this presentation file lectured in international conference in new research of Electrical and engineering and computer science. Abstract This paper presents a novel and uniform algorithm for edge detection based on SVM (support vector machine) with Three-dimensional Gaussian radial basis function with kernel. Because of disadvantages in traditional edge detection such as inaccurate edge location, rough edge and careless on detect soft edge. The experimental results indicate how the SVM can detect edge in efficient way. The performance of the proposed algorithm is compared with existing methods, including Sobel and canny detectors. The results shows that this method is better than classical algorithm such as canny and Sobel detector.

1. Gaussian Three-Dimensional SVM for Edge
Detection Applications
Authors: Safar Irandoust-Pakchin - Aydin Ayanzadeh
Siamak Beikzadeh
Computer Science Department, Faculty of Mathematical Sciences,
University Of Tabriz, Iran
GAUSSIAN THREE-DIMENSIONAL SVM FOR EDGE DETECTION APPLICATIONS SAFAR IRANDOUST-PAKCHIN, AYDIN AYANZADEH, SIAMAK BEIKZADEH 1

2. Outline
 Introduction
 Use Of Edge Detection
 Edge Detection Methods
 What Is the SVM?
 Connecting Between Edge and SVM
 Proposed Method For Edge Detection
 Result of Experiments
 Conclusion
GAUSSIAN THREE-DIMENSIONAL SVM FOR EDGE DETECTION APPLICATIONS SAFAR IRANDOUST-PAKCHIN, AYDIN AYANZADEH, SIAMAK BEIKZADEH 2

3. Introduction
 Edge: Area of significant change in the image
intensity, contrast
 Edge Detection: Locating areas with strong
intensity contrasts.
GAUSSIAN THREE-DIMENSIONAL SVM FOR EDGE DETECTION APPLICATIONS, SAFAR IRANDOUST-PAKCHIN, AYDIN AYANZADEH, SIAMAK BEIKZADEH 3

4. Use of Edge Detection
 Extracting information about the image: location of
objects present in the image, their shape, size, image
sharpening and enhancement
 Detect of discontinuities in depth
 Detect of discontinuities in surface orientation
 Detect of changes in material properties
 Detect of variations in scene illumination
GAUSSIAN THREE-DIMENSIONAL SVM FOR EDGE DETECTION APPLICATIONS SAFAR IRANDOUST-PAKCHIN, AYDIN AYANZADEH, SIAMAK BEIKZADEH 4

5. Methods Of Edge Detection
 First Order Derivative
 Roberts Operator
 Sobel Operator
 Prewitt Operator
 Second Order Derivative
 Laplacian
 Laplacian of Gaussian
 Difference of Gaussian
 Optimal Edge Detection
 Canny Edge Detection
GAUSSIAN THREE-DIMENSIONAL SVM FOR EDGE DETECTION APPLICATIONS SAFAR IRANDOUST-PAKCHIN, AYDIN AYANZADEH, SIAMAK BEIKZADEH 5

6. What Is the SVM?
GAUSSIAN THREE-DIMENSIONAL SVM FOR EDGE DETECTION APPLICATIONS SAFAR IRANDOUST-PAKCHIN, AYDIN AYANZADEH, SIAMAK BEIKZADEH 6
 Support vectors in non-separable classification
 Support vectors in nonlinear classification
SV in non separable classificationSV in nonlinear classification

7. Connecting Between Edge and SVM
 The image used to train the SVM classify
into two Zone:
 Dark Zone
 Bright Zone
 Our Proposed method trained edges in
three mode:
 Vertical Edge
 Horizontal Edge
 Diagonal Edge
GAUSSIAN THREE-DIMENSIONAL SVM FOR EDGE DETECTION APPLICATIONS SAFAR IRANDOUST-PAKCHIN, AYDIN AYANZADEH, SIAMAK BEIKZADEH 7
Vertical Edge
Diagonal Edge Horizontal Edge

8. Proposed Method For Edge Detection
min
1
2
𝛼 𝑇
𝐻𝛼 + 𝑓 𝑇
𝛼
St 𝑖 𝛼𝑖 𝑦𝑖
◦ 𝛼𝑖 ≥
GAUSSIAN THREE-DIMENSIONAL SVM FOR EDGE DETECTION APPLICATIONS SAFAR IRANDOUST-PAKCHIN, AYDIN AYANZADEH, SIAMAK BEIKZADEH
(1)
𝐺𝑎𝑢𝑠𝑠𝑖𝑎𝑛 𝐾𝑒𝑟𝑛𝑒𝑙 = exp(
1
−2𝜎2 𝑥𝑖 − 𝑥𝑗
2
) (2)
𝐻𝑖𝑗 = 𝑦𝑖. 𝑦𝑗. 𝑥𝑖
𝑇
. 𝑥𝑗 ⟶ 𝐻 = 𝑦𝑖. 𝑦𝑗. Ker (𝑥𝑖, 𝑥𝑗)
𝐻 = 𝑦𝑖 𝑦𝑗 𝑦𝑧 Ker (𝑥𝑖, 𝑥𝑗, 𝑥 𝑧) (4)
(3)
8

