Performance Evaluation and Comparison of Various

8/3/2019 Performance Evaluation and Comparison of Various

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An edge is the boundary between anobject and the background, and

indicates the boundary betweenoverlapping objects.

Edges in images are areas with strong

intensity contrastsa jump in intensityfrom one pixel to the next.


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significantly reduces theamount of data

filters out useless information

preserves the importantstructural properties Useful in applications such as:

object detection and recognition

segmentation

tracking

Why edgedetection?

Refraction or poor focus

False edge detection

Missing true edges

Edge localization

High computational time

Problems due to noise

Why not:The

problems


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To do the comparison of various edgedetection techniques and analyze the

performance of the various techniques indifferent conditions


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PROBLEM:We have analyzed and did the visual comparison of the

most commonly used Gradient and Laplacian based EdgeDetection techniques for problems of inaccurate edgedetection, missing true edges,producing thin or thick lines and problems due to noise etc.The software is developed using MATLAB 7.6.0 (R2008a).


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The ability to measure gray-level transitionsin a meaningful way.

(R.C. Gonzales & R. E. WoodsDigitalImage Processing)


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IDEAL EDGE RAMP EDGE


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Gradient: The gradient method detects theedges by looking for the maximum andminimum in the first derivative of the image.

Laplacian: The Laplacian method searchesfor zero crossings in the second derivative ofthe image to find edges. An edge has the one-

dimensional shape of a ramp and calculatingthe derivative of the image can highlight itslocation.


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MARR HILDRETH EDGE DETECTOR CANNY EDGE DETECTOR

SOBEL EDGE DETECTOR

ROBERTS EDGE DETECTOR

PREWITT EDGE DETECTOR


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DetectedEdgeTRSH

x

yxI

,

x

yxI

,

TRSH

yxI ,

x x


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Original First Derivative

yxI , x

yxI

,

DetectedNotEdgeTRSHx

yxI

,

TRSH


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Gradient requires computing partialderivatives:

Since were dealing with digitalquantities , so we use a digital

approximation about a point :


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Cross gradient operators

Diagonal edge detection needs 2-D

mask*Gx = (z9-z5) Gy = (z8-z6)

0 0 0

0 -1 0

0 0 1

0 0 0

0 0 -1

0 1 0


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*Masks that are symmetric about thecentre point are more useful for

computing edge detection: smallest onebeing 3X3

They take into account nature of dataon opposite sides of the center pointand thus carry more informationregarding the direction of an edge.


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Uses 3X3 convolution masks, one estimatingthe gradient in x-direction (rows) and theother in the y-direction (columns).

These approximations are more accuratethan Roberts operators.

-1 -1 -1

0 0 0

1 1 1

-1 0 1

-1 0 1

-1 0 1

321987zzzzzzGx 741963 zzzzzzGy


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A slight variation in Prewitt operators, aweight of 2 in the center coefficient,

which provides image smoothing. Performs a 2-D spatial gradient

measurement on an image

Calculates the approximate absolutegradient magnitude at each point ininput image (which should be ingrayscale)


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321987

22 zzzzzzGx 741963 22 zzzzzzGy

Prewitt masks are simpler to implementthan these but Sobel masks have betternoise suppression, which makes thempreferable.*

-1 -2 -1

0 0 0

1 2 1

-1 0 1

-2 0 2

-1 0 1


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Prewitt

Sobel

0 1 1

-1 0 1

-1 -1 0

-1 -1 0

-1 0 1

0 1 1

0 1 2

-1 0 1

-2 -1 0

-2 -1 0

-1 0 1

0 1 2


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Coefficients of all the masks sum to zero

thus giving a response of zero in uniformregions(areas of constant intensity)

Computing the magnitude requiressquares and square roots calculationswhich are pose computational burdenso an approach which is frequently usedto approximate grad values is

It still preserves relative changes inintensity levels


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The Laplacian of an image highlightsregions of rapid intensity change and istherefore often used for edge detection.

Its often applied to an image that has firstbeen smoothed with somethingapproximating a Gaussian Smoothing filterin order to reduce its sensitivity to noise*.

It normally takes a single gray level imageas input and produces another gray levelimage as output.


