Study And Comparison Of Various Techniques Of Image Edge .

Gurjeet Singh et al Int. Journal of Engineering Research and ApplicationsISSN : 2248-9622, Vol. 4, Issue 3( Version 1), March 2014, pp.908-912RESEARCH ARTICLEwww.ijera.comOPEN ACCESSStudy and Comparison of Various Techniques of Image EdgeDetectionGurjeet Singh*, Er. Harjinder singh***(Department of Electronics and Communication Engineering, Punjabi University, Patiala, Punjab, India.)** (Department of Electronics and Communication Engineering, Punjabi University, Patiala, Punjab, India.)ABSTRACTAn edge may be defined as a set of connected pixels that forms a boundary between two disjoints regions.Image Edge detection reduces the amount of data and filters out useless information, while preserving theimportant structural properties in an image. Edge detection plays an important role in digital image processingand practical aspects of our daily life. In this paper we studied various edge detection techniques as Prewitt,Robert, Sobel, LoG and Canny operators. On comparing them we conclude that canny edge detector performsbetter than all other edge detectors on various aspects such as it is adaptive in nature, performs better for noisyimage, gives sharp edges, low probability of detecting false edges.Keywords – Canny detector, edge, edge detector, Prewitt operator, Roberts operator, Sobal opertorI. INTRODUCTIONEdge detection is a basic tool used in imageprocessing study, for feature detection and extraction,which aim to identify points in a image wherebrightness of digital image changes sharply and finddiscontinuities. The purpose of image edge detectionis significantly reducing the amount of data in animage data and preserves the structural properties forimage processing. Edge detection is difficult to applyin noisy images, since both the noise and edgescontain high-frequency content. Attempts to reducethe noise from image result in blurred and distortededges. Operators used on noisy images are typicallymuch larger in scope, so they can enough data todiscount localized noisy image pixels. Therefore, theobjective is to compare various edge detectiontechniques and analyze the performance in terms ofexamples.II.THEORETICAL CONCEPTS:There are so many ways to perform edgedetection. However, different methods of edgedetection may be grouped into two categories:2.1 First Order Derivative based Edge Detection(Gradient method):It is based on the use of a first order derivative orcan say gradient based. The magnitude of gradientcomputed gives edge strength and the gradientdirection that is always perpendicular to the directionof image edge. If I (i , j) be the input image, thenimage gradient is calculated by following formula; I (i, j) iWhere: I (i, j)is the gradient in i direction. i I (i, j)is the gradient in j direction. jThe gradient magnitude can be calculated by theformula:G Gi 2 Gj 22.2 Second Order Derivative Based EdgeDetection (Laplacian based Edge Detection):This method search for zero crossings in thesecond derivative of the image to find out edges. Animage edge has the one-dimensional shape of a rampand find out the derivative of the image can highlightits location. This method is characteristic of the“gradient filter” family of edge detection filters. Apixel location is only declared an edge location, if thevalue of its gradient exceeds some threshold. Asmentioned earlier, edges have higher pixel intensityvalues than those are surrounding it. So once athreshold is set, the gradient value with the thresholdvalue can be compared and an edges can be detectedwhenever the threshold is exceeded. Furthermore,when the first derivative is at a maximum peak, thesecond derivative is zero. As a result, anotheralternative to finding the location of an image edge isto locate zeros in the second derivative of image. I (i, j) I (i, j) j i jwww.ijera.com908 P a g e

Gurjeet Singh et al Int. Journal of Engineering Research and ApplicationsISSN : 2248-9622, Vol. 4, Issue 3( Version 1), March 2014, pp.908-912www.ijera.com2.2 Sobal Operator:(A) ideal step edge, (b) first order derivation and (c)second order derivation.Thisapproach uses zero-crossing operator which acts bylocating zeros of the second derivatives of image I(i,j). The differential operator is used in the so-calledzero-crossing edge detectors, 2 I 2 I 2 I i 2 j 2Thresholding allocates a range of pixel values toobject of interest. It works best with greyscale imagesthat utilize the whole range of greyscale. For theimage I(i,j), the threshold image g(i, j) is defined as,g (i, j) 1 if I i, j T0 if I i, j TSobel operator is a discrete differentiationoperator used to calculate an approximation of thegradient of an image intensity function for edgedetection. At each pixel of an image, it gives eitherthe corresponding gradient vector or normal to thevector. this convolves the input image with kerneland computes the gradient magnitude and direction.It uses following 3x3 two kernels, 1 1 2 1 and D 2Di 000 j 1 1 21 1 2 1 000As compared to Roberts operator have slowcomputation ability but as it has large kernel so it isless sensitive to noise as compared to Robertsoperator. As having larger mask, errors due to noiseare reduced by local averaging within theneighborhood of the mask.Flow chart of general algorithm for classicaloperatorsSTARTWhere T is the threshold value.Read the image and convolve with filterIII.EDGE DETECTION TECHNIQUESRobert, Sobel, Prewitt are classified asclassical operators which are simple and easy tooperate but highly sensitive to noise. Classicaloperators and canny operator are under the categoryof first order derivative based edge detection(Gradient method). Marr-Hildreth edge detector is agradient based operator which uses the Laplacian totake the second derivative of an image.Convolve the resultant image withchosen mask in i-axisConvolve the resultant image withchosen mask in j-axisSet the threshold value T3.1 Roberts Operator:It is a gradient based operator. It computes thesum of the squares of the difference betweendiagonally adjacent image pixels through discretedifferentiation and then calculate approximategradient of an image. The input image is convolvedwith default kernels of operator and gradientmagnitude and directions are computed. It usesfollowing 2 x2 two kernels, 0 1 0 andDj Di 1 0 1 1 0 The advantage of this operator is simplicity buthaving small kernel it is highly sensitive to noise andnot much compatible with today‟s technology.www.ijera.comFor a pixel say M(i,j)NoCompute the gradient magnitude say GIs G TConsiderthe nextneighborpixel.Mark pixel as an „edge‟END909 P a g e

