Abstract: We present Dictionary Fields, a novel neural representation which decomposes a signal into a product of factors, each represented by a classical or neural field representation, operating on transformed input coordinates. More specifically, we factorize a signal into a coefficient field and a basis field, and exploit periodic coordinate transformations to apply the same basis functions across multiple locations and scales. Our experiments show that Dictionary Fields lead to improvements in approximation quality, compactness, and training time when compared to previous fast reconstruction methods. Experimentally, our representation achieves better image approximation quality on 2D image regression tasks, higher geometric quality when reconstructing 3D signed distance fields, and higher compactness for radiance field reconstruction tasks. Furthermore, Dictionary Fields enable generalization to unseen images/3D scenes by sharing bases across signals during training which greatly benefits use cases such as image regression from partial observations and few-shot radiance field reconstruction.
Latex Bibtex Citation:
@INPROCEEDINGS{Chen2023SIGGRAPH,
  author = {Anpei Chen and Zexiang Xu and Xinyue Wei and Siyu Tang and Hao Su and Andreas Geiger},
  title = {Dictionary Fields: Learning a Neural Basis Decomposition},
  booktitle = {International Conference on Computer Graphics and Interactive Techniques (SIGGRAPH)},
  year = {2023}
}

Abstract: We present Factor Fields, a novel framework for modeling and representing signals. Factor Fields decomposes a signal into a product of factors, each represented by a classical or neural field representation which operates on transformed input coordinates. This decomposition results in a unified framework that accommodates several recent signal representations including NeRF, Plenoxels, EG3D, Instant-NGP, and TensoRF. Additionally, our framework allows for the creation of powerful new signal representations, such as the "Dictionary Field" (DiF) which is a second contribution of this paper. Our experiments show that DiF leads to improvements in approximation quality, compactness, and training time when compared to previous fast reconstruction methods. Experimentally, our representation achieves better image approximation quality on 2D image regression tasks, higher geometric quality when reconstructing 3D signed distance fields, and higher compactness for radiance field reconstruction tasks. Furthermore, DiF enables generalization to unseen images/3D scenes by sharing bases across signals during training which greatly benefits use cases such as image regression from sparse observations and few-shot radiance field reconstruction.
Latex Bibtex Citation:
@ARTICLE{Chen2023ARXIV,
  author = {Anpei Chen and Zexiang Xu and Xinyue Wei and Siyu Tang and Hao Su and Andreas Geiger},
  title = {Factor Fields: A Unified Framework for Neural Fields and Beyond},
  journal = {Arxiv},
  year = {2023}
}

Abstract: Visually exploring in a real-world 4D spatiotemporal space freely in VR has been a long-term quest. The task is especially appealing when only a few or even single RGB cameras are used for capturing the dynamic scene. To this end, we present an efficient framework capable of fast reconstruction, compact modeling, and streamable rendering. First, we propose to decompose the 4D spatiotemporal space according to temporal characteristics. Points in the 4D space are associated with probabilities of belonging to three categories: static, deforming, and new areas. Each area is represented and regularized by a separate neural field. Second, we propose a hybrid representations based feature streaming scheme for efficiently modeling the neural fields. Our approach, coined NeRFPlayer, is evaluated on dynamic scenes captured by single hand-held cameras and multi-camera arrays, achieving comparable or superior rendering performance in terms of quality and speed comparable to recent state-of-the-art methods, achieving reconstruction in 10 seconds per frame and real-time rendering.
Latex Bibtex Citation:
@ARTICLE{Song2023TVCG,
  author = {Liangchen Song and Anpei Chen and Zhong Li and Zhang Chen and Lele Chen and Junsong Yuan and Yi Xu and Andreas Geiger},
  title = {NeRFPlayer: Streamable Dynamic Scene Representation with Decomposed Neural Radiance Fields},
  journal = {IEEE Transactions on Visualization and Computer Graphics (TVCG)},
  year = {2023}
}

Abstract: We present TensoRF, a novel approach to model and reconstruct radiance fields. Unlike NeRF that purely uses MLPs, we model the radiance field of a scene as a 4D tensor, which represents a 3D voxel grid with per-voxel multi-channel features. Our central idea is to factorize the 4D scene tensor into multiple compact low-rank tensor components. We demonstrate that applying traditional CP decomposition - that factorizes tensors into rank-one components with compact vectors -- in our framework leads to improvements over vanilla NeRF. To further boost performance, we introduce a novel vector-matrix (VM) decomposition that relaxes the low-rank constraints for two modes of a tensor and factorizes tensors into compact vector and matrix factors. Beyond superior rendering quality, our models with CP and VM decompositions lead to a significantly lower memory footprint in comparison to previous and concurrent works that directly optimize per-voxel features. Experimentally, we demonstrate that TensoRF with CP decomposition achieves fast reconstruction (<30 min) with better rendering quality and even a smaller model size (<4 MB) compared to NeRF. Moreover, TensoRF with VM decomposition further boosts rendering quality and outperforms previous state-of-the-art methods, while reducing the reconstruction time (<10 min) and retaining a compact model size (<75 MB).
Latex Bibtex Citation:
@INPROCEEDINGS{Chen2022ECCV,
  author = {Anpei Chen and Zexiang Xu and Andreas Geiger and Jingyi Yu and Hao Su},
  title = {TensoRF: Tensorial Radiance Fields},
  booktitle = {European Conference on Computer Vision (ECCV)},
  year = {2022}
}