Calculate the output size in convolution layer

How do I calculate the output size in a convolution layer?

For example, I have a 2D convolution layer that takes a 3x128x128 input and has 40 filters of size 5x5.

you can use this formula [(W−K+2P)/S]+1.

• W is the input volume - in your case 128
• K is the Kernel size - in your case 5
• P is the padding - in your case 0 i believe
• S is the stride - which you have not provided.

So, we input into the formula:

Output_Shape = (128-5+0)/1+1

Output_Shape = (124,124,40)

NOTE: Stride defaults to 1 if not provided and the 40 in (124, 124, 40) is the number of filters provided by the user.

You can find it in two ways: simple method: input_size - (filter_size - 1)

W - (K-1)
Here W = Input size
            K = Filter size
            S = Stride
            P = Padding

But the second method is the standard to find the output size.

Second method: (((W - K + 2P)/S) + 1)
        Here W = Input size
        K = Filter size
        S = Stride
        P = Padding 

Let me start simple; since you have square matrices for both input and filter let me get one dimension. Then you can apply the same for other dimension(s). Imagine your are building fences between trees, if there are N trees, you have to build N-1 fences. Now apply that analogy to convolution layers.

Your output size will be: input size - filter size + 1

Because your filter can only have n-1 steps as fences I mentioned.

Let's calculate your output with that idea. 128 - 5 + 1 = 124 Same for other dimension too. So now you have a 124 x 124 image.

That is for one filter.

If you apply this 40 times you will have another dimension: 124 x 124 x 40

Here is a great guide if you want to know more about advanced convolution arithmetic: https://arxiv.org/pdf/1603.07285.pdf

Formula : n[i]=(n[i-1]−f[i]+2p[i])/s[i]+1

where,

n[i-1]=128

f[i]=5

p[i]=0

s[i]=1

so,

n[i]=(128-5+0)/1+1 =124

so the size of the output layer is: 124x124x40 Where '40' is the number of filters

(1241243)*40 = 1845120 width = 124 height = 124 depth = 3 no. of filters = 40 stride = 1 padding = 0