The basis of Image Processing-weekend playtalk convolution

Play: convolution

 

Convolution is actually a product summation replacement in an image that achieves smooth or filtering.

Reference Formula

Xiaojiang has been dealing with convolution recently. He needs to deal with it several times a day. He is always troubled because he did not learn Signals and Systems in college, so I thought I had to fully understand the convolution. My colleagues in the same office also asked me what convolutional is. My sister told me yesterday: "I already wanted to understand this problem !" After some time of thinking, I have some interesting experiences to share with you.

I have heard that the computation physicist such as convolution has never thoroughly understood the meaning of computation. Try the following carefully.


We all know this formula, but what is its physical significance? We have done a lot of things with convolution. During signal processing, the output function is the convolution of the Input Function and the system function, during image processing, the two sets of images with different resolutions can be processed smoothly after convolution. Convolution can even be used in exam cheating. To make a photo look like two people at the same time, you only need to Convolution the two images. This is a smooth process, but how can we really establish a relationship between formulas and reality? That is to say, can we find a convenient and specific example in our life to express the physical meaning of formulas? I think of one of the following:
For example, your boss ordered you to work, but you went downstairs to play billiards. Later, the boss found that he was very angry and slapped you (Note: This is the input signal, pulse ), as a result, your face will gradually drum up a pack, and your face will be a system, and the pack will be the response of your face to the slap, in this way, it is associated with the meaning of the signal system. We also need some assumptions to ensure the rigor of the arguments: assume that your face is a linear, constant system, that is, no matter when the boss slapped you, playing in the same position on your face (this seems to require your face to be smooth enough. If you say that you have a lot of acne, or even the whole face is continuously inaccessible everywhere, it is too difficult, I have nothing to say. Haha) Your face will always drum up a bag of the same height at the same time interval, it is assumed that the size of the drum package is used as the system output. Okay, now we can go to the core content-convolution!
If you go down to play billiards every day, the boss will slap you every day. However, after the boss slapped you, you will get swollen in five minutes, so it takes a long time, you even adapted to this kind of life ...... If one day, the boss can't bear it, and starts to fan your process continuously at an interval of 0.5 seconds, the problem will come. The first time you fan up your pack has not been swollen yet, the second slap is coming. The bag on your face may be twice as high as it is. The boss keeps fan you, and the pulse keeps acting on your face. The effect is constantly superimposed, in this way, the results can be summed up, and the result is a function of changing the height of the package on your face (Be careful with understanding). If the boss is a bit more harsh, the frequency is getting higher and higher, so that you cannot tell the time interval clearly, then the sum becomes a point. It can be understood in this way, at a fixed moment in this process, what is the correlation between the bulge of the bag on your face? This is related to the previous attacks! However, each contribution is different. The sooner the slice is played, the smaller the contribution is. That is to say, the output at a certain time point is the output at a certain point formed by the superposition of multiple previous input times multiplied by their respective attenuation coefficients, and then the output points at different time points are put together to form a function, this is convolution. The convolution function is the function of changing the package size over time on your face. Originally, your package can reduce swelling in a few minutes, but if you hit it continuously, it will not be swollen for a few hours. Isn't this a smooth process? Reflected in the Cambridge University formula,

 

 

 

F (a) is the slap in the, and g (x-A) is the role of the slap in the at the X moment. It's okay to combine it and then combine it, do you mean this? I think this example is very vivid,

 

 

 

Do you have a more detailed understanding of convolution?
I am busy opening my questions recently, but I 'd like to relax after the weekend. In fact, I really hope my friends can leave a message to me and post your thoughts on this article. If you have any questions, please submit them. In the lower part of this article, I will introduce another abstract example to help you better understand the connection between mathematics and life from convolution.
Finally, I would like to remind you not to try it yourself ......

 

What is convolution:

Settings:F(X),G(X) Is two product functions on R1, for Integral (for example ):

 

FunctionFAndGIt is the integral of the product of one function after one function is flipped and translated, and is a function of the translation volume.

Convolution occurs on the basis of signals and linear systems or in the background. Signals and linear systems are discussed about the changes that occur after a signal passes through a linear system, that is, the mathematical relationship between the output signal and the input signal is a linear computing relationship.

In statistics, weighted moving average is a convolution. In probability theory, the sum of the two independent statistical variables X and Y is the convolution of the probability density functions of X and Y. In acoustics, an echo can be represented by a convolution of the source sound and a function that reflects various reflection effects. In electronic engineering and signal processing, the output of any linear system can be obtained by convolution of the input signal and system function (system impulse response. In physics, any linear system (conforming to the superposition principle) has convolution.

Convolution is a linear operation. Common mask operations in image processing are convolution and are widely used in image filtering .. Gaussian transformation is the convolution of images using Gaussian Functions.

Convolution theorem:

Convolution is performed in the time domain, and the product is in the frequency domain.

 

 

Convolution smooth

Translation and flip

Http://blog.csdn.net/carina197834/article/details/8043654http://blog.csdn.net/xiaojiang0805/article/details/7602099

The basis of Image Processing-weekend playtalk convolution