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Gaussian Three-Dimensional SVM for Edge Detection Applications

Authors : Safa r I randous t -Pakchin - Aydin Ayanzadeh

Siamak Be ikzadeh

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

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

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

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

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

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

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

Proposed Method For Edge Detection

St

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

(1)

𝐺𝑎𝑢𝑠𝑠𝑖𝑎𝑛 𝐾𝑒𝑟𝑛𝑒𝑙=exp (1

−2𝜎2‖𝑥𝑖−𝑥 𝑗‖2) (2)

(4)

(3)

8

,…, )

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

Our Proposed kernel

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.

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

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

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.

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.

GAUSSIAN THREE-DIMENSIONAL SVM FOR EDGE DETECTION APPLICATIONS, SAFAR IRANDOUST-PAKCHIN, AYDIN AYANZADEH, SIAMAK BEIKZADEH 15

ConclusionAdvantage 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.

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