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Tensor4D : Efficient Neural 4D Decomposition for High-fidelity Dynamic Reconstruction and Rendering
Ruizhi Shao, Zerong Zheng, Hanzhang Tu, Boning Liu, Hongwen Zhang, Yebin Liu
TL;DR
Dynamic 4D scene representations face high computation and memory costs, especially when extending explicit grids with time. Tensor4D hierarchically decomposes 4D fields into three time-aware volumes and nine feature planes, then learns coarse and fine scales; experiments report high-quality reconstruction and rendering from sparse-view or monocular inputs.
Problem
Dynamic NeRF representations require costly 4D-field fitting, while adding time to voxel grids or triplanes can exponentially increase memory usage.
Method
Tensor4D hierarchically decomposes a 4D field into three time-aware volumes and nine feature planes, with coarse-to-fine factorization for structural and detailed changes.
Results
Tensor4D achieves high-quality dynamic reconstruction and rendering for sparse-view camera settings and monocular inputs.
Takeaways & Limitations
The compact factorized representation supports efficient reconstruction while reducing memory consumption for dynamic scenes.
Takeaways & Limitations
A pre-set scene bounding box is necessary, and strong regularization limits handling of challenging cases such as fluid and fog.
Abstract
from arXiv · showhide
We present Tensor4D, an efficient yet effective approach to dynamic scene modeling. The key of our solution is an efficient 4D tensor decomposition method so that the dynamic scene can be directly represented as a 4D spatio-temporal tensor. To tackle the accompanying memory issue, we decompose the 4D tensor hierarchically by projecting it first into three time-aware volumes and then nine compact feature planes. In this way, spatial information over time can be simultaneously captured in a compact and memory-efficient manner. When applying Tensor4D for dynamic scene reconstruction and rendering, we further factorize the 4D fields to different scales in the sense that structural motions and dynamic detailed changes can be learned from coarse to fine. The effectiveness of our method is validated on both synthetic and real-world scenes. Extensive experiments show that our method is able to achieve high-quality dynamic reconstruction and rendering from sparse-view camera rigs or even a monocular camera. The code and dataset will be released at https://liuyebin.com/tensor4d/tensor4d.html.
1. Introduction
Tensor4D addresses the cost and memory barriers of dynamic 4D scene representation with a compact hierarchical decomposition. It applies this representation to sparse-view and monocular reconstruction while retaining high-quality rendering.
- Dynamic scene reconstruction requires high-quality, photorealistic rendering for applications including AR/VR and 3D content production.
- Mesh-based methods can produce reconstruction errors and rendering artifacts around thin structures, specular surfaces, and topological changes.
- MLP-based dynamic NeRF methods often incur high time and computation costs when fitting 4D functions, sometimes requiring dozens of hours on high-end GPUs.
- Adding time to voxel-grid or triplane representations can exponentially increase memory footprint, hindering high-quality dynamic modeling.
- Tensor4D models a 4D field with three time-aware volumes and nine feature planes, avoiding high-resolution 4D tensor construction while supporting coarse-to-fine learning.
- The factorized representation supports efficient, compact reconstruction for sparse fixed-camera inputs and monocular inputs, including time-conditioned radiance and motion fields.
2. Related Work
Prior work spans classical and neural approaches for dynamic reconstruction, with neural methods extending radiance fields through time conditioning, deformation, explicit grids, and compact encodings. Tensor4D targets free-view dynamic synthesis from extremely sparse cameras while addressing the limitations of low-resolution or costly representations.
- Classical dynamic reconstruction uses silhouette, stereo, flow, segmentation, and photometric cues, while RGBD systems estimate non-rigid deformation using depth sensors.
- Neural implicit representations support static-scene surface reconstruction and volume-rendered novel-view synthesis, motivating extensions to dynamic scenes.
- Dynamic NeRF methods either condition radiance fields on time or deform a canonical radiance field using a motion field.
- Voxel, hashing, and tensor-based representations accelerate NeRF training or rendering by replacing fully implicit computation with compact structures.
- Existing low-resolution volumetric designs can limit high-quality image rendering, whereas Tensor4D aims at free-view synthesis from extremely sparse cameras.
3. Method
Tensor4D decomposes dynamic 4D fields hierarchically into compact components and supports both time-conditioned radiance and motion-field representations. A coarse-to-fine strategy improves efficiency by separating structural changes from high-resolution dynamic details.
- The method combines hierarchical tri-projection decomposition with coarse-to-fine training to learn 4D fields at modest training-time and GPU-memory cost.
- Spatio-temporal 4D representation: NeRF-T represents a dynamic field that maps position and time to feature and density values, while viewing direction determines RGB color.
