Atrous convolution study notes

The theme of this blog comes from this article - How to understand Dilated Convolutions (dilated convolutions) , but the author seems to have written it a long time ago, and the text layout is very confusing. I will write a new one myself.

1. Proposal of dilated convolution

1. Multi-Scale Context Aggregation by Dilated Convolutions
2. Dilated Residual Networks

Here are a paper note recommended by the original author. If you are interested, you can take a look at the paper note - CVPR 2017 Dilated Residual Networks .

2. Difficulties in understanding

The picture above is the original picture of the paper Multi-Scale Context Aggregation by Dilated Convolutions . We can ask a few questions.

• What does the red dot mean?
• Why does the image size not change with dilated convolution?
• What does the outermost image in the picture represent?

This picture comes from the blog A guide to receptive field arithmetic

The picture above can help you better understand the receptive field intuitively. This picture comes from a blog, A guide to receptive field arithmetic for Convolutional Neural Networks . If you don’t understand it, you can read the Chinese translation version , which is very valuable for reference. .

According to the calculation formula of the receptive field, we

$$l_k=l_{k-1}+\left(\left(f_k-1\right)\ast \coprod _{i=1}^{k-1}{s}_i\right)$$

Among them, $l_k$is the $k-$Receptive field size of layer$1$$f_k$is the convolution kernel size of the current layer, $s_i$This is number $The\; step\; size\; of\; layer\; i$ . The calculation formula of atrous convolution can be deduced, which is essentially adding 0 in the middle of the convolution sum, which expands the size of the convolution sum.

Let the size of the ordinary convolution sum be $f_k$, then the size of the equivalent atrous convolution kernel is $d_k$, there is a formula

$$d_k=(f_k-1)\times (\mathrm{rate}-1)+f_k$$

Back to the original question

• What does the red dot mean? Represents the center of the receptive field
• The size of the feature map obtained by dilated convolution is unchanged

Regarding the calculation of feature map size, we have the following formula

$$n_{\text{out }}=\lfloor \frac{n_{\text{in }}+2p-k}{s}\rfloor +1$$

Among them, $n_{\text{out }}$ 和 $n_{\text{in }}$The sub-table represents the feature map scale of the output and input, $k$ represents the convolution kernel size,$p$ represents the size of the padding,$s$ represents the stride of the convolution.