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Representing 3D surfaces as level sets of continuous functions over R3 is the common denominator of neural implicit representations, which recently enabled remarkable progress in geometric deep learning and computer vision tasks. In order to represent 3D motion within this framework, it is often assumed (either explicitly or implicitly) that the transformations which a surface may undergo are homeomorphic: this is not necessarily true, for instance, in the case of fluid dynamics. In order to represent more general classes of deformations, we propose to apply this theoretical framework as regularizers for the optimization of simple 4D implicit functions (such as signed distance fields). We show that our representation is capable of capturing both homeomorphic and topology-changing deformations, while also defining correspondences over the continuously-reconstructed surfaces.
The latest trends in inverse rendering techniques for reconstruction use neural networks to learn 3D representations as neural fields. NeRF-based techniques fit multi-layer perceptrons (MLPs) to a set of training images to estimate a radiance field which can then be rendered from any virtual camera by means of volume rendering algorithms. Major drawbacks of these representations are the lack of well-defined surfaces and non-interactive rendering times, as wide and deep MLPs must be queried millions of times per single frame. These limitations have recently been singularly overcome, but managing to accomplish this simultaneously opens up new use cases. We present KiloNeuS, a new neural object representation that can be rendered in path-traced scenes at interactive frame rates. KiloNeuS enables the simulation of realistic light interactions between neural and classic primitives in shared scenes, and it demonstrably performs in real-time with plenty of room for future optimizations and extensions.