- Spatio-temporal 4D representation: D-NeRF maps each time-dependent scene point into canonical coordinates, where a canonical radiance field predicts color and density.
- Motivation: Both NeRF-T and D-NeRF require modeling a 4D field, whose MLP-based optimization can make training and rendering computationally expensive.
- Hierarchical Tri-projection Decomposition: Tensor4D first projects a 4D field into three time-aware volumes and then decomposes each volume into three feature planes, yielding nine planes.
- Hierarchical Tri-projection Decomposition: The nine-plane representation reduces space complexity from O(n^4) to O(n^2) and queries values through plane projection and bilinear interpolation.
- Applications: The decomposition applies to time-conditioned radiance fields and 4D flow fields for multiview and single-view reconstruction.
- Coarse-to-fine Strategy: Coarse training uses 128 × 128 planes for robust, fast convergence, followed by 512 × 512 planes to represent dynamic details and improve rendering quality.
4. Tensor4D for Dynamic Reconstruction
Tensor4D applies hierarchical 4D tensor decomposition to dynamic reconstruction under sparse multi-view and monocular settings. The method uses scale-specific factorization, regularization, and separate field decompositions to balance efficiency, detail, and robustness.
- 4.1. Multi-view Reconstruction: Tensor4D factorizes 4D NeRF-T fields into low- and high-resolution feature planes for sparse multi-view reconstruction.The multi-view system adopts the 4D decomposition with a coarse-to-fine strategy.
- 4.2. Monocular Reconstruction: For monocular reconstruction, Tensor4D separately factorizes 4D flow fields and the 3D canonical representation.The flow fields use coarse decomposition, while the canonical representation uses both coarse and fine decomposition.
- 4.1. Multi-view Reconstruction: The multi-view system queries features from both resolutions and feeds them with positional encoding into geometry and color networks for volume rendering.The geometry MLP predicts density and high-dimensional features, while the color MLP predicts RGB values.
- 4.1. Multi-view Reconstruction: Coarse-to-fine factorization enables effective recovery of high-fidelity dynamic details while maintaining efficient reconstruction.The system also regularizes feature planes with TV loss and geometry with a surface constraint.
- 4.2. Monocular Reconstruction: The monocular pipeline predicts point motion from flow features and appearance from canonical features before volume rendering and joint loss optimization.Its total training objective includes color, feature regularization, and surface constraint losses.
- 4.1. Multi-view Reconstruction: Tensor4D produces space- and time-novel-view renderings from sparse fixed-camera inputs, including four front-view and twelve circular-camera configurations.The framework covers both multi-view and monocular reconstruction settings.
5. Experiment
Tensor4D is evaluated on monocular synthetic and sparse-view real-world datasets against several dynamic-scene baselines. The experiments report improved reconstruction and rendering quality, reduced training time or memory in relevant comparisons, and benefits from regularization and hierarchical decomposition.
- Experimental setup: The evaluation covers monocular synthetic scenes and sparse-view real-world sequences, using four camera views for reconstruction and two held-out views for quantitative evaluation.The real-world capture system uses six synchronized, calibrated cameras; the monocular benchmark includes three D-NeRF scenes with 50–200 training frames.
- Qualitative results: Tensor4D recovers fine appearance details and produces fewer artifacts than competing methods on monocular synthetic sequences.Reported details include thin finger motions, semi-transparent silk, hand-object interaction, facial expressions, and cloth wrinkles.
- Monocular comparison: Tensor4D outperforms the compared methods in rendering quality and accuracy on the monocular synthetic benchmark.The paper attributes this conclusion to the qualitative comparisons and the quantitative results in Table 1.
- Efficiency: Tensor4D requires significantly less training time than D-NeRF, NeRF-T, and NeuS-T in monocular and multi-view scenarios.Compared with TiNeuVox, it also reduces memory consumption while enabling higher spatial resolutions of 512^3 versus 256^3.
- Ablation study: Ablations show that smoothness regularization and hierarchical decomposition improve rendering quality and performance in both multi-view and monocular cases.The full method outperforms versions without regularization, while hierarchical decomposition outperforms a six-plane decomposition.
6. Discussion
The discussion identifies a required scene bounding box and strong regularization as limitations of Tensor4D. These constraints affect out-of-box reconstruction and challenging fluid or fog scenes, respectively.
- Limitations: Tensor4D requires a pre-set scene bounding box, limiting reconstruction of backgrounds or objects outside that box.The limitation follows from decomposing 4D fields into several 2D feature planes.
- Limitations: Strong regularization improves robustness under sparse views but limits performance on challenging fluid and fog cases.The paper identifies this as a trade-off of the regularization terms.