9. 𝑘(𝑥1, 𝑥2,…, 𝑥 𝑛)
𝒙 = 𝒊=𝟏
𝒏
𝒙 𝒊
𝒏
𝒚 = 𝒊=𝟏
𝒏
𝒚 𝒊
𝒏
𝒛 = 𝒊=𝟏
𝒏
𝒛𝒊
𝒏
𝑹𝒂𝒅𝒊𝒖𝒔 𝑺𝒒𝒖𝒂𝒓𝒆 = (𝑿 − 𝒙) 𝟐
+ (𝒀 − 𝒚) 𝟐
+(𝒁 − 𝒛) 𝟐
GAUSSIAN THREE-DIMENSIONAL SVM FOR EDGE DETECTION APPLICATIONS SAFAR IRANDOUST-PAKCHIN, AYDIN AYANZADEH, SIAMAK BEIKZADEH
Proposed Method For Edge Detection(continue)
X, Y and Z is Center Of Gravity (COG)
distance from vector to COG as Radius square
9
𝐾𝑒𝑟 = exp(
1
2𝜎2
𝑅𝑎𝑑𝑖𝑢𝑠 𝑆𝑞𝑢𝑎𝑟𝑒) Our Proposed kernel

10. Result of Experiments
SVM classification with propose method in
optimization mode with c=10 and σ =0.6
GAUSSIAN THREE-DIMENSIONAL SVM FOR EDGE DETECTION APPLICATIONS SAFAR IRANDOUST-PAKCHIN, AYDIN AYANZADEH, SIAMAK BEIKZADEH 10
 We set the optimize value in our experiment
and obtain an efficient results in simulation
according to below Fig.

11. GAUSSIAN THREE-DIMENSIONAL SVM FOR EDGE DETECTION APPLICATIONS SAFAR IRANDOUST-PAKCHIN, AYDIN AYANZADEH, SIAMAK BEIKZADEH 11
Result Of Experiments (continue)
We explain two classifier to clarify
our work:
 Sphere Classifier
 Circle Classifier
Sphere Classifier Circle Classifier

12. Result of Experiments (Continue)
Grayscale Image
Sobel
Canny
Proposed Method
GAUSSIAN THREE-DIMENSIONAL SVM FOR EDGE DETECTION APPLICATIONS, SAFAR IRANDOUST-PAKCHIN, AYDIN AYANZADEH, SIAMAK BEIKZADEH 12
 Advantage of Proposed Method
 SVM has higher classification accuracy
in Edge Detection
 More sensitive in detecting
 More fine and fewer spurious
structures than Sobel and Canny
detectors

13. Result of Experiments (Continue)
GAUSSIAN THREE-DIMENSIONAL SVM FOR EDGE DETECTION APPLICATIONS SAFAR IRANDOUST-PAKCHIN, AYDIN AYANZADEH, SIAMAK BEIKZADEH 13
Grayscale Image
Sobel
Canny
Proposed Method
SVM is not perfect in the following picture for
this reason:
 SVM has same performance in the pictures
that has more detail. So it’s not prefer to
used in high particularity pictures.

14. Tabel1. The statistics of the process time for different edge detectors
Tested image Proposed Method(s) Canny(s) Sobel(s)
House 0.83 0.94 0.19
Tire 0.71 0.87 0.22
Cameraman 1.02 1.22 0.27
Result of Experiments (Continue)
GAUSSIAN THREE-DIMENSIONAL SVM FOR EDGE DETECTION APPLICATIONS SAFAR IRANDOUST-PAKCHIN, AYDIN AYANZADEH, SIAMAK BEIKZADEH 14
Result of elapse time in our
experiment clarify that :
 SVM is faster than Canny in elapse
time of the detect edges.
 But SVM is so slower than Sobel
method for simplicity of this
classical method in detecting
the edge.

15. GAUSSIAN THREE-DIMENSIONAL SVM FOR EDGE DETECTION APPLICATIONS, SAFAR IRANDOUST-PAKCHIN, AYDIN AYANZADEH, SIAMAK BEIKZADEH 15
Conclusion
Advantage of proposed method :
 It is more accurate than other method in detect of edge location.
 Faster than other classical method such as canny but so slower than Sobel method.
 Detect edges more fine and fewer spurious structures than canny detector.
 Did not create excessive edge in some zone of the edges.

16. 16GAUSSIAN THREE-DIMENSIONAL SVM FOR EDGE DETECTION APPLICATIONS , SAFAR IRANDOUST-PAKCHIN, AYDIN AYANZADEH, SIAMAK BEIKZADEH