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As I understand STN as described by the the deepmind paper https://arxiv.org/abs/1506.02025

  • allow a neural network to learn how to perform spatial transformations on the input image in order to enhance the geometric invariance of the model.

whereas Deformable Convolutions https://arxiv.org/abs/1703.06211

  • add 2D offsets to the regular grid sampling locations in the standard convolution.

From the paper:

...deformable convolution does not adopt a global parametric transformation and feature warping. Instead, it samples the feature map in a local and dense manner. To generate new feature maps, it has a weighted summation step, which is absent in STN.

To me STNs augment the input image whereas DC augment the kernel shape. Results should be similar/same in terms of field of view of the network? Please correct me if mistaken.

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The main difference, as they mentioned in the paper, is that STN has a global parameter to transform the features. That is, it computes one set of parameters to transform the input. DC computes a 2D offset map for each location in the input, so for each location in the input features there is a separate transformation.

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  • $\begingroup$ The 2D offset map is fixed for an input layer, so I am not sure what you mean by 'for each location in the input'. $\endgroup$ – Benedict K. Jun 12 '18 at 16:23
  • $\begingroup$ The offset map is learned via a convolution of the input feature map. 'For each location in the input' I am referring to each pixel has its own 2D offset. This is illustrated in Figure 2 of the paper. $\endgroup$ – kenny Jun 12 '18 at 20:11
  • $\begingroup$ Right but the offset is shared throughout the input feature map. So let's assume a 25x25x50 input map with h x w x nbr features then the offset is the same for each pixel x 50. There was some confusion about this on medium/reddit. $\endgroup$ – Benedict K. Jun 18 '18 at 9:49

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