Dilated Convolution

For a convolution

$$ f*h(x) = \sum_{s+t=x} f(s) h(t), $$

the dilated version of it is1

$$ f*_l h(x) = \sum_{s+t*l=x} f(s) h(t), $$

where $l$ is the dilation factor.


  1. Yu2015 Yu F, Koltun V. Multi-Scale Context Aggregation by Dilated Convolutions. arXiv [cs.CV]. 2015. Available: http://arxiv.org/abs/1511.07122  ↩︎

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Lei Ma (2022). 'Dilated Convolution', Datumorphism, 08 April. Available at: https://datumorphism.leima.is/cards/math/convolution-dilated/.