A Deformable Kernels is a type of convolutional operator for deformation modeling. DKs learn free-form offsets on kernel coordinates to deform the original kernel space towards specific data modality, rather than recomposing data. This can directly adapt the effective receptive field (ERF) while leaving the receptive field untouched. They can be used as a drop-in replacement of rigid kernels.

As shown in the Figure, for each input patch, a local DK first generates a group of kernel offsets ${\Delta \mathcal{k}}$ from input feature patch using the light-weight generator $\mathcal{G}$ (a 3$\times$3 convolution of rigid kernel). Given the original kernel weights $\mathcal{W}$ and the offset group ${\Delta \mathcal{k}}$, DK samples a new set of kernel $\mathcal{W}'$ using a bilinear sampler $\mathcal{B}$. Finally, DK convolves the input feature map and the sampled kernels to complete the whole computation.

Source: Deformable Kernels: Adapting Effective Receptive Fields for Object Deformation


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