Presented By:-
Akshay P. Dhande

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Study and Comparison of Various Image Edge Detection Techniques
ABSTRACT
Edges characterize boundaries and are therefore a problem of fundamental importance in image processing. Image Edge detection significantly reduces the amount of data and filters out useless information, while preserving the important structural properties in an image. Since edge detection is in the forefront of image processing for object detection, it is crucial to have a good understanding of edge detection algorithms. In this paper the comparative analysis of various Image Edge Detection techniques is presented. The software is developed using MATLAB 7.0. It has been shown that the Canny’s edge detection algorithm performs better than all these operators under almost all scenarios. Evaluation of the images showed that under noisy conditions Canny, LoG( Laplacian of Gaussian), Robert, Prewitt, Sobel exhibit better performance, respectively. 1. It has been observed that Canny’s edge detection algorithm is computationally more expensive compared to LoG( Laplacian of Gaussian), Sobel, Prewitt and Robert’s operator.
Keywords: Edge Detection, Noise, Digital Image Processing
1. INTRODUCTION
Edge detection refers to the process of identifying and locating sharp discontinuities in an image. The discontinuities are abrupt changes in pixel intensity which characterize boundaries of objects in a scene. Classical methods of edge detection involve convolving the image with an operator (a 2-D filter), which is constructed to be sensitive to large gradients in the image while returning values of zero in uniform regions. There are an extremely large number of edge detection operators available, each designed to be sensitive to certain types of edges. Variables involved in the selection of an edge detection operator include Edge orientation, Noise environment and Edge structure. The geometry of the operator determines a characteristic direction in which it is most sensitive to edges. Operators can be optimized to look for horizontal, vertical, or diagonal edges. Edge detection is difficult in noisy images, since both the noise and the edges contain high- frequency content. Attempts to reduce the noise result in blurred and distorted edges. Operators used on noisy images are typically larger in scope, so they can average enough data to discount localized noisy pixels. This
results in less accurate localization of the detected edges. Not all edges involve a step change in intensity. Effects such as refraction or poor focus can result in objects with boundaries defined by a gradual change in intensity [1]. The operator needs to be chosen to be responsive to such a gradual change in those cases. So, there are problems of false edge detection, missing true edges, edge localization, high computational time and problems due to noise etc. Therefore, the objective is to do the comparison of various edge detection techniques and analyze the performance of the various techniques in different conditions.
There are many ways to perform edge detection. However, the majority of different methods may be grouped into two categories
Gradient based Edge Detection:
The gradient method detects the edges by looking for the maximum and minimum in the first derivative of the image.
Laplacian based Edge Detection:
The Laplacian method searches for zero crossings in the second derivative of the image to find edges. An edge has the one-dimensional shape of a ramp and calculating the derivative of the image can highlight its location.
Suppose we have the following signal, with an edge shown by the jump in intensity below:
If we take the gradient of this signal (which, in one dimension, is just the first derivative with respect to t) we get the following:
Clearly, the derivative shows a maximum located at the center of the edge in the original signal. This method of locating an edge is characteristic of the “gradient filter” family of edge detection filters and includes the Sobel method. A pixel location is declared an edge location if the value of the gradient exceeds some threshold. As mentioned before, edges will have higher pixel intensity values than those surrounding it. So once a threshold is set, you can compare the gradient value to the threshold value and detect an edge whenever the threshold is exceeded [2]. Furthermore, when the first derivative is at a maximum, the second derivative is zero. As a result, another alternative to finding the location of an edge is to locate the zeros in the second derivative. This method is known as the Laplacian and the second derivative of the signal is shown below:
In this paper we analyzed and did the visual comparison of the most commonly used Gradient and Laplacian based Edge Detection techniques. In section 2 the problem definition is presented. In section 3 the various edge detection techniques have been studied and analyzed. In section 4 the visual comparisons of various edge detection techniques have been done by developing software in MATLAB 7.0. Section 5 discusses the advantages and disadvantages of various edge detection techniques. Section 6 discusses the conclusion reached by analysis and visual comparison of various edge detection techniques developed using MATLAB 7.0
2. PROBLEM DEFINITION
There are problems of false edge detection, missing true edges, producing thin or thick lines and problems due to noise etc. In this paper we analyzed and did the visual comparison of the most commonly used Gradient and Laplacian based Edge Detection techniques for problems of inaccurate edge detection, missing true edges, producing thin or thick lines and problems due to noise etc. The software is developed using MATLAB 7.
