CNN层输出体积计算：公式((n + 2p - f / s) + 1)使用是否正确？

Short answer: No — the formula you've written has a critical order-of-operations error that makes it invalid for calculating CNN layer output dimensions.

The Correct Formula #

The standard formula for computing the output height/width of a convolutional or pooling layer is:

output_size = floor((n + 2p - f) / s) + 1

Where:

• n: Input height or width dimension
• p: Padding added to each side of the input
• f: Size of the convolutional/pooling kernel
• floor(): Ensures we get an integer (since you can't have a fraction of a pixel in output)

What's Wrong With Your Formula? #

Your formula ((n + 2p - f / s) + 1) incorrectly applies division only to the filter size f, instead of dividing the entire (n + 2p - f) term by the stride s. This breaks the calculation entirely, as we'll see with examples from your provided layers.

Let's Verify With Your Layer Data #

Let's use the layers you listed to demonstrate why the correct formula works and yours doesn't:

1. POOL 1 Layer

• Input size (from CONV 1 output): 1242 × 378
• Output size: 621 × 189
• Assume standard max pooling parameters: f=2, s=2, p=0
  • Correct formula: (1242 + 0 - 2) / 2 + 1 = 1240/2 +1 = 620 +1 =621 (matches the given output perfectly)
  • Your formula: ((1242 +0 - 2/2)+1) = (1242 -1)+1=1242 (way off, gives the input size instead of the pooled output)

2. CONV 2 Layer

• Input size (from POOL 1 output): 621 ×189
• Output size: 310 ×94
• Reverse-engineering parameters: Let's say s=2, p=0, f=3
  • Correct formula: (621 +0 -3)/2 +1 =618/2 +1=309+1=310 (matches the output)
  • Your formula: ((621+0 -3/2)+1)=621-1.5+1=620.5 (non-integer result, which is impossible for a layer output)

3. POOL 2 Layer

• Input size (from CONV 2 output): 310 ×94
• Output size: 78 ×24
• Reverse-engineering parameters: f=4, s=4, p=1
  • Correct formula: (310 +2*1 -4)/4 +1=(312-4)/4 +1=308/4+1=77+1=78 (matches)
  • Your formula: ((310+2 -4/4)+1)=312-1+1=312 (completely incorrect, gives input size again)

Key Takeaway #

The division in the formula must apply to the entire (n + 2p - f) term, not just the filter size. Using the correct order of operations ensures you get valid, integer output dimensions that match real CNN layer behavior.

内容的提问来源于stack exchange，提问作者user9516512