Comprehension of atitit image processing Attilax summary of convolution

Atitit An understanding of image processing convolution Attilax Summary

convolutionthe operations can be divided into inversion, translation, multiplication, summation.

in image processing, the image is a large matrix, convolutionA template is a small matrix. According to the above process, the small matrix is reversed, and then translated to a position, the small matrix of each small lattice corresponding to a large matrix inside a small lattice, and then the corresponding small lattice inside the number of multiplication, the corresponding small multiply multiply the result of summing, the final result is assigned to the small matrix corresponding to the middle of the image of the cell value, Replace the original value. The above mentioned, inversion, translation, multiplication, summation.
General Image convolutionis to start traversing to the last pixel (small) from the first pixel (small). After the smooth, fuzzy,Sharpening,Edge Extractionis essentially a convolution, but the template is different.

The above is only one-dimensional case, when a two-dimensional digital image convolution, its mathematical significance can be explained as follows:

The source image is used as the input source data, the image processed later is the convolution output result, convolution operand as Filter

in the a convolution operation is performed on each pixel point of the source image in XY two directions. :

Pink squares every time in X/y forward a pixel square, it will produce a new output pixel, the image of the dark blue generation

The table is going to output the pixel squares, and after all the pixel squares, all the output pixels are obtained.

in the figure, the pink matrix represents the convolution operand matrix, and black represents the source image – each square represents a pixel point.

Image Processing-linear filtering-1 basis (correlation operator, convolution operator, edge effect)

This paper discusses the method of generating the output image by using the small neighborhood of pixels in the input image, which is called filtering (filtering) in signal processing. Among them, the most commonly used is linear filtering : The output pixel is the weighted sum of the input neighborhood pixels

Second: convolution in Digital image processing application

a digital image can be regarded as a discrete function of a two-dimensional space can be expressed as f (x, y), assuming that there is a two-dimensional convolution

as a function C (U, v) , will produce the output image g (x, Y) = f (x, y) *c (u,v), the use of convolution can be achieved for image blur, edge detection, produce the effect of embossing image.

A simple digital image convolution process can be as follows:

1. reading the source image pixels

2. applying the convolution operand matrix to produce the target image

3. normalization of the target image

4. processing boundary pixels

Basic concepts of linear filtering and convolution

linear filtering can be said to be the most basic method of image processing, it can allow us to process the image, resulting in a lot of different effects. The practice is simple. First, we have a two-dimensional filter matrix (with a tall name called convolution kernel) and a two-dimensional image to be processed. Then, for each pixel of the image, the product of its neighborhood pixel and the corresponding element of the filter matrix is computed and then added up as the value of the pixel position. This completes the filtering process.

Second, the Magic convolution core

As mentioned above, the image filtering process is to apply a small convolution core to the image, that small convolution nucleus in the end what magic, can make an image from the appalling to become delicious. Let's take a glimpse of some simple, but not simple, convolution-kernel magic.

Image Sharpening Filter Sharpness Filter

image sharpening and edge detection is very much like, first find the edge, and then add the edge to the original image above, thus strengthening the edge of the image, so that the image looks sharper. The combination of the two operations is sharpening the filter, that is, on the basis of the edge detection filter, and then in the center of the position plus 1, so that the filtered image and the original image will have the same brightness, but will be more sharp.

If we increase the nuclear, we can get a finer sharpening effect.

In addition, the following filters will emphasize the edges more:

the main emphasis is on the details of the image. The simplest 3x3 sharpening filter is as follows:

The difference between the current point and the surrounding point is actually calculated, and then the difference is added to the original position. In addition, the weighted value of the middle point is greater than all weights and more than 1, which means that thepixel remains the original value.

Edge Detection Edge Detection

We're looking for the horizontal edge: It's important to note that the elements of the matrix here are 0 , so the filtered image will be very dark, only the edge of the place is bright.

Why is this filter able to find the horizontal edge? Because the convolution of this filter is equivalent to a discrete version of the derivative: you subtract the current pixel value from the previous pixel value, so you can get the difference or slope of the function in both positions. The following filter can find the vertical edge, where the pixel values on and below the pixels are used:

and the filter below can be found $ degree of Edge: Take -2 not for anything, just to get the elements of the Matrix and for 0 only.

The filter below will detect the edges in all directions. :

to detect edges, we need to calculate the gradient in the direction of the image. Convolution the image with the following convolution core, it is possible. But in practice, this simple method will amplify the noise. Also, it should be noted that all the values of the matrix add up to 0.

Embossed Embossing Filter

an embossed filter can give an image a 3D the effect of the shadow. Just subtract the pixels from the other side of the pixel on the center side. At this point, the pixel value may be negative, we use the negative as a shadow, a positive number as the light, and then we add an offset to the resulting image . At this point, most of the images become gray.

Some knowledge points of image convolution and filtering -zouxy09 's column - Blog channel -CSDN.NET.html

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Comprehension of atitit image processing Attilax summary of convolution