Gurjeet Singh et al Int. Journal of Engineering Research and ApplicationsISSN : 2248-9622, Vol. 4, Issue 3( Version 1), March 2014, pp.908-912STEP II: Finding gradients2.3 Prewitt Operator:The function of Prewitt edge detector is almostsame as of sobel detector but have different kernels: 1 1 1 Di 0 0 0 and 1 1 1 www.ijera.com 1 0 1 D j 1 0 1 1 0 1 Prewitt edge operator gives better performancethan that of Sobel operator and Roberts operator.3.4 Canny Operator:Canny edge detector is a advanced algorithmderived from the previous work of Marr and Hildreth.It is an optimal edge detection technique as providegood results in detection, in clear response and inlocalization. It is widely used in current imageprocessing techniques used in everywhere with furtherimprovements.In this step we detect the edges where the changein greyscale intensity is maximum. Required areas aredetermined with the help of gradient of an image.Generally, Sobel operator is used to determine thegradient at each pixel of smoothed image. Sobeloperators in i and j directions are given below, 1 2 1 1 0 1 and D 0 0 0 Di 2 0 2 j 1 2 1 1 0 1 These sobel masks are convolved with smoothedimage and gives gradients in i and j directions.Gi Di * F(i, j) and G j D j * F(i, j)Therefore edge strength or magnitude of gradientof a pixel is given by,G Gi 2 G j 2Flow chart of canny edge detection algorithmThe direction of gradient is given by,START: Read the input image. Gj Gi arctan SMOOTHING: Removing noise by Gaussian filter.COMPUTE GRADIENTS: Edge should bemarked where the gradients of the image has large.Gi and G j are the gradients in the i and jdirections respectively.STEP III: Non maximum suppressions:NON MAXIMUM SUPRESSION: Only localmaxima should be marked as edge.Non maximum suppression is carried out topreserves all local maxima in gradient image, anddeleting everything else, this results in thin edges. Fora pixel M (i, j):THRESHOLDING: Final edges are determined bysuppressing all not connected edges to strong one. Firstly round the gradient direction nearly45 , then compare the gradient magnitude of thepixels in positive and negative gradient directions i.eif gradient direction is east then compare gradient ofthe pixel with west direction say E (i, j) and W (i, j)respectively.END: Input image resulted into edge extractedimage.Canny edge detection algorithmSTEP I: Noise reduction by smoothingNoise contained image is smoothed by convolvingthe input image I (i, j) with Gaussian filter G.Mathematically, the smooth resultant image is givenby,F (i, j) G*I(i, j)Prewitt operators are simpler to operator ascompared to sobel operator but more sensitive tonoise. If the edge strength of image pixel M (i, j) islarger than that of E (i, j) and W (i, j), then preservesthe value of gradient and mark M (i, j) as edge pixel,if not then suppressed.STEP IV: Hysteresis thresholding:The output of non-maxima suppression stillcontains the local maxima created by noise in image.Instead choosing a single threshold, for avoiding theproblem of streaking two thresholds t high and tlow areused.For a pixel M(i, j) having gradient magnitude Gfollowing conditions exists to detect pixel as edge:www.ijera.com910 P a g e

Gurjeet Singh et al Int. Journal of Engineering Research and ApplicationsISSN : 2248-9622, Vol. 4, Issue 3( Version 1), March 2014, pp.908-912 If G tlow than discard the edge. Ifwww.ijera.com4.1 Image Lina:G than t high keep the edge. G and t high and any of its neighborsin a 3 3 region around it have gradientmagnitudes greater than t high keep the edge. If tlow If none of pixel (x, y)‟s neighbors have highgradient magnitudes but at least one falls betweent high and tlow search the 5 5 region to see oGCannyany of these pixels have a magnitude greater thant high . If so, keep the edge. Else, discard the edge.3.5 Laplacian of Gaussian or Marr HildrithOperator:The Marr-Hildreth edge detector was a verypopular edge operator before the Canny proposed hisalgorithm. It is a gradient based operator which usesthe Laplacian to take out the second derivative of animage. It works on zero crossing method. LOG usesboth Gaussian and laplacian operator so that Gaussianoperator reduces the noise and laplacian operatordetects the sharp edges in an image.4.2 Image Butterfly:The Gaussian function is defined by the formula: i2 j 2 G(i, j) exp 2 2 2 2 1OriginalWhere 2 2LoG 2 G (i, j) 2 G (i, j) i j i 2 j 2 2 2 4 i2 j2 exp 2 2 The Marr–Hildreth operator, however, suffersfrom two main limitations. It gives responses that donot correspond to edges, so-called "false edges", andlocalization error may be severe at curved edges.IV.Prewitt4.3 Image Bird:FIGURES AND TABLESDifferent edge detection techniques arecompared by using different images. Theperformance of these techniques may also evaluatedin terms of SNR factor.Originalwww.ijera.comSobalRoberts911 P a g e