XEC-605 DIGITAL IMAGE PROCESSING ASSIGNMENT TOPIC: EDGE DETECTION :

PRESENTED BY NAME : A.ANUSIYA CLASS : III –YEAR ECE ‘A’ SEC REG. NO : 111011013591 ROLL NO: 6 DATE : 29-04-2014 XEC-605 DIGITAL IMAGE PROCESSING ASSIGNMENT TOPIC: EDGE DETECTION

introduction:

Using computers to do image processing has two objectives : First, create more suitable images for people to observe and identify. Second, we wish that computers can automatically recognize and understand images . The edge of an image is the most basic features of the image. It contains a wealth of internal information of the image. Therefore, edge detection is one of the key research works in image processing. introduction

THE PRINCIPLE OF EDGE DETECTION:

In digital image, the so-called edge is a collection of the pixels whose gray value has a step or roof change, and it also refers to the part where the brightness of the image local area changes significantly. The gray profile in this region can generally be seen as a step. That is, in a small buffer area, a gray value rapidly changes to another whose gray value is largely different with it. Edge widely exists between objects and backgrounds, objects and objects, primitives and primitives . The edge of an object is reflected in the discontinuity of the gray. THE PRINCIPLE OF EDGE DETECTION

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The basic idea of edge detection is as follows: First, use edge enhancement operator to highlight the local edge of the image . Then, define the pixel "edge strength" and set the threshold to extract the edge point set. However , because of the noise and the blurring image, the edge detected may not be continuous. So , edge detection includes two contents . First is using edge operator to extract the edge point set. Second is removing some of the edge points from the edge point set, filling it with some another and linking the obtained edge point set into lines.

AN EDGE DETECTION MODEL BASED SOBEL OPERATOR:

Compared to other edge operator, Sobel has two main advantages : Since the introduction of the average factor, it has some smoothing effect to the random noise of the image . Because it is the differential of two rows or two columns, so the elements of the edge on both sides has been enhanced, so that the edge seems thick and bright . AN EDGE DETECTION MODEL BASED SOBEL OPERATOR

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Gradient corresponds to first derivative, and gradient operator is a derivative operator. For a continuous function f (x , y), in the position (x, y), its gradient can be expressed as a vector (the two components are two first derivatives which are along the X and Y direction respectively ): The magnitude and direction angle of the vector are : mag ( f ) = I f(2 ) I ø ( x,y ) = arc tan [G(x)/G(y)] f( x,y )=[ Gx Gy ]

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Gx and Gy need a template each, so there must be two templates combined into a gradient operator. The two 3x3 template used by Sobel are showed as (a) and (b). Every point in the image should use these two kernels to do convolution. One of the two kernels has a maximum response to the vertical edge and the other has a maximum response to the level edge. The maximum value of the two convolutions is used as the output bit of the point, and the result is an image of edge amplitude.

SOBEL EDGE OPERATOR:

-1 -2 -1 0 0 0 1 2 1 SOBEL EDGE OPERATOR -1 0 1 -2 0 2 -1 0 1 Convolution On template SI ( b) Convolution template S2 Figure I. Sobel edge operator

THE PRINCIPLE OF WAVELET THRESHOLD DE-NOISING:

Those traditional methods which use the base function with infinite width (for example, Fourier transform uses sinusoidalcurvelet as its orthogonal basis function) exist many flaws. The reason why wavelet de-noising method is successful is that wavelet transform has the following important features: The nature of low-entropy: The sparse distribution of wavelet coefficients makes the entropy of the transformed signal reducing. The nature of multi-resolution: By adopting the approach of multi-resolution, we can describe the non-stationary characteristics of the signal very well in order to extract and protect the feature . THE PRINCIPLE OF WAVELET THRESHOLD DE-NOISING

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3. The nature of de-correlation: The wavelet transform can be de-related to the signal and the noise tends to be whitening after transformation, so it is more conducive to de-noising in the wavelet domain than in the time domain. 4. The diversity nature of wavelet selection: The wavelet transform can select transform radix flexibly . So we can choose different wavelet functions for different applications in order to get the best treatment effect.In recent years, with the application and development

THE IMPROVED ALGORITHM:

The advantage of Sobel edge operand is its smoothing effect to the random noises in the image. And because it is the differential separated by two rows or two columns, so the edge elements on both sides have been enhanced and make the edge seems thick and bright. Sobel operator is a gradient operator. The first derivative of a digital image is based on avariety of two-dimensional gradient approximation, andgenerates a peak on the first derivative of the image, or generates a zero-crossing point on the second derivative. Calculate the magnitude and the argument value of the image horizontal and vertical first-order or second-order gradients, at last calculate modulus maxima along the angular direction and obtain the edge of the image. THE IMPROVED ALGORITHM

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Therefore this paper combines Sobel operator and soft-threshold wavelet de-noising . The core idea of the algorithm is: (1) Do wavelet decomposition to the image matrix and get the wavelet coefficients with noises . ( 2) Process the wavelet coefficients HL, LH and HH obtained by the decomposition, and keep the low frequency coefficients unchanging. (3) Select an appropriate threshold to remove Gaussian white noise signals. (4) Do inverse wavelet transformation to the image matrix and get the image matrix after de-noising . ( 5) Custom template edge coefficient according to the Sobel operator template showed in Figure 1.

EXPERIMENTAL RESULTS AND ANALYSIS:

This paper will use a Lena image with Gaussian white noise as the original image. First, use the traditional edge detection operators (include Sobel operator, Prewitt operator,Laplacian operator and Canny operator) to do edge detection to the noisy image. Then , use the commonly used methods which combine mean de-noising and Sobel operator or median filtering and Sobel operator. However, these methods can not remove salt and pepper noise very well. At last, the paper proposes the Sobel edge detection operator based on soft-threshold wavelet de-noising. EXPERIMENTAL RESULTS AND ANALYSIS

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Use the Lena image with Gaussian white noise as the original image. First, use the traditional edge detection operators to do edge detection, and the results are showed in Figure 2,3,4,5,6 : Figure 2. the original Lena image Figure 3. Sobel edge detection operator

From the figures above we can see that after adding Gaussian white noises to the image, using the traditional operators to do edge detection to the images will detect all the noise points and will also blur the edge details of the images. Even the detection result of the classical Canny operator is unsatisfactory either. This is because that the traditional edge detection operators mostly use the differences of the neighborhood gray values. The firstderivative'sextreme range of the adjacent pixels' edge will change obviously, so they can detect image edge . However, when the image adulterates lots of noise signals, there are gray value differences between white noises and image signals , and they can be detected easily. This leads to the poor detection effect of the classical operators .

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Figure 6. Canny edge detection operator Figure 7. median filter and Sobel operator

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In order to overcome this defect, the paper combines some commonly used de-noising methods and these classical operators , such as median filter and mean filter de- noising,see in Figure 7 and 8:

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