6.70

58.030

5.08

56.670

4.24

56.477

3.86

76.152

4.0

40

6.210

Sobel

6.70

07.825

5.08

86.452

4.23

76.091

3.87

05.821

4.0

40

5.867

Roberts

4.25

04.427

3.47

24.805

2.18

52.855

1.76

52.435

1.8

16

2.471

Tab

le9.

PR

valu

esfo

ran

imag

ew

ith

am

ediu

mnum

ber

ofdet

ails

(MD

)


avelet

db2

db4

db6

db8

db10

Opera

tor

Old

New

Old

New

Old

New

Old

New

Old

New

Level1

Canny

70.1

1171.230

69.1

2771.555

67.7

8770.466

68.0

5769.417

68.4

20

70.459

LoG

80.6

1280

.029

80.7

1380

.131

81.0

1680

.593

80.8

9480

.399

81.0

20

80.5

43Pre

witt

64.3

3863

.895

58.0

6358.180

62.1

6561

.852

59.8

0459.969

60.5

13

60.4

54Sobel

64.2

5963

.817

58.4

3558.711

62.3

4062

.180

59.9

9260.167

60.9

24

60.6

59Roberts

52.6

9252

.351

56.1

2153

.588

49.4

4647

.979

53.2

0451

.154

49.3

77

47.7

62

Level2

Canny

79.2

4179.417

80.7

6680.868

79.8

1179.977

80.1

9580.628

79.9

64

81.130

LoG

74.0

3473

.853

74.9

8874

.765

74.4

9874

.087

73.8

2673

.502

75.3

16

74.9

86Pre

witt

57.1

6456

.225

51.8

6251

.670

50.1

9851.235

47.0

2047.824

50.5

19

51.654

Sobel

57.1

8656

.503

51.9

5451

.833

50.4

0951.258

47.0

4047.927

50.5

45

51.554

Roberts

48.5

1645

.265

45.5

1146.339

42.0

7541

.858

37.1

9037.934

39.9

90

40.475

Level3

Canny

69.1

4873.049

66.3

0270.065

67.7

0471.391

66.0

9669.790

66.0

69

70.312

LoG

61.9

5463.395

51.6

1954.322

45.8

4048.129

41.8

2444.563

39.6

93

41.655

Pre

witt

48.6

0450.094

36.4

8739.421

32.0

2835.209

29.1

7632.407

29.6

50

33.184

Sobel

48.6

7050.230

36.4

0739.104

32.0

8035.073

29.3

0932.294

29.6

56

32.994

Roberts

41.7

2437.448

29.3

6831.066

21.0

3821.889

19.9

5120.950

20.8

29

21.832

Tab

le10

.P

Rva

lues

for

anim

age

wit

ha

hig

hnum

ber

ofdet

ails

(HD

)


4 CONCLUSIONS

This paper proposed a new approach to edge detection in the images on which thewavelet decomposition was applied to the third level. As mother wavelet, Daubechieswas used from the second to the tenth order. The analyzed images are categorizedinto three complexity criteria, so they consist of a small, medium and high numberof details. F measure, FoM, and PR were used for an objective measure. Theproposed approach provides significant improvements in edge detection for almostall operators (Canny, LoG, Prewitt, Sobel).

Depending on the number of details in the image, the decomposition level aswell as db wavelet, the improvements are different. With a small number of details,the greatest improvements were achieved with the Canny operator. Other oper-ators also achieved improvement but depending on the db wavelet order. Basedon the obtained results, in the image with a small number of details, it can beseen that best improvements are achieved in the third level using Laplacian oper-ators. In the image with the medium number of details, in the first level similarresults are generally obtained, while in the second and the third levels improvementis made using the proposed approach. For images with a high number of details,better or similar values are obtained using the proposed approach. What can beconcluded is that in the second level, the best values are obtained by gradient op-erators.

Considering that the compression ratio is higher of the image with a highernumber of details, based on this fact, it can be concluded that the detection willalso be poorer, and consequently there will be a lower F values, FoM values andPR values. Since the proposed approach is intended for systems where compressionis used, i.e. compressed image processing, it can be concluded that increasing thedegree of compression also provides a better difference, or better value using theproposed approach.

Today’s systems require image quality to be as good as possible, with as muchcompression as possible in order to process these images in real time, such as edgedetection, segmentation, streaming, streaming in systems using augmented reality,etc. The proposed approach can find many practical applications in all systemswhere real-time information needs to be processed, especially in television systems,but it also provides a good basis for the direction of future research related tocompression and edge detection.

Acknowledgment

This work was done within the research project of the Ministry of Science andTechnological Development of Serbia TR35026 and III47016.


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Vladimir Maksimovi�c received his B.Sc. and M.Sc. degrees inelectrical engineering from the Faculty of Technical Sciences inKosovska Mitrovica, University of Pristina, Serbia. He is Ph.D.candidate at the same faculty and his areas of research includeimage processing, telecommunications and multimedia systems.He has authored several scientific papers.

Branimir Jak�si�c received his B.Sc. and M.Sc. degrees in elec-trical engineering from the Faculty of Technical Sciences in Ko-sovska Mitrovica, University of Pristina, Serbia, and his Ph.D.degree in electrical engineering from the Faculty of ElectronicEngineering, University of Nis, Serbia in 2015. He is AssistantProfessor at the Faculty of Technical Sciences in Kosovska Mitro-vica. Areas of his research include telecommunications and mul-timedia systems. He has authored over 70 scientific papers onthe above subject.

Mile Petrovi�c is Full Professor at the Department of Elec-tronics and Telecommunications Engineering at the Faculty ofTechnical Sciences in Kosovska Mitrovica, Serbia. He has exten-sive experience in digital broadcasting systems and multimediaapplications, mobile technology and digital image processing. Heis the author of over 100 scientific peer-reviewed papers, initia-tor of a number of international Tempus projects in the countryand certified patents. He has participated in scientific researchprojects as well as in projects for the modernization and enhanc-ing quality of higher education. He is author of many textbooks

and scientific articles in the field of mobile radio and telecommunication networks.

Petar Spalevi�c received his B.Sc. degree from the Faculty ofElectronic Engineering, University of Pristina, in 1997 and hisM.Sc. and Ph.D. degrees from the Faculty of Electronic Engi-neering, University of Nis in 1999 and 2003, respectively. Heis Professor at the Faculty of Technical Sciences, Departmentof Telecommunications in Kosovska Mitrovica. His primary re-search interests are statistical communications theory, opticaland wireless communications, applied probability theory and op-timal receiver design.


Stefan Pani�c received his M.Sc. and Ph.D. degrees in electri-cal engineering from the Faculty of Electronic Engineering, Nis,Serbia, in 2007 and 2010, respectively. His research interestsin mobile and multi-channel communications include statisticalcharacterization and modelling of fading channels, performanceanalysis of diversity combining techniques, outage analysis ofmulti-user wireless systems subject to interference. Within dig-ital communication, his current research interests include theinformation theory, source and channel coding, and signal pro-cessing. He has published over 40 SCI indexed papers. Currently

he is Associated Professor at the Department of Informatics, Faculty of Natural Scienceand Mathematics, University of Pristina.

new approach to edge detection on different

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