Dynamic Scene Modeling

• Dynamic Scene Modeling is a comprehensive set of techniques that reconstruct, represent, and analyze evolving environments by integrating geometry, appearance, and temporally varying motion.
• Techniques such as 4D Gaussian splatting, bandlimited and factorized fields, and hierarchical scene graphs enable high photorealism, efficiency, and semantic interpretability.
• Applications range from urban driving to human performance analysis, achieving robust quantitative metrics (e.g., PSNR >30 dB) and supporting real-time editing and simulation.

Dynamic scene modeling is the set of techniques and mathematical frameworks for reconstructing, representing, and reasoning about environments in which the spatial arrangement of physical entities evolves over time. In contemporary computer vision and graphics research, this typically entails producing representations that jointly capture geometry (shape, topology), appearance (color, reflectance), and temporally varying motion for both rigid and non-rigid elements—from moving vehicles in urban driving scenes to non-rigid human performance. Methods span explicit representations (point clouds, Gaussians, meshes), factorized space-time fields, dynamic scene graphs, and neural volumetric models, with research increasingly focused on achieving high photorealism, efficiency, compactness, semantic interpretability, and support for downstream tasks such as editing and physical reasoning.

1. Spatiotemporal Parameterizations and Representations

Dynamic scene modeling necessitates capturing the evolution of scene structure across time, demanding rich spatiotemporal parameterizations. One successful paradigm is the extension of 3D Gaussian splatting to higher dimensions and temporal bases:

• 4D Gaussian Splatting: The domain is extended to $(x,y,z,t)\in\mathbb{R}^4$. Each primitive is a 4D anisotropic Gaussian with mean $\mu_i \in \mathbb{R}^4$, full covariance $\Sigma_i \in \mathbb{R}^{4\times4}$, and opacity and appearance coefficients (e.g., 4D spherindrical harmonics). Rendering proceeds by projecting the conditional 3D slice at query time $t$ to the image plane and composite with front-to-back alpha blending. This enables truly simultaneous optimization and deployment of space-time volumes supporting novel time and view synthesis (Yang et al., 2024, Yang et al., 2023).
• Bandlimited and Factorized Fields: Some approaches, such as BLiRF, model each spatiotemporal field as a low-rank sum of separable spatial and temporal bases:

$$S(\mathbf{x},t) = \sum_{j=1}^K \tilde{b}_j(\mathbf{x})\,\beta_j(t).$$

This explicit factorization decouples high-frequency spatial content from low-bandwidth temporal signal and is highly expressive for smooth yet non-rigid motions (Ramasinghe et al., 2023).

• Anchor/Seed Grid Decompositions: Methods including SD-GS, EDGS, and LocalDyGS segment the volume using grids or scattered anchors/seeds, each responsible for a local region in spacetime, with per-anchor temporal decoders generating dynamic Gaussians or features (Yao et al., 10 Jul 2025, Kong et al., 27 Feb 2025, Wu et al., 3 Jul 2025).
• Hierarchical and Instance-Aware Approaches: Dynamic content is decomposed into static and dynamic constituents (as in BézierGS, DynaSplat), with further hierarchical decomposition into global (object-level) and local (primitive-level) motion models or semantic instances for editing and tractable learning (Ma et al., 27 Jun 2025, Deng et al., 11 Jun 2025, Waczyńska et al., 2024, Jiang et al., 2 Apr 2026).

2. Motion and Temporal Modeling

Capturing object and scene dynamics requires parameterizing motion over time. Strategies include:

• Parametric Curves and Trajectories: Explicit object trajectories are parameterized as learnable Bézier curves of order $n$,

$$\mu_{\mathrm{center}}(t,g) = \sum_{i=0}^n b_{i,n}(t) C_i^g,$$

and similar local Bézier curve offsets, with control points jointly optimized for smooth, globally consistent motion and natural pose correction (Ma et al., 27 Jun 2025).

