The network can handle topological variations by modeling a family of shapes in a higher-dimensional space.
Back in June 2021, a team of developers from Google Research had presented a neural network that can handle topological variations by modeling a family of shapes in a higher-dimensional space called HyperNeRF. With this network, the team has managed to bypass the struggle of deformation-based approaches when it comes to model changes in topology.
By lifting NeRFs into a higher-dimensional space, and by representing the 5D radiance field corresponding to each individual input image as a slice through this "hyper-space", the team had achieved more realistic renderings and more accurate geometric reconstructions.
"Our method is inspired by level set methods, which model the evolution of surfaces as slices through a higher dimensional surface. We evaluate our method on two tasks: (I) interpolating smoothly between "moments", i.e., configurations of the scene, seen in the input images while maintaining visual plausibility, and (II) novel-view synthesis at fixed moments," commented the team.