RDA-INR: Riemannian Diffeomorphic Autoencoding via Implicit Neural Representations

Diffeomorphic registration frameworks such as Large Deformation Diffeomorphic Metric Mapping (LDDMM) are used in computer graphics and the medical domain for atlas building, statistical latent modeling, and pairwise and groupwise registration. In recent years, researchers have developed neural network-based approaches regarding diffeomorphic registration to improve the accuracy and computational efficiency of traditional methods. In this work, we focus on a limitation of neural network-based atlas building and statistical latent modeling methods, namely that they either are (i) resolution dependent or (ii) disregard any data- or problem-specific geometry needed for proper mean-variance analysis. In particular, we overcome this limitation by designing a novel encoder based on resolution-independent implicit neural representations. The encoder achieves resolution invariance for LDDMM-based statistical latent modeling. Additionally, the encoder adds LDDMM Riemannian geometry to resolution-independent deep learning models for statistical latent modeling. We investigate how the Riemannian geometry improves latent modeling and is required for a proper mean-variance analysis. To highlight the benefit of resolution independence for LDDMM-based data variability modeling, we show that our approach outperforms current neural network-based LDDMM latent code models. Our work paves the way for more research into how Riemannian geometry, shape respectively image analysis, and deep learning can be combined.