How to understand the principle of convolution?

Convolution is a mathematical operation, which is widely used in signal processing, image processing and deep learning. Simply put, convolution is the "sliding product" operation between one function and another.

In the discrete case, there are two sequences f and g, both of which are n in length, so the calculation of convolution can be expressed as: c [n] = σ _ {k =-∞} {∞} f [n-k] g [k]. This formula means that for each element of the sequence F, we multiply it with all the elements of the sequence G, and then add up all the products to get the convolution result.

An important property of convolution is that it keeps the shape of the function. This is because convolution operation is actually looking for the correlation between two functions. If two functions have a large value at a certain position, their convolution will also have a large value at this position. Therefore, by observing the results of convolution, we can understand some characteristics of the original function, such as its periodicity and symmetry.

In deep learning, Convolutional Neural Network (CNN) is a model that uses convolution operation to process images. The convolution layer in CNN can be regarded as a filter, which can extract some features in the image, such as edges and corners. Through multi-layer convolution layer, CNN can gradually extract more complex features, thus realizing the task of image classification and detection.