Learning Structured Deformations using Diffeomorphic Registration
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Studying organ motion or pathology progression is an important task in diagnosis and therapy of various diseases. Typically, this task is approached by deformable registration of successive images followed by the analysis of the resulting deformation field(s). Most registration methods require prior knowledge in the form of regularization of the image transformation which is often sensitive to tuneable parameters. Alternatively, we present a registration approach which learns a low-dimensional stochastic parametrization of the deformation -- unsupervised, by looking at images. Hereby, spatial regularization is replaced by a constraint on this parameter space to follow a prescribed probabilistic distribution, by using a conditional variational autoencoder (CVAE). This leads to a generative model designed to be structured and more anatomy-invariant which makes the deformation encoding potentially useful for analysis tasks like the transport of deformations. We also constrain the deformations to be diffeomorphic using a new differentiable exponentiation layer. We used data sets of 330 cardiac and 1000 brain images and demonstrate accurate registration results comparable to two state-of-the-art methods. Besides, we evaluate the learned deformation encoding in two preliminary experiments: 1) We illustrate the model's anatomy-invariance by transporting the encoded deformations from one subject to another. 2) We evaluate the structure of the encoding space by clustering diseases.
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