  Equivariance to random image transformations is an effective method to learn
landmarks of object categories, such as the eyes and the nose in faces, without
manual supervision. However, this method does not explicitly guarantee that the
learned landmarks are consistent with changes between different instances of
the same object, such as different facial identities. In this paper, we develop
a new perspective on the equivariance approach by noting that dense landmark
detectors can be interpreted as local image descriptors equipped with
invariance to intra-category variations. We then propose a direct method to
enforce such an invariance in the standard equivariant loss. We do so by
exchanging descriptor vectors between images of different object instances
prior to matching them geometrically. In this manner, the same vectors must
work regardless of the specific object identity considered. We use this
approach to learn vectors that can simultaneously be interpreted as local
descriptors and dense landmarks, combining the advantages of both. Experiments
on standard benchmarks show that this approach can match, and in some cases
surpass state-of-the-art performance amongst existing methods that learn
landmarks without supervision. Code is available at
www.robots.ox.ac.uk/~vgg/research/DVE/.
