Spatial transformations are used often to align medical images in a common coordinate system as well as to represent and compare shapes. These transformations are not only expected to align images and/or shapes, but also produce "anatomically feasible" correspondences, which is usually enforced through some smoothness-based metric or regularization of the deformation field. Alternatively, population-based regularizations have been shown to produce anatomically accurate correspondences in cases where anatomically naive regularizations, such as smoothness, fail.  In recent years, deep networks have been used to generate spatial transformations in an unsupervised manner, and, once trained, these networks can register images in much less time and with comparable accuracy to that of conventional, optimization-based methods. However, the deformation fields produced by these networks require smoothness penalties, just as conventional registration methods, and therefore are prone to ignoring population-level statistics of the transformations. Here, we propose a novel neural network architecture that uses the population-level statistics of the spatial transformations to regularize the transformations learned by neural networks for image registration. This regularization is a low-dimensional cooperative autoencoder, which learns and adapts to the population of transformations required to align input images. The proposed neural network architecture produces deformation fields that describe the population-level features and associated correspondences in a manner that is anatomically relevant and statistically compact relative to state-of-the-art approaches



We extend the use of this cooperative autoencoder as a regularizer, applied on intermediate features learned during a task such as image classification specifically in problems with reduced/limited training data.