  We address the problem of semantic correspondence, that is, establishing a
dense flow field between images depicting different instances of the same
object or scene category. We propose to use images annotated with binary
foreground masks and subjected to synthetic geometric deformations to train a
convolutional neural network (CNN) for this task. Using these masks as part of
the supervisory signal offers a good compromise between semantic flow methods,
where the amount of training data is limited by the cost of manually selecting
point correspondences, and semantic alignment ones, where the regression of a
single global geometric transformation between images may be sensitive to
image-specific details such as background clutter. We propose a new CNN
architecture, dubbed SFNet, which implements this idea. It leverages a new and
differentiable version of the argmax function for end-to-end training, with a
loss that combines mask and flow consistency with smoothness terms.
Experimental results demonstrate the effectiveness of our approach, which
significantly outperforms the state of the art on standard benchmarks.
