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EDGE DETECTION

Presentation by Sarbjeet Singh

(National Institute of Technical Teachers Training and research) Chandigarh


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10/29/2014 ECE - Sarbjeet Singh 2

CONTENTS

Introduction Types of Edges Steps in Edge Detection Methods of Edge Detection

First Order Derivative Methods First Order Derivative Methods - Summary

Second Order Derivative Methods Second Order Derivative Methods - Summary

Optimal Edge Detectors Canny Edge Detection

Edge Detector Performance

Application areas


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INTRODUCTION

Edge - Area of significantchange in the imageintensity / contrast

Edge Detection

Locating areas withstrong intensity contrasts

Use of Edge Detection Extracting informationabout the image. E.g.location of objects

present in the image,their shape, size, imagesharpening andenhancement


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TYPES OF EDGES

Variation ofIntensity / GrayLevel

Step Edge

Ramp Edge

Line Edge

Roof Edge


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Steps in Edge Detection

Filtering Filter image to improveperformance of the Edge Detector wrt noise

Enhancement Emphasize pixels having

significant change in local intensity Detection Identify edges - thresholding

Localization Locate the edge accurately,estimate edge orientation


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Noisy Image

Example of Noisy Image


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METHODS OF EDGE DETECTION

First Order Derivative / Gradient Methods

Roberts Operator

Sobel Operator

Prewitt Operator

Second Order Derivative

Laplacian

Laplacian of Gaussian

Difference of Gaussian

Optimal Edge Detection

Canny Edge Detection


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First Derivative

At the point of greatestslope, the firstderivative has maximum

value E.g. For a Continuous 1-

dimensional function f(t)



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Gradient

For a continuous two dimensionalfunction Gradient is defined as

y

f

xf

Gy

GxyxfG )],([

GyGxGyGxG 22

Gx

Gy1tan


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Gradient

Approximation of Gradient for adiscrete two dimensional function

Convolution Mask

Gx=

Gy=

Differences are computed at theinterpolated points [i, j+1/2] and[i+1/2, j]

-1 1-1 1

],1[],[

],[]1,[

jifjifGy

jifjifGx

1 1

-1 -1

-1 1

1

-1


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Gradient Methods RobertsOperator

Provides an approximation to the gradient

Convolution Mask Gx=

Gy =

Differences are computed at the interpolated points [i+1/2,j+1/2] and not [i, j]

1 00 -1

0 -1

1 0

)1,(),1()1,1(),()],([ jifjifjifjifGyGxjifG


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Roberts Operator - Example

The output imagehas been scaled bya factor of 5

Spurious dotsindicate that theoperator issusceptible to

noise


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Gradient Methods Sobel Operator

The 3X3 convolution mask smoothes the image bysome amount , hence it is less susceptible to noise. Butit produces thicker edges. So edge localization is poor

Convolution Mask

Gx = Gy=

The differences are calculated at the center pixel of themask.

-1 0 1-2 0 2

-1 0 1

1 2 10 0 0

-1 -2 -1


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Sobel Operator - Example

Compare the output ofthe Sobel Operator withthat of the RobertsOperator: The spurious edges are

still present but theyare relatively lessintense compared togenuine lines

Roberts operator hasmissed a few edges

Sobel operator detectsthicker edges

Will become more clearwith the final demo

Outputs of Sobel (top) and Roberts operator


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Gradient Methods PrewittOperator

It is similar to the Sobel operator but uses slightlydifferent masks

Convolution Mask

Px=

Py=

-1 0 1-1 0 1

-1 0 1

1 1 1

0 0 0-1 -1 -1


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First Order Derivative Methods -Summary

Noise simple edge detectors are affectedby noise filters can be used to reducenoise

Edge Thickness Edge is several pixels

wide for Sobel operatoredge is not

localized properly Roberts operator is very sensitive to noise Sobel operator goes for averaging and

emphasizes on the pixel closer to thecenter of the mask. It is less affected bynoise and is one of the most popular EdgeDetectors.


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Second Order Derivative Methods

Zero crossing of the second derivativeof a function indicates the presence ofa maxima


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Second Order Derivative Methods -Laplacian

Defined as

Mask

Very susceptible to noise, filteringrequired, use Laplacian of Gaussian

0 1 01 -4 1

0 1 0


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Second Order Derivative Methods -Laplacian of Gaussian

Also called Marr-Hildreth EdgeDetector

Steps Smooth the image using Gaussian filter

Enhance the edges using Laplacianoperator

Zero crossings denote the edge location Use linear interpolation to determine the

sub-pixel location of the edge


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Laplacian of Gaussian contd.

Defined as

Greater the value of s, broader is the

Gaussian filter, more is the smoothing Too much smoothing may make the

detection of edges difficult


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Laplacian of Gaussian - contd.

Also called the Mexican Hat operator


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Laplacian of Gaussian contd.

Mask

Discrete approximation to LoG function with Gaussian = 1.4


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Second Order Derivative MethodsDifference of Gaussian - DoG

LoG requires large computation timefor a large edge detector mask

To reduce computationalrequirements, approximate the LoGby the difference of two LoG theDoG

2

2

)2

22(

2

1

)2

22(

22),(

22

21

ss

ssyxyx

eeyxDoG


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Difference of Gaussian contd.

