There are too many things in life that are difficult to control, not the small strength of human beings, but the nature of many things often depends on the randomness of some details in the background of the cosmic environment. Life is often unhappy, but it is no different from the speaker. When I was a child, I encountered unhappy things and liked to think about things in books. I think I am the most practical in explaining research knowledge. I didn't pretend to accept it, so I can open my heart and forget the troubles in the world. Now it seems that I was a little naive at that time. I think I wouldn't want to be addicted to it if it wasn't for making a living. Besides, I'm not good at technology myself. There are too many disturbing things in the world of flowers and flowers, but fortunately, the pursuit of essence is still my persistent obsession.

Personally, there are many basic theories to be studied in cv field. Although I have done several projects, I still have to go back and discuss some basic concepts. So, let's start with convolution.

First, it is not limited to the field of images. In fact, convolution has a specific physical meaning. I am scientific and automatic. At that time, I learned the concept of convolution, but I failed to understand it deeply. Later, when I first came into contact with convolutional neural network, I found that it seemed to subvert the previous understanding. But in fact, there is no cognitive connection between sensibility and rationality.

Anyone who has studied physics knows that there is the concept of impulse in physics, which can be simply described as the result F*t when the force f acts on the time t. If the impulse remains unchanged and the time t is infinitely short, an image with the maximum height and the minimum width will be formed in the coordinate system with t as the abscissa and f as the ordinate. In order to calculate impulse, the area of impulse can be calculated by integration, which is called convolution in mathematics.

Convolution is actually born for the impact function. "Shock wave function" is a symbol proposed by Dirac to solve some instantaneous physical phenomena. Convolution in "signal and system" is used to represent the response of the system to the input signal. Assuming that the response function of system H is h(t), at time T, its input is x(t) and its output is y(t), then intuitively, its output should be y(t)=x(t)h(t). However, this is not the case. The output of the system is not only related to the response of the current time t, but also related to the time t. T) The corresponding response is x(t)h(t-s), which can be continuous or discrete, but it can always be understood that the response at time t is equal to the superposition of the responses generated by each input signal at time t.. Can be expressed as:

In image processing, the convolution between the template and the image can be described as: for each point on the image, the template rotates 180 degrees. Why do you want to rotate it can be known from the convolution formula. Mathematically, we know that the image of f(-x) is the inverse of f(x) to Y axis, and h(-m) is the inverse of g(m) sequence. After H (n is rotated, it is the same as the original template, so the template does not rotate, and then the central point of the template coincides with the point. The point on the template is multiplied by the corresponding point on the image, and then the convolution value of the point is obtained. Every point on the image is treated like this. If the corner points on the image cannot correspond to the points on the template, they are usually filled with 0, which is the filling method. Convolution is an integral operation to find the overlapping area of two curves. It can be regarded as weighted summation, which can be used to eliminate noise and enhance features. Layer-by-layer convolution in deep convolution network is essentially a large number of convolution kernels playing different roles, some are denoising, some are sharpening, some are edge enhancement, some are filtering and so on.

Usually, the image is a discrete convolution. Take discrete convolution calculation as an example. For S2 equation, n is the length of signal f(n), y(n) is the convolution result sequence, and the length is len(f(n))+len(g(n))- 1.

Take the three-factor signal as an example:

The end result is:

y(n)=[2 7 13 1 1 3]

The calculation process is as follows:

The corresponding two-dimensional convolution is defined as follows:

There is also a more vivid diagram, aiming at the 3*3 convolution kernel:

Convolution understanding in image processing;

To sum up, although the concept of convolution has different meanings in different fields, it seems to have a * * * property, which can be summarized as the modulation or pollution of a physical quantity or a system input.

At this point, I finally have a basic understanding of the definition and calculation of convolution. From sensibility to rationality is a process of knowledge theorization, and from rationality to sensibility is a process of further sublimating knowledge and improving the level of understanding. In this process, I often have a feeling that everything is unified. Well, that's a bit much.

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