  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.
