Dynamic Neural Surfaces for Elastic 4D Shape Representation and Analysis
This work addresses the challenge of analyzing deforming 3D shapes over time for applications in fields like computer graphics and medical imaging, offering a novel continuous approach that improves upon traditional discretization methods.
The authors tackled the problem of statistical analysis of 4D surfaces (3D shapes deforming over time) by proposing Dynamic Spherical Neural Surfaces (D-SNS), a continuous representation that avoids upfront discretization, enabling direct computation of tasks like registration and geodesics with demonstrated efficiency on human and face datasets.
We propose a novel framework for the statistical analysis of genus-zero 4D surfaces, i.e., 3D surfaces that deform and evolve over time. This problem is particularly challenging due to the arbitrary parameterizations of these surfaces and their varying deformation speeds, necessitating effective spatiotemporal registration. Traditionally, 4D surfaces are discretized, in space and time, before computing their spatiotemporal registrations, geodesics, and statistics. However, this approach may result in suboptimal solutions and, as we demonstrate in this paper, is not necessary. In contrast, we treat 4D surfaces as continuous functions in both space and time. We introduce Dynamic Spherical Neural Surfaces (D-SNS), an efficient smooth and continuous spatiotemporal representation for genus-0 4D surfaces. We then demonstrate how to perform core 4D shape analysis tasks such as spatiotemporal registration, geodesics computation, and mean 4D shape estimation, directly on these continuous representations without upfront discretization and meshing. By integrating neural representations with classical Riemannian geometry and statistical shape analysis techniques, we provide the building blocks for enabling full functional shape analysis. We demonstrate the efficiency of the framework on 4D human and face datasets. The source code and additional results are available at https://4d-dsns.github.io/DSNS/.