A low-rank tensor is a multidimensional array of data that can be accurately represented or approximated using a small number of simpler, lower-dimensional components. Extending the concept of a low-rank matrix to higher dimensions, a low-rank tensor captures the primary structures and correlations within multi-way data through factorizations such as canonical polyadic decomposition or Tucker decomposition. By decomposing complex multidimensional grids or features into compact factor products of vectors and matrices, low-rank tensors significantly reduce memory storage requirements and computational complexity while preserving essential informational patterns.
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 CANDECOMP/PARAFAC (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).