Advantage of DoG

Close approximation of LoG

Less computation effort

Width of edge can be adjusted bychanging s1 and s2


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Second Order Derivative MethodsSummary

Second Order Derivative methodsespecially Laplacian, are verysensitive to noise

Probability of false and missing edgesremain

Localization is better than Gradient

Operators


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Optimal Edge Detector

Optimal edge detector depending on

Low error rate edges should not be missedand there must not be spurious responses

Localizationdistance between points marked

by the detector and the actual center of theedge should be minimum

Response Only one response to a single edge

One dimensional formulation Assume that 2D images have constant cross

section in some direction


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First Criterion: Edge Detection

Response of filter to the edge:

RMS response of filter to noise :

First criterion: output Signal to Noise

Ratio


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Second Criterion: Edge Localization

A measure that increases as thelocalization increases is needed

Reciprocal of RMS distance of themarked edge from center of true edgeis taken as the measure of localization

Localization is defined as:


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Third Criterion Elimination ofmultiple responses

In presence of noise several maxima aredetected it is difficult to separate noisefrom edge

We try to obtain an expression for thedistance between adjacent noise peaks

The mean distance between the adjacentmaxima in the output is twice the distance

between the adjacent zero crossings in thederivative of output operator


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Noise estimation

Important to estimate the amount of noisein the image to set thresholds

Noise component can be efficiently isolated

using Weiner Filteringrequires the

knowledge of the autocorrelation ofindividual components and their cross-correlation

Noise strength is estimated by GlobalHistogram Estimation


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Thresholding

Broken edges due to fluctuation ofoperator output above and below thethreshold results in Streaking

Use double thresholding to eliminatestreaking


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Two Dimensional Edge Detection

In two dimensions edge has both positionand direction

A 2-D mask is created by convolving alinear edge detection function aligned

normal to the edge direction with aprojection function parallel the edgedirection

Projection function is Gaussian with samedeviation as the detection function

The image is convolved with a symmetric2-D Gaussian and then differentiatednormal to the edge direction


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Implementation of Canny EdgeDetector

Step 1

Noise is filtered out usually a Gaussian filteris used

Width is chosen carefully Step 2

Edge strength is found out by taking thegradient of the image

A Roberts mask or a Sobel mask can be used

GyGxGyGxG 22


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Implementation of Canny EdgeDetector contd.

Step 3

Find the edge direction

Step 4

Resolve edge direction

Gx

Gy1tan


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Canny Edge Detector contd.

Step 5

Non-maxima suppression trace alongthe edge direction and suppress any

pixel value not considered to be an edge.Gives a thin line for edge

Step 6

Use double / hysterisis thresholding toeliminate streaking


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Canny Edge Detector contd.

Compare the results of Sobel andCanny


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Edge Detector Performance

Criteria

Probability of false edges

Probability of missing edges

Error in estimation of edge angle

Mean square distance of edge estimatefrom true edge

Tolerance to distorted edges and otherfeatures such as corners and junctions


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Figure of Merit

Basic errors in a Edge Detector

Missing Edges

Error in localizing

Classification of noise as Edge

IA: detected edges

II: ideal edges

d : distance between actual and ideal edges

a: penalty factor for displaced edges

IA

i iIA dIIFM

121

1

),max(

1

a


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Applications

Enhancement of noisy images satellite images, x-rays, medicalimages like cat scans

Text detection

Mapping of roads

Video surveillance, etc.


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Applications

Canny Edge Detector for RemoteSensing Images

Reasons to go for Canny Edge Detector

Remote sensed images are inherentlynoisy

Other edge detectors are very sensitiveto noise


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Edge map of remote sensed image using Canny


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Thank You



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References Machine Vision Ramesh Jain, Rangachar Kasturi, Brian G Schunck,

McGraw-Hill, 1995 INTRODUCTION TO COMPUTER VISION

AND IMAGE PROCESSING - by Luong Chi MaiDepartment of Pattern Recognition and Knowledge EngineeringInstitute of Information Technology, Hanoi, Vietnamhttp://www.netnam.vn/unescocourse/computervision/computer.htm

The Hypermedia Image Processing Reference -http://homepages.inf.ed.ac.uk/rbf/HIPR2/hipr_top.htm A Survey and Evaluation of Edge Detection Operators Application to

Medical Images Hanene Trichili, Mohamed-Salim Bouhlel, Nabil Derbel,Lotfi Kamoun, IEEE, 2002

Using The Canny Edge Detector for Feature Extraction and Enhancement ofRemote Sensing Images - Mohamed Ali David Clausi, Systems DesignEngineering, University of Waterloo, IEEE 2001

A Computational Approach to Edge DetectionJohn Canny, IEEE, 1986
http://www.netnam.vn/unescocourse/computervision/computer.htmhttp://www.netnam.vn/unescocourse/computervision/computer.htmhttp://www.netnam.vn/unescocourse/computervision/computer.htmhttp://homepages.inf.ed.ac.uk/rbf/HIPR2/hipr_top.htmhttp://homepages.inf.ed.ac.uk/rbf/HIPR2/hipr_top.htmhttp://homepages.inf.ed.ac.uk/rbf/HIPR2/hipr_top.htmhttp://www.netnam.vn/unescocourse/computervision/computer.htmmailto:[email protected]

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