【導讀】對梯度近似級對于邊緣檢測是非常重要的。為邊緣獲得適當?shù)慕^對梯度幅度主要在與。Sobel算子就是在圖像上進行2-D的空間梯度測量。Sobel邊緣檢測器采用一對3×3的卷積模板，一塊估計x－方向的梯度，Sobel檢測器對于圖像中的噪音很敏感，它能有效地突。因此，Sobel算子被建議用在數(shù)據(jù)傳輸中的大量數(shù)據(jù)通信。數(shù)字圖像處理提高了在極不利條件下所拍攝的圖。圖像處理允許更廣泛的范圍被應用到輸入數(shù)據(jù)，以避免如噪。聲和信號失真集結(jié)在加工過程中存在的問題。方，數(shù)字圖像處理技術不斷發(fā)展。隨著20世紀快速計算機和信號處理器的應用，數(shù)字圖像處理變成了圖像處理最。這一過程涉及圖像的增強或操縱，導致產(chǎn)生另一圖像，冗余數(shù)據(jù)的清除和。檢測圖像亮度的急劇變化的目的是要捕捉重要的事件。理的一套規(guī)則給出一個邊緣響應。高斯加權(quán)而給出同位素反應被實現(xiàn)。半徑通常是像素，給出37像素的遮罩，最

　　

【正文】 ent of a twovariable function (the image intensity function) at each image point is a 2D vector with the ponents given by the derivatives in the horizontal and vertical directions. At each image point, the gradient vector points to the direction of largest possible intensity increase, and the length of the gradient vector corresponds to the rate of change in that direction. This implies that the result of the Sobel operator at any image point which is in a region of constant image intensity is a zero vector and at a point on an edge is a vector which points across the edge, from darker to brighter values. The algorithm for developing the Sobel model for edge detection is given below. Pseudocodes for Sobel edge detection method Input: A Sample Image Output: Detected Edges Step 1: Accept the input image Step 2: Apply maskGx,Gy to the input image Step 3: Apply Sobel edge detection algorithm and the gradient Step 4: Masks manipulation of Gx,Gy separately on the input image Step 5: Results bined to find the absolute magnitude of the gradient 2y2x GGG ?? （ 11） Step 6: the absolute magnitude is the output edges Second order derivative operators A maximum of the first derivative will occur at a zero crossing of the second derivative. To get both horizontal and vertical edges, we look at second derivative in both the x and y directions. This is the Laplacian of I where 22222I yIxI ??????? （ 12） The Laplacian is linear and rotationally symmetric. Thus, if one search for the zero crossing of the image that is first smoothed with a Gaussian mask and then the second derivative is calculated。 or one can convolve the image with the Laplacian of the Gaussian also known as the LoG operator. ? ? IGI ????? 22 G （ 13） The edge is modeled by specifying its four degrees of freedom: its position, its orientation, and the constant intensities on either side of the step. The data is matched by seeking the least squares error fit of the parametric model to the image window but such an approach is generally and putationally expensive. Normally what is done is that both the image data and the model are represented over small windows by their first derivative coefficients in a particular 2D orthonormal series expansion. In this case the optimization reduces to just one variable: the orientation of the edge. Results and Discussion The Sobel operator performs a 2D spatial gradient measurement on an image. Typically, it is used to find the approximate absolute gradient magnitude at each point I of an input grayscale image. The Sobel edge detector uses a pair of 3 x 3 convolution masks, one estimating gradient in the xdirection and the other estimating gradient in y direction. A convolution is usually much smaller than the actual image. As a result, the mask is slide over the image manipulating a square of pixels at a time. The mask is slides over an area where the input image changes with that pixel’s value and then shifts one pixel to the right and continues to the right until it reaches the end of the row which automatically starts again at the beginning of the next row. It is important to note that pixels in the first row and last row, as well as the first and last column cannot be manipulated by a 3 x 3 mask. This is because when placing the centre of the mask over a pixel in the first row for example, the mask will be outside the image boundaries. The Gx mask highlights the edges in the horizontal direction while the Gymask highlights the edges in vertical direction. After taking the magnitude of both, the resulting output detects edges in both directions. This is done by: (1) Applying noise smoothing to the original image (2) Filtering the original image following two kernels gives the result in Table 1. Table 1 Filtering Results of the two Kernel Kernel1= xG Kernel 2= yG 1 0 1 1 2 1 2 0 2 0 0 0 1 0 1 1 2 1 Obtaining1I and 2I (3) Estimating the gradient magnitude at each pixel as ? ? ? ? ? ?2221, ITjiG ?? （ 14） (4) Marking the pixel as edge points if G(i, j ) t results the image in Figure 3 Figure 3 The Detected Image Edge Practical Implications and Importance of Edge Detection The following advantages of Sobel edge detector justify its superiority over other edge detection techniques: i. Edge Orientation: 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. ii. Noise Environment: Edge detection is difficult in noisy images, since both the noise and the edges contain highfrequency 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. iii. Edge Structure: 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. The operator is chosen to be responsive to such a gradual cha nge in those cases. Newer waveletbased techniques actually characterize the nature of the transition for each edge in order to distinguish, for example, edges associated with hair from edges associated with a face. Edges play quite an important role in many applications of image processing, in particular for machine vision systems that analyze scenes of manmade objects under controlled illumination conditions. Detecting edges of an image represents significantly reduction the amount of data and filters out useless information, while preserving the important structural properties in an image. He