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Gradientbased Operator with use ofLaplacian to take 2nd derivative.

Step difference will be represented by azero crossing in the 2nd derivative asshown earlier.


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1. Smooth the image using a Gaussian. Thissmoothing reduces the amount of error

found due to noise.2. Apply a two dimensional Laplacian to

the image:

This operation is the equivalent of taking the secondderivative of the image.


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This Laplacian will be rotation invariant and is oftencalled the Mexican Hat operator because of itsshape.

3. LoopthroughLaplacianand look for sign changes.If there is a sign change and the slope across this signchange is greater than some threshold, mark thispixel as an edge.


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Since both the Gaussian and theLaplacian kernels are usually much

smaller than the image, this methodusually requires far fewer arithmeticoperations.

The LoG (Laplacian of Gaussian)

kernel can be pre-calculated inadvance so only one convolution needsto be performed at run-time on theimage.


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Created by JohnCanny for his

Masters thesis atMIT in 1983 [2], andstill outperformsmany of the newer

algorithms thathave beendeveloped.


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Low error rate: It is important that edgesoccurring in images should not be

missed and that there be no responsesto non-edges.

The second criterion is that the edgepoints be well localized.*

A third criterion is to have only oneresponse to a single edge*.


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STEP-1. Smooth the image with a twodimensional Gaussian. In most cases thecomputation of a two dimensionalGaussian is costly, so it is approximatedby two one dimensional Gaussians*, onein the x-direction and the other in the y-direction.


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2. Take the gradient of the image. Thisshows changes in intensity, and highlightsregions with high spatial derivatives,which indicate the presence ofedges.*Calculate the approx. magnitudeor edge strength:

The direction is computed:

=arctan(gy/gx)

{Exception for gx=0 case:

=0 if gy=0o & =90oif gy0}


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Next comes resolving the edgeorientation into one of the four possible

direction in a matrix:the edge orientation has to be resolvedinto one of these four directionsdepending on which direction it is closestto (e.g. if the orientation angle is foundto be 3o, make it 0o).

Color range & setvalue

Orientation

Yellow - 0o 0o to 22.5o &157.5o to 180o

Green45o 22.5o to 67.5o

Blue90o 67.5o to 112.5o

Red135o 112.5o to 157.5o


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3. Non maximal suppression: Edges willoccur at points the where the gradient is

at a maximum. Therefore, all points notat a maximum should be suppressed.

Trace along the edge in the edgedirection and suppress any pixel value(set it equal to 0) that is not consideredto be an edge.

This will give a thin line in the outputimage.


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Image File

MATLAB

Display

EdgeDetection


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Threshold :specifies the sensitivitythreshold for the Laplacian of Gaussian

method. Sigma: is the standard deviation of the

LoG filter. The default sigma is 2; the sizeof the filter is nXn, where n =

ceil(sigma*3)*2+1.


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Threshold: specifies sensitivity thresholds forthe Canny method. thresh is a 2-elementvector in which the 1is the low threshold,

and the 2 is the high threshold. If youspecify a scalar forthresh, this value is usedfor the high threshold and 0.4*thresh is usedfor the low threshold.

Sigma: is the standard deviation of theGaussian filter. The default sigma is 1; thesize of the filter is chosen automatically,based on sigma.


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One test image was artificial and theother was a real world photograph.

All color images were converted tograyscale using MatlabsRBG2GRAYfunction.

Various threshold, sigma, slope, etc.values were chosen by hand.

High threshold for Canny = 0.15 andlower threshold=0.4*0.15


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Edge detection of all five types wasperformed on wheel.jpg. Canny yielded thebest results.

Canny yields thin lines for its edges by usingnon-maximal suppression. Canny alsoutilizes hysteresis with thresholding.

Second order derivative tests yield better

results than first order derivatives If hysteresis is used with LoG operator, results

would be close to Canny method. edge_detection1.m
http://edge_detection1.m/http://edge_detection1.m/


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for Marr Hildreth Operator withthreshold=0: If a threshold of 0 is

specified, the output image has closedcontours, because it includes all the zerocrossings in the input image.

