image processing- edge detection

EDGE DETECTION

Presentation by Sarbjeet Singh(National Institute of Technical Teachers Training and research) Chandigarh

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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 significant change in the image intensity / contrast

Edge Detection – Locating areas with strong intensity contrasts

Use of Edge Detection – Extracting information about the image. E.g. location of objects present in the image, their shape, size, image sharpening and enhancement

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TYPES OF EDGES

Variation of Intensity / Gray Level Step Edge Ramp Edge Line Edge Roof Edge

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Steps in Edge Detection Filtering – Filter image to improve

performance 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

First Derivative• At the point of greatest

slope, the first derivative has maximum value – E.g. For a Continuous 1-

dimensional function f(t)

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Gradient

For a continuous two dimensional function Gradient is defined as

y

fx

f

Gy

GxyxfG )],([

GyGxGyGxG 22

Gx

Gy1tan

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Gradient Approximation of Gradient for a

discrete two dimensional function Convolution Mask

Gx=

Gy =

Differences are computed at the interpolated 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 – Roberts Operator

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 0

0 -1

0 -1

1 0

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

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Roberts Operator - Example The output image

has been scaled by a factor of 5

Spurious dots indicate that the operator is susceptible to noise

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Gradient Methods – Sobel Operator

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

Convolution Mask

Gx = Gy=

The differences are calculated at the center pixel of the mask.

-1 0 1

-2 0 2

-1 0 1

1 2 1

0 0 0

-1 -2 -1

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Sobel Operator - Example

Compare the output of the Sobel Operator with that of the Roberts Operator: The spurious edges are

still present but they are relatively less intense compared to genuine lines

Roberts operator has missed a few edges

Sobel operator detects thicker edges

Will become more clear with the final demo

Outputs of Sobel (top) and Roberts operator

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Gradient Methods – Prewitt Operator It is similar to the Sobel operator but uses slightly

different 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 affected

by noise – filters can be used to reduce noise

Edge Thickness – Edge is several pixels wide for Sobel operator– edge is not localized properly

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

emphasizes on the pixel closer to the center of the mask. It is less affected by noise and is one of the most popular Edge Detectors.

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Second Order Derivative Methods

Zero crossing of the second derivative of a function indicates the presence of a maxima

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Second Order Derivative Methods - Laplacian

Defined as

Mask

Very susceptible to noise, filtering required, use Laplacian of Gaussian

0 1 0

1 -4 1

0 1 0

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Second Order Derivative Methods - Laplacian of Gaussian

Also called Marr-Hildreth Edge Detector

Steps Smooth the image using Gaussian filter Enhance the edges using Laplacian

operator 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 , 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 Methods - Difference of Gaussian - DoG

LoG requires large computation time for a large edge detector mask

To reduce computational requirements, approximate the LoG by the difference of two LoG – the DoG

22

)2

22(

21

)2

22(

22),(

22

21

yxyx

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 by

changing 1 and 2

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Second Order Derivative Methods - Summary

Second Order Derivative methods especially Laplacian, are very sensitive to noise

Probability of false and missing edges remain

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 missed and there must not be spurious responses

Localization – distance between points marked by the detector and the actual center of the edge 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 the localization increases is needed

Reciprocal of RMS distance of the marked edge from center of true edge is taken as the measure of localization

Localization is defined as:

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Third Criterion – Elimination of multiple responses

In presence of noise several maxima are detected – it is difficult to separate noise from edge

We try to obtain an expression for the distance between adjacent noise peaks

The mean distance between the adjacent maxima in the output is twice the distance between the adjacent zero crossings in the derivative of output operator

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Noise estimation Important to estimate the amount of noise

in the image to set thresholds Noise component can be efficiently isolated

using Weiner Filtering – requires the knowledge of the autocorrelation of individual components and their cross-correlation

Noise strength is estimated by Global Histogram Estimation

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Thresholding

Broken edges due to fluctuation of operator output above and below the threshold – results in Streaking

Use double thresholding to eliminate streaking

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Two Dimensional Edge Detection In two dimensions edge has both position

and direction A 2-D mask is created by convolving a

linear edge detection function aligned normal to the edge direction with a projection function parallel the edge direction

Projection function is Gaussian with same deviation as the detection function

The image is convolved with a symmetric 2-D Gaussian and then differentiated normal to the edge direction

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Implementation of Canny Edge Detector

Step 1 Noise is filtered out – usually a Gaussian filter is

used Width is chosen carefully

Step 2 Edge strength is found out by taking the

gradient of the image A Roberts mask or a Sobel mask can be used

GyGxGyGxG 22

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Implementation of Canny Edge Detector – 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 along

the 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 to

eliminate streaking

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Canny Edge Detector – contd.

Compare the results of Sobel and Canny

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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 estimate

from true edge Tolerance to distorted edges and other

features 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 : penalty factor for displaced edges

IA

i iIA dIIFM

121

1

),max(

1

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Applications

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

Text detection Mapping of roads Video surveillance, etc.

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Applications

Canny Edge Detector for Remote Sensing Images Reasons to go for Canny Edge Detector –

Remote sensed images are inherently noisy

Other edge detectors are very sensitive to 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 of Remote Sensing Images - Mohamed Ali David Clausi, Systems Design Engineering, University of Waterloo, IEEE 2001

A Computational Approach to Edge Detection – John Canny, IEEE, 1986