• Sparse and Bandlimited Temporal Bases: For ambient/periodic motion, trajectory components are expressed via discrete cosine transforms or learned bandlimited MLP priors, supporting compactness and temporal coherence for phenomena such as leaf flutter or cyclical part motion (Shih et al., 2024, Ramasinghe et al., 2023).
• Deformation and Residual Fields: Hierarchical models split motion into coarse rigid transformations (neighborhood means / object-level) and fine local deformations (residual MLP decoders per anchor or primitive, sometimes conditioned on spatial features and view direction). This supports both articulated and non-rigid motion (Deng et al., 11 Jun 2025, Wu et al., 3 Jul 2025, Yao et al., 10 Jul 2025).
• Instance-Aware Semantic Tracking: Instance segmentation and semantic consistency over time can be enforced by supervision with temporally aligned masks and high-level language/model embeddings, improving decomposition, editing, and interpretability (Jiang et al., 2 Apr 2026).

3. Rendering, Optimization, and Losses

Dynamic scene rendering builds on differentiable volumetric compositing, adapted for time-varying geometry and appearance.

• Gaussian Splatting with Temporal Conditioning: At each time $t$, dynamic Gaussians are projected and composited following conditional means and covariances, often tile-wise for efficiency. Both appearance and alpha are potentially time- and view-dependent via spherical harmonics or harmonics-indexed by time-shifted bases (Yang et al., 2024, Ma et al., 27 Jun 2025, Yang et al., 2023).
• Loss Design: Training objectives typically comprise:
  • Photometric image reconstruction ($L_1$, SSIM)
  • Depth alignment to lidar or monocular priors ($L_{\text{depth}}$)
  • Semantic/instance alignment (per-instance mask, LM-derived embeddings, cross-entropy, KL divergence)
  • Temporal regularization: explicit velocity or temporal smoothness, inter-curve consistency (e.g., limiting the variation of per-primitive offsets for rigid objects), temporal self-supervision by motion propagation
  • Physically-based regularization: opacity as function of angle/distance, total-variation over model parameters, sparsity penalties (Ma et al., 27 Jun 2025, Deng et al., 11 Jun 2025, Yang et al., 2024, Jiang et al., 2 Apr 2026, Chen et al., 2023).
• Optimization: Models are optimized end-to-end (typically with Adam). Some methods jointly solve for static and dynamic part parameters, while others alternate stage-wise. Densification (splitting Gaussians in high-error areas) and pruning (dropping low-importances) ensure compactness and focus (Yang et al., 2024, Yao et al., 10 Jul 2025, Kong et al., 27 Feb 2025, Ma et al., 27 Jun 2025).

4. Dynamic-Static Separation, Compression, and Efficiency

Efficient dynamic modeling requires minimizing redundancy and cost in both storage and runtime.

• Dynamic-Static Decomposition: Methods such as BézierGS and DynaSplat separate scene elements into static and dynamic parts, typically using a combination of offset-variance statistics and 2D flow-consistency tests for robust classification. Only dynamic elements are sent through expensive temporal decoders or MLPs, reducing computation (Ma et al., 27 Jun 2025, Deng et al., 11 Jun 2025, Kong et al., 27 Feb 2025).
• Anchor/MLP Hierarchies: Using anchor points or grids with compact per-anchor features and offsets, memory and computation are minimized, enabling decoding of per-frame dynamic primitives as needed (SD-GS, EDGS, LocalDyGS) (Yao et al., 10 Jul 2025, Kong et al., 27 Feb 2025, Wu et al., 3 Jul 2025).
• Compression (CompGS++ and Related): By predicting temporal/spatial redundancy, quantizing parameters, and entropy coding residuals, compact representations for dynamic 3D scenes can achieve $\mu_i \in \mathbb{R}^4$0 compression with negligible fidelity loss (Liu et al., 17 Apr 2025).
• GPU-Accelerated Splatting and Pruning: All contemporary systems target parallel rasterization, tile-based depth sorting, and aggressive culling (time-marginal filtering) to achieve real-time rendering ($\mu_i \in \mathbb{R}^4$1100 FPS) at high spatial and temporal resolutions (Yang et al., 2024, Yang et al., 2023, Yao et al., 10 Jul 2025).

