image processing- edge detection
-
Upload
sarbjeet-singh -
Category
Technology
-
view
16.439 -
download
4
description
Transcript of image processing- edge detection
EDGE DETECTION
Presentation by Sarbjeet Singh(National Institute of Technical Teachers Training and research) Chandigarh
04/12/23 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
04/12/23 ECE - Sarbjeet Singh 3
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
04/12/23 ECE - Sarbjeet Singh 4
TYPES OF EDGES
Variation of Intensity / Gray Level Step Edge Ramp Edge Line Edge Roof Edge
04/12/23 ECE - Sarbjeet Singh 5
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
04/12/23 ECE - Sarbjeet Singh 6
Noisy Image
Example of Noisy Image
04/12/23 ECE - Sarbjeet Singh 7
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)
04/12/23 ECE - Sarbjeet Singh 8
04/12/23 ECE - Sarbjeet Singh 9
Gradient
For a continuous two dimensional function Gradient is defined as
y
fx
f
Gy
GxyxfG )],([
GyGxGyGxG 22
Gx
Gy1tan
04/12/23 ECE - Sarbjeet Singh 10
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
04/12/23 ECE - Sarbjeet Singh 11
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
04/12/23 ECE - Sarbjeet Singh 12
Roberts Operator - Example The output image
has been scaled by a factor of 5
Spurious dots indicate that the operator is susceptible to noise
04/12/23 ECE - Sarbjeet Singh 13
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
04/12/23 ECE - Sarbjeet Singh 14
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
04/12/23 ECE - Sarbjeet Singh 15
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
04/12/23 ECE - Sarbjeet Singh 16
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.
04/12/23 ECE - Sarbjeet Singh 17
Second Order Derivative Methods
Zero crossing of the second derivative of a function indicates the presence of a maxima
04/12/23 ECE - Sarbjeet Singh 18
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
04/12/23 ECE - Sarbjeet Singh 19
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
04/12/23 ECE - Sarbjeet Singh 20
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
04/12/23 ECE - Sarbjeet Singh 21
Laplacian of Gaussian - contd.
Also called the Mexican Hat operator
04/12/23 ECE - Sarbjeet Singh 22
Laplacian of Gaussian – contd. Mask
Discrete approximation to LoG function with Gaussian = 1.4
04/12/23 ECE - Sarbjeet Singh 23
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
04/12/23 ECE - Sarbjeet Singh 24
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
04/12/23 ECE - Sarbjeet Singh 25
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
04/12/23 ECE - Sarbjeet Singh 26
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
04/12/23 ECE - Sarbjeet Singh 27
First Criterion: Edge Detection
Response of filter to the edge:
RMS response of filter to noise :
First criterion: output Signal to Noise Ratio
04/12/23 ECE - Sarbjeet Singh 28
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:
04/12/23 ECE - Sarbjeet Singh 29
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
04/12/23 ECE - Sarbjeet Singh 30
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
04/12/23 ECE - Sarbjeet Singh 31
Thresholding
Broken edges due to fluctuation of operator output above and below the threshold – results in Streaking
Use double thresholding to eliminate streaking
04/12/23 ECE - Sarbjeet Singh 32
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
04/12/23 ECE - Sarbjeet Singh 33
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
04/12/23 ECE - Sarbjeet Singh 34
Implementation of Canny Edge Detector – contd.
Step 3 Find the edge direction
Step 4 Resolve edge direction
Gx
Gy1tan
04/12/23 ECE - Sarbjeet Singh 35
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
04/12/23 ECE - Sarbjeet Singh 36
Canny Edge Detector – contd.
Compare the results of Sobel and Canny
04/12/23 ECE - Sarbjeet Singh 37
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
04/12/23 ECE - Sarbjeet Singh 38
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
04/12/23 ECE - Sarbjeet Singh 39
Applications
Enhancement of noisy images – satellite images, x-rays, medical images like cat scans
Text detection Mapping of roads Video surveillance, etc.
04/12/23 ECE - Sarbjeet Singh 40
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
04/12/23 ECE - Sarbjeet Singh 41
Edge map of remote sensed image using Canny
04/12/23 ECE - Sarbjeet Singh 42
Thank You
04/12/23 ECE - Sarbjeet Singh 43
04/12/23 ECE - Sarbjeet Singh 44
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