* Edge detection is the name for a set of mathematical methods which aim at identifying points in a digital image at which the image brightness changes sharply or, more formally, has discontinuities. The points at which image brightness changes sharply are typically organized into a set of curved line segments termed edges. * Edge detection is one of the fundamental steps in image processing, image analysis, image pattern recognition, and computer vision techniques.
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*Edge detection is the name for a set of mathematical methods which aim at identifying points in a digital image at which the image brightness changes sharply or, more formally, has discontinuities. The points at which image brightness changes sharply are typically organized into a set of curved line segments termed edges.
*Edge detection is one of the fundamental steps in image processing, image analysis, image pattern recognition, and computer vision techniques.
*Edge detection is a very important area in the field of Computer Vision. Edges define the boundaries between regions in an image, which helps with segmentation and object recognition. They can show where shadows fall in an image or any other distinct change in the intensity of an image. *Edge detection is a fundamental of low level image processing and good edges are necessary for higher level processing
• Which was invented by Marr and Hildreth (1980) who combined Gaussian filtering with the Laplacian.
• This algorithm is not used frequently in machine vision.
• The second derivative of smoothed step edge is a function that crosses zero at the location of edge.
Detection of DiscontinuitiesGradient Operators (laplacian of guassian:
LOG)*Second-order derivatives: (The Laplacian)*The Laplacian of an 2D function f(x,y) is defined as
*Two forms in practice:
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*The Laplacian of a Gaussian sometimes is called the Mexican hat function. It also can be computed by smoothing the image with the Gaussian smoothing mask, followed by application of the Laplacian mask.
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The Laplacian of a Gaussian (LoG)
A Gaussian function
Detection of DiscontinuitiesGradient Operators (laplacian of guassian:
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Detection of DiscontinuitiesGradient Operators (laplacian of guassian:
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Detection of DiscontinuitiesGradient Operators (laplacian of guassian:
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Sobel gradient
Laplacian maskGaussian smooth function
Detection of DiscontinuitiesGradient Operators (laplacian of guassian: LOG)
Advantages •Easy to detect edges and their orientations. In this cross operator detection of edges and their orientations is said to be simple due to the approximation of the gradient magnitude is simple. •The second advantage is the fixed characteristics in all directions.
Disadvantages:• It is very sensitive to the noise. In detecting the edges and their orientations are increased in the noise to the image this will eventually degrade the magnitude of the edges. •The second disadvantage is that, the operation gets diffracted by some of the existing edges in the noisy image.
The behavior of the LoG zero crossing edge detector is largely governed by the standard deviation of the Gaussian used in the LoG filter. The higher this value is set, the more smaller features will be smoothed out of existence, and hence fewer zero crossings will be produced. Hence, this parameter can be set to remove unwanted detail or noise as desired. The idea that at different smoothing levels different sized features become prominent is referred to as `scale'.
This image contains detail at a number of different scales.
The image is the result of applying a LoG filter with Gaussian standard deviation 1.0.
Note that in this and in the following LoG output images, the true output contains negative pixel values. For display purposes the graylevels have been offset so that displayed graylevel 128 corresponds to an actual value of zero, and rescaled to make the image variation clearer.
The image shows the zero crossings from this image. Note the large number of minor features detected, which are mostly due to noise or very faint detail. This smoothing corresponds to a fine `scale'.
This image is the result of applying a LoG filter with Gaussian standard deviation 2.0 and
The image shows the zero crossings. Note that there are far fewer detected crossings, and that those that remain are largely due to recognizable edges in the image. The thin vertical stripes on the wall, for example, are clearly visible.
This image is the output from a LoG filter with Gaussian standard deviation 3.0. This corresponds to quite a coarse `scale'
The is the zero crossings in this image. Note how only the strongest contours remain, due to the heavy smoothing. In particular, note how the thin vertical stripes on the wall no longer give rise to many zero crossings.
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