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In [4D U-Nets for Multi-Temporal Remote Sensing Data Classification] they give the following formula for the traditional 2D CNN. But I’m confused about the w_i,j in this formula:

enter image description here

From my knowledge I would say that if you have a NxNxd input, your kernel will have shape HxWxd in this case. So the ‘depth’ of the kernel matches the ‘depth’ of the input. In this formula it seems that they are re-using the same HxW kernel against every ‘depth’ level d.

I would therefore say that it should be w_i,j,c instead of w_i,j.

Am I missing something here?

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You are not missing anything. You are right, the article is mistaken.

You can check the renowned CS231N course documentation to check for yourself: https://cs231n.github.io/convolutional-networks/

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  • $\begingroup$ Thanks! I will have a look at the documentation $\endgroup$
    – Tim Driessen
    May 4 at 6:48

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