  Joint image filters are used to transfer structural details from a guidance
picture used as a prior to a target image, in tasks such as enhancing spatial
resolution and suppressing noise. Previous methods based on convolutional
neural networks (CNNs) combine nonlinear activations of spatially-invariant
kernels to estimate structural details and regress the filtering result. In
this paper, we instead learn explicitly sparse and spatially-variant kernels.
We propose a CNN architecture and its efficient implementation, called the
deformable kernel network (DKN), that outputs sets of neighbors and the
corresponding weights adaptively for each pixel. The filtering result is then
computed as a weighted average. We also propose a fast version of DKN that runs
about seventeen times faster for an image of size 640 x 480. We demonstrate the
effectiveness and flexibility of our models on the tasks of depth map
upsampling, saliency map upsampling, cross-modality image restoration, texture
removal, and semantic segmentation. In particular, we show that the weighted
averaging process with sparsely sampled 3 x 3 kernels outperforms the state of
the art by a significant margin in all cases.
