Convolutional Neural Networks (CNN)
1, the basic principle of calculation
Dynamic Process:
The weight of the filter (filter) is determined based on the features you want to detect. In deep learning, you are also training. Different detection characteristics, the weight is not the same.
The above single-layer image generally represents a gray-white image. It is a colorless RGB image that contains three layers of the same size. In this case, the corresponding filter must also be changed into three layers. The number (number of channels) must always be consistent with the number of image layers. . .
Note that the output is a single-layer map
Because when a three-channel filter is convolved with the image, the sum of the two numbers is directly weighted to calculate their sum and a result, rather than a hierarchical calculation.
2, the size of the convolution output
In the above two examples, the 5*5 image gets a 3*3 result from the 3*3 filter, and the 6*6*3d image gets a 4*4*1d result from the 3*3*3d filter. From the single-layered example, we probably already know how to calculate it, and then convert it into a formula to express it.
According to the calculations, each time the convolved image becomes smaller, the above still only has a step size of 1 (that is, it moves only one at a time). There are two disadvantages:
1. After each convolution, the image will shrink. After many convolutions, it may become very small and small.
2, will lose the corner of the edge of the important information, see the image below
At the top edge, the number of pixels detected from left to right is 1, 2, 3, 2, 1, respectively. The visible corner edge is detected only once, and the middle can be detected multiple times. This results in the loss of corner information. . The solution is to join Padding.
3, adding Padding and later calculations
Adding padding means adding a layer of pixels (or multiple layers) to the edge of the original image before convolving, which is also called zero padding (since most of the time we add elements are 0).
From the above figure, if the convolution is to obtain the same image size as the original image, then the number of Padding layers added should be (f - 1)/2, which also shows that the filter f we use is generally an odd number. , In order to get rid of the calculation, to obtain symmetric filling, there is a reason that an odd number of filters will have a center point. Sometimes, in the computer vision calculation, a center point will be much more convenient.
Attachment: The convolution of Padding = 0 is called the convolution of Valid Convolution to join Padding in order to get the same image as the original image. It is called Same Convolution.
3, adding the stride step (Stride)
The above calculations are based on a step size of 1. Let's look at the case where the step size is 2:
In the convolution operation, if the filter exceeds the image frame, the general operation is no operation.
4, three-dimensional convolution
(1) Original RGB three-dimensional map
(2) Multiple filters (convolution kernels)
The above operations are all based on a single filter, whether single or multi-layer, a filter can only detect one feature. To detect multiple features, we need multiple filters.
5, summary
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