Cannys method is still preferred since it

produces single pixel thick, continuousedges.

edge_detection2.m


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Motion blur was applied to wheel.jpg

Four edge detection methods: Prewitt,

Sobel, Roberts and Canny were utilized.

No method appeared to be useful for

real world applications. However, Cannyproduced the best the results out of theset.

edge_detection3.m


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Gaussian blur was applied to wheel.jpg

The edge detection methods previously

used were utilized again on this new image. No method appeared to be useful for real

world applications. This was expected asGaussian noise corrupts edges and image

detail making it difficult to distinguish clearregions in an image.

edge_detection4.m


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Gaussian blur was applied to wheel.jpg. Then,a 3x3 average filter was applied to this image.

No method appeared to be useful for realworld applications.

However, Prewitt and Sobel were the mostaffective out of the set. This was because thesefilters have a larger mask size than Roberts andthus can show gradient information over a

larger area. This is useful because image averaging spreads

each pixels information over an area largerthan one pixel, in this case a 3x3 area.

edge_detection5.m


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We studied Canny, Marr Hildreth, Roberts, Sobel,and Prewitt edge detection masks.

Noise can affect the results of these edge detection

algorithms. In environments where edge detection is used,motion blur is often a problem. For non noisy images, Canny appeared to work the best. In noisy environments, Prewitt or Sobel yield best results

after an average filter is applied. However, these resultsappeared to not be very useful in real-world applications.

In motion blurry environments, Canny seemed to be themost affective of the four filters. However, the results itproduced would be hard to utilize in a real worldenvironment.


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Canny algorithm is adaptable to various environments- Real time implementations in DSPs or FPGAs- Fast embedded PCs

Edge detection algorithms have been modified in

many ways to solve multiple problems like:

- Feature extraction: chin contour estimation.A modified canny edge detector to detect the

potential chin edges, that is edges connectedtogether to form a continuous form.- Removing facial blemishes.

The program would remove them and fill them in witha value that would render the removed blemish

undetectable to the human eye


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As a conclusion, we usually use the edge

detectors in some of these fields, which

are highly interrelated : Computer vision

Digital image processing

Feature extraction Edge detection

Scale space


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[1] Canny, John, "A Computational Approach to EdgeDetection," IEEE Transactions on Pattern Analysis andMachine Intelligence,Vol. PAMI-8, No. 6, 1986, pp. 679-698.

[2] Lim, Jae S., Two-Dimensional Signal and Image Processing,Englewood Cliffs, NJ, Prentice Hall, 1990, pp. 478-488.

[3] Parker, James R., Algorithms for Image Processing andComputer Vision, New York, John Wiley & Sons, Inc., 1997,pp. 23-29.

[4] Gonzalez R.C., Woods R.E., Digital Image Processing, ThirdEdition, Prentice Hall, 2009.

[5] W. E. Grimson and E. C. Hildreth. Comments on Digitalstep edges from zero crossings of second directionalderivatives. IEEE Trans. Pattern Anal. Machine Intell., vol.PAMI-7, no. 1, pp. 121-129, 1985


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[6] Nadernejad E., Edge Detection Techniques:Evaluations and Comparisons, Applied MathematicalSciences, Vol. 2, 2008, no. 31, 15071520

[7] R. Owens, "Lecture 6", Computer Vision IT412,10/29/1997.http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/OWENS/LECT6/node2.html

[8] S. Price, "Edges: The Canny Edge Detector", July 4, 1996.http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/MARBLE/low/edges/canny.html

[9] Seventh International Conference onControl,Automation, Robotics and Vision(ICARCV02),Dec 2002, Singapore. Chin ContourEstimation Using Modified Canny Edge Detector.
http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/OWENS/LECT6/node2.htmlhttp://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/OWENS/LECT6/node2.htmlhttp://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/MARBLE/low/edges/canny.htmlhttp://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/MARBLE/low/edges/canny.htmlhttp://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/MARBLE/low/edges/canny.htmlhttp://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/MARBLE/low/edges/canny.htmlhttp://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/OWENS/LECT6/node2.htmlhttp://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/OWENS/LECT6/node2.html


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Performance Evaluation and Comparison of Various

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