Invnet: A Deep Learning Approach To Invert Complex Deformation Fields

Inverting a deformation field is a crucial part for numerous image registration methods and has an important impact on the final registration results. There are methods that work well for small and relatively simple deformations. However, a problem arises when the deformation field consists of complex and large deformations, potentially including folding. For such cases, the state-of-the-art methods fail and the inversion results are unpredictable. In this article, we propose a deep network using the encoder-decoder architecture to improve the inverse calculation. The network is trained using deformations randomly generated using various transformation models and their compositions, with a symmetric inverse consistency error as the cost function. The results are validated using synthetic deformations resembling real ones, as well as deformation fields calculated during registration of real histology data. We show that the proposed method provides an approximate inverse with a lower error than the current state-of-the-art methods.