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So I was reading this paper: https://arxiv.org/pdf/1409.1556.pdf

VERY DEEP CONVOLUTIONAL NETWORKS FOR LARGE-SCALE IMAGE RECOGNITION Karen Simonyan∗ & Andrew Zisserman+ Visual Geometry Group, Department of Engineering Science, University of Oxford

and at a point it mentions: "It is easy to see that a stack of two 3 × 3 conv. layers (without spatial pooling in between) has an effective receptive field of 5 × 5; three such layers have a 7 × 7 effective receptive field."

I don't understand how these effective receptive fields are calculated in relation to the convolutions / convolution units.

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  • $\begingroup$ Please add a complete citation for the paper. $\endgroup$ – gung - Reinstate Monica May 10 '16 at 1:10
  • $\begingroup$ @gung I kinda added it now, not sure if you meant that though. $\endgroup$ – Pf Spf May 10 '16 at 1:13
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When you center a 3x3 filter in the top left corner of a region then that filter extends one unit above and one unit to the left of the original region. So, convolving a 3x3 filter with another 3x3 filter will produce a 5x5 filter since the 3x3 filter has been extended by one pixel in each direction.

If the size of the filter is an odd number of pixels ($n$) then it will increase the receptive field by $n - 1$ pixels.

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  • $\begingroup$ I totally understand adding 3x3 conv layer increases the receptive field from 3x3 to 5x5 to 7x7 and so on. By I can't understand what you're saying "If the size of the filter is an odd number of pixels (n) then it will increase the receptive field by n−1 pixels". when kernel is 3x3, the receptive increase at first stage 5x5 - 3x3 = 16. Why do you say it's n-1? (if we say n = 9, it doesn't match either) $\endgroup$ – Chan Kim Jun 12 '16 at 15:19

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