3. EDGE DETECTION TECHNIQUES
3.1 Sobel Operator
The operator consists of a pair of 3×3 convolution kernels as shown in Figure 1. One kernel is simply the other rotated by 90°.
Gx Gy
FIGURE 1: Masks used by Sobel Operator
These kernels are designed to respond maximally to edges running vertically and horizontally relative to the pixel grid, one kernel for each of the two perpendicular orientations. The kernels can be applied separately to the input image, to produce separate measurements of the gradient component in each orientation (call these Gx and Gy). These can then be combined together to find the absolute magnitude of the gradient at each point and the orientation of that gradient [3]. The gradient magnitude is given by:
Typically, an approximate magnitude is computed using:
G = Gx + Gy
which is much faster to compute.
The angle of orientation of the edge (relative to the pixel grid) giving rise to the spatial gradient is given by:
θ = arctan(Gy / Gx)
3.2 Robert’s cross operator:
The Roberts Cross operator performs a simple, quick to compute, 2-D spatial gradient measurement on an image. Pixel values at each point in the output represent the estimated absolute magnitude of the spatial gradient of the input image at that point. The operator consists of a pair of 2×2 convolution kernels as shown in Figure 2. One kernel is simply the other rotated by 90°[4]. This is very similar to the Sobel operator.
FIGURE 2: Masks used for Robert operator.
These kernels are designed to respond maximally to edges running at 45° to the pixel grid, one kernel for each of the two perpendicular orientations. The kernels can be applied separately to the input image, to produce separate measurements of the gradient component in each orientation (call these Gx and Gy). These can then be combined together to find the absolute magnitude of the gradient at each point and the orientation of that gradient. The gradient magnitude is given by:
although typically, an approximate magnitude is computed using:
G = Gx + Gy
which is much faster to compute.
The angle of orientation of the edge giving rise to the spatial gradient (relative to the pixel grid orientation) is given by:
θ = arctan(Gy / Gx) − 3π / 4
3.3 Prewitt’s operator:
Prewitt operator [5] is similar to the Sobel operator and is used for detecting vertical and horizontal edges in images.
-1 0 +1
-1 0 +1
-1 0 +1
Gx Gy
FIGURE 3: Masks for the Prewitt gradient edge detector
3.4 Laplacian of Gaussian:
The Laplacian is a 2-D isotropic measure of the 2nd spatial derivative of an image. The Laplacian of an image highlights regions of rapid intensity change and is therefore often used for edge detection. The Laplacian is often applied to an image that has first been smoothed with something approximating a Gaussian Smoothing filter in order to reduce its sensitivity to noise. The operator normally takes a single gray level image as input and produces another gray level image as output.
The Laplacian L(x,y) of an image with pixel intensity values I(x,y) is given by:
L(x,y)= ∂ 2I + ∂ 2I
∂ x2 ∂ y
Since the input image is represented as a set of discrete pixels, we have to find a discrete convolution kernel that can approximate the second derivatives in the definition of the Laplacian[5]. Three commonly used small kernels are shown in Figure 4.
Because these kernels are approximating a second derivative measurement on the image, they are very sensitive to noise. To counter this, the image is often Gaussian Smoothed before applying the Laplacian filter. This pre-processing step reduces the high frequency noise components prior to the differentiation step.
In fact, since the convolution operation is associative, we can convolve the Gaussian smoothing filter with the Laplacian filter first of all, and then convolve this hybrid filter with the image to achieve the required result. Doing things this way has two advantages: Since both the Gaussian and the Laplacian kernels are usually much smaller than the image, this method usually requires far fewer arithmetic operations.
The LoG (`Laplacian of Gaussian')[6] kernel can be pre-calculated in advance so only one convolution needs to be performed at run-time on the image.