From: Wizard under the Stars
receptive field
To follow this post, I assume that you are familiar with the CNN concept, You can refresh your CNN knowledge by going through the paper “A Guide to convolution arithmetic for deep learning [1] “. It will not take you more than half an hour if you have some prior knowledge about CNNs. This post is in fact inspired by that paper and uses similar notations.
The fixed-sized CNN feature map visualization
The receptive field is defined as the region in the input space that a particular CNN’s feature is looking at (i.e. be affected by). A receptive field of a feature can be fully described by its center location and its size. Figure 1 shows some receptive field examples. By applying a convolution C with kernel size k =3×3, padding size p = 1×1, stride s = 2×2 on an input map 5×5, we will get an output feature map 3×3 (green map). Applying the same convolution on top of the 3×3 feature map, we will get a 2×2 feature map (orange map). The number of output features in each dimension can be calculated using the following formula, which is explained in detail in [1].
Note that in this post, to simplify things, I assume the CNN architecture to be symmetric, and the input image to be square. So both dimensions have the same values for all variables. If the CNN architecture or the input image is asymmetric, you can calculate the feature map attributes separately for each dimension.
Figure 1: Two ways to visualize CNN feature maps. In all cases, we uses the convolution C with kernel size k = 3×3, padding size p = 1×1, stride s = 2×2. (Top row) Applying the convolution on a 5×5 input map to produce the 3×3 green feature map. (Bottom row) Applying the same convolution on top of the green feature map to produce the 2×2 orange feature map. (Left column) The common way to visualize a CNN feature map. Only looking at the feature map, we do not know where a feature is looking at (the center location of its receptive field) and how big is that region (its receptive field size). It will be impossible to keep track of the receptive field information in a deep CNN. (Right column) The fixed-sized CNN feature map visualization, where the size of each feature map is fixed, and the feature is located at the center of its receptive field.
The left column of Figure 1 shows a common way to visualize a CNN feature map. In that visualization, although by looking at a feature map, we know how many features it contains. It is impossible to know where each feature is looking at (the center location of its receptive field) and how big is that region (its receptive field size). The right column of Figure 1 shows the fixed-sized CNN visualization, which solves the problem by keeping the size of all feature maps constant and equal to the input map. Each feature is then marked at the center of its receptive field location. Because all features in a feature map have the same receptive field size, We can simply draw a bounding box around one feature to represent its receptive field size. We don’t have to map this bounding box all the way down to the input layer since the feature map is already represented in the same size of the Input layer. Figure 2 shows another example using the same convolution but applied on a bigger input map — 7×7. We can either plot the fixed-sized CNN feature maps in 3D (Left) or in 2D (Right). Notice that the size of the receptive field in Figure 2 escalates very quickly to the point that the receptive field of the center feature of the second feature layer covers almost the whole input map. This is an important insight which was used to improve the design of a deep CNN.
Figure 2: Another fixed-sized CNN feature map representation. The same convolution C is applied on a bigger input map with i = 7×7. I drew the receptive field bounding box around the center feature and removed the padding grid for a clearer view. The fixed-sized CNN feature map can be presented in 3D (Left) or 2D (Right).
Links:
https://medium.com/@nikasa1889/a-guide-to-receptive-field-arithmetic-for-convolutional-neural-networks-e0f514068807
Original link:
http://weibo.com/1785748853/EDjvmvu04?from=page_1005051785748853_profile&wvr=6&mod=weibotime&type=comment#_rnd1491560422 638