5. Semantic, Structured, and Relational Scene Modeling

Beyond geometry and appearance, dynamic scene models increasingly encode semantic and structural information:

• Instance- and Language-Aware Gaussians: Embedding each primitive with learnable semantic features, supervised by instance masks and LLM-derived sentence embeddings, supports temporally consistent 4D reconstruction, open-vocabulary querying, and robust segmentation (Jiang et al., 2 Apr 2026).
• Scene Graphs: Dynamic scene graphs formalize nodes (objects, anatomy, rooms) and time-evolving edges (relations, interactions) for high-level reasoning, tracking, and workflow modeling. Architectures process both spatial and temporal adjacency with GNNs and attention, yielding interpretable, prototype-based analysis of events (Holm et al., 16 Dec 2025, Kurenkov et al., 2023).
• Editing and Interaction: Models such as D-MiSo and Proactive Scene Decomposition enable explicit editing of object trajectories, scene composition, and decomposition by mapping Gaussians to mesh-like abstractions, or leveraging human-object interaction cues as drivers of decomposition granularity and as triggers for progressive online updates (Waczyńska et al., 2024, Li et al., 17 Oct 2025).

6. Benchmarks, Empirical Results, and Comparative Analysis

Dynamic scene modeling pipelines are evaluated on both synthetic (D-NeRF, NeRF-DS, HyperNeRF, PanopticSports) and real-world (Waymo Open Dataset, nuPlan, KITTI, N3DV, VRU Basketball, HOI4D, MHOI) benchmarks.

• Quantitative Performance: Contemporary methods achieve PSNR often exceeding 30 dB, SSIM $\mu_i \in \mathbb{R}^4$2, and LPIPS $\mu_i \in \mathbb{R}^4$3 on realistic dynamic test sets (Ma et al., 27 Jun 2025, Yang et al., 2024, Yao et al., 10 Jul 2025, Deng et al., 11 Jun 2025).
• Efficiency Gains: Memory usage can be reduced by 40–60%, with 2×–3× speedups in FPS, and real-time $\mu_i \in \mathbb{R}^4$4100–300 FPS, via memory-efficient anchor decomposition and dense pruning (Yao et al., 10 Jul 2025, Kong et al., 27 Feb 2025).
• Semantic and Workflow Modeling: Scene graph-based models yield interpretable, robust predictions, achieving high accuracy and F1 in surgical workflow and household object tracking under severe data scarcity (Holm et al., 16 Dec 2025, Kurenkov et al., 2023).
• Ablations and Limitations: Ablation studies confirm the necessity of hierarchical motion, semantic and temporal regularization; misclassification of subtle motion, anchor over/under-densification, and memory scaling for long videos remain open challenges (Yao et al., 10 Jul 2025, Ma et al., 27 Jun 2025, Deng et al., 11 Jun 2025).

7. Open Problems and Future Directions

Key unsolved challenges in dynamic scene modeling include:

• Scalability to extremely long or crowded scenes, mitigated via hierarchical seeding, learned 4D partitioning, and advanced compression (Yang et al., 2024, Liu et al., 17 Apr 2025).
• Non-rigid, aperiodic, or impulsive motion modeling—current DCT/bandlimited priors or local MLPs may fail under abrupt global dynamics (Shih et al., 2024, Kong et al., 27 Feb 2025).
• Explicit semantics and physical reasoning, with integration of high-level priors, object affordances, or interaction graphs.
• Generalization to monocular or partially observed scenarios, requiring more powerful priors or explicit amodal completion mechanisms (Kong et al., 27 Feb 2025, Wu et al., 3 Jul 2025).
• Real-time editing and simulation, robust online updates, and closed-loop integration with task-driven robotics and embodied AI.

Dynamic scene modeling thus encompasses a spectrum from pixel-accurate, high-frequency spatiotemporal reconstruction to structured, interpretable, and edit-friendly representations. State-of-the-art approaches demonstrate the viability of unified, efficient, and expressive techniques spanning Gaussian splatting, factorized neural fields, scene graphs, and hybrid representations, but scalability, interpretability, and support for a broad range of dynamic phenomena remain active research frontiers.