Incremental Local Radiance Field Hierarchy

• Incremental local radiance field hierarchies are systems that subdivide large-scale 3D scenes into compact, localized radiance fields for efficient reconstruction.
• They leverage hash-grid or tensor-factorized backends to optimize each local field, drastically reducing memory usage and computational overhead.
• This approach addresses monocular depth ambiguity and pose drift, achieving high-fidelity view synthesis and scalable, drift-free reconstructions.

An incremental local-radiance-field hierarchy is a system for large-scale 3D scene reconstruction that adaptively partitions space into a sequence of compact, locally defined radiance fields (RFs). This approach addresses key scalability, memory, and alignment challenges that arise when using neural radiance fields (NeRFs) for photorealistic synthesis across extended or unbounded trajectories, particularly from monocular video. Rather than modeling an entire scene with a single global NeRF—whose capacity and memory demands grow prohibitively with scene extent—an incremental hierarchy maintains a series of local hash-grid NeRFs or tensor-factorized radiance fields, each optimized for a limited spatial region and periodically "frozen" as the camera moves forward. Methods developed in (Syed et al., 20 Dec 2025) and (Meuleman et al., 2023) demonstrate that such hierarchies enable drift-free registration, bounded memory usage, and high-fidelity view synthesis for city-scale reconstructions and long unconstrained monocular input.

1. Motivation and Overview

The radiance-field reconstruction of extended or unbounded scenes from video encounters three principal roadblocks: (1) scale ambiguity in monocular depth leading to geometry artifacts; (2) pose-drift over long, unconstrained camera trajectories; and (3) intractable memory requirements and photometric inconsistencies in global scene representations. A global NeRF’s hash grid or tensor representation must span hundreds of meters, entailing unbounded parameter growth. Unstructured, large-baseline motion causes a global field to fail in capturing fine details or registering disparate parts.

Incremental local-radiance-field hierarchies partition the scene into a succession of spatially local RFs, each responsible for a region typically spanning ∼2×2×2 m after applying contraction mappings (cf. NeRF++). The current region is represented by an MLP with a hash-grid (Instant-NGP (Syed et al., 20 Dec 2025)) or TensoRF (Meuleman et al., 2023) backend. When the camera trajectory leaves the current region—detected via contracted coordinate criteria or spatial window overlap—a new local field is spawned, and optimization for the previous field ceases (i.e., the field is "frozen"). The hierarchy grows incrementally along the camera path, and older fields are not revisited or retrained, capping memory and compute.

2. Local Field Parameterization and Formalism

Each local radiance field is defined as an MLP with hash-grid or tensor-factorized parameterization:

• Hash-Grid MLP: $$g_{\phi_k} : (\mathbf{x}, \mathbf{d}) \mapsto (\sigma, c)$$ parameterized by $\phi_k$ for region $k$, where $\mathbf{x}\in\mathbb{R}^3$ is contracted to $\|\mathbf{x}\|_\infty \leq 1$, and $\mathbf{d}\in\mathbb{S}^2$ is the unit view direction (Syed et al., 20 Dec 2025).
• Tensor Factorization: TensoRF (Meuleman et al., 2023) with basis vectors for density and color queried at the contracted or shifted coordinates, followed by a light-weight MLP for view dependency.
• Each hash-grid uses $L=16$ tables of size $M\approx2^{19}$; the MLP has ~32k parameters (Syed et al., 20 Dec 2025).
• Only the current and immediately preceding fields require gradient storage, while frozen fields are used only for forward evaluation.

The spatial scope of each field is managed by a contraction function (as in NeRF++ or TensoRF), ensuring that even in unbounded world coordinates, each local region is bounded for computational efficiency.

3. Dynamic Allocation, Freezing, and Overlap Criteria

The system operates in a loop over sliding or expanding temporal windows:

• For each window of $N=32$ frames (Syed et al., 20 Dec 2025) or stage-bounded window (Meuleman et al., 2023), three phases occur:
  • Depth warm-up (fix pose & radiance, optimize depth).
  • Feature bundle adjustment (FBA) pose refine (fix depth & radiance, update poses).
  • Radiance fine-tune (fix depth & pose, optimize active local RF).
• After each iteration, it is checked whether the current active rays or pose trajectory exits the contracted unit cube of the field:

$$out_k = \frac{\left|\left\{ r : ||\mathbf{x}_r||_\infty > 1 \right\}\right|}{\text{number of rays}}$$

If $out_k > \tau$ with $\tau=0.80$ (Syed et al., 20 Dec 2025), the current field is "frozen" (gradients disconnected; optimizer states discarded), and a new field is allocated.

Overlap between sequential fields is enforced by (1) soft temporal supervision windows of $\Delta T \approx 30$ frames (Meuleman et al., 2023) and (2) an L2 handover loss aligning the predicted color on a thin shell near the unit-cube boundary:

$$\mathcal{L}_{\text{handover}} = \sum_{r : ||\mathbf{x}_r||_\infty \in [0.95, 1.05]} \| c_{k+1}(\mathbf{x}_r, \mathbf{d}_r) - c_k(\mathbf{x}_r, \mathbf{d}_r) \|_2^2$$

with $\lambda_h=1.0$.

4. Hierarchical Structure and Inference Mechanism

Although lacking a balanced spatial tree, the sequence $\{\mathcal{R}_1,\dots,\mathcal{R}_K\}$ forms a time-ordered partition of space. This "hierarchy" is sequential: each field covers the region traversed during its window, overlapping with adjacent fields for smooth handoff.

During inference (view synthesis or rendering), a given sample point $\mathbf{x}$ is mapped into each field’s contracted coordinates, and the earliest field $k$ for which $\|\mathbf{x}\|_\infty\leq 1$ is used to evaluate $g_{\phi_k}(\mathbf{x}, \mathbf{d})$. All other fields return zero density, yielding constant-time (O(1)) network selection per sample (Syed et al., 20 Dec 2025). This strategy prevents unnecessary computation over stale or irrelevant fields.

In (Meuleman et al., 2023), this overlapping-block mechanism also ensures that memory and optimization budget follows the camera’s progression, rather than accumulating with total scene size.

5. Integration with Depth and Pose Estimation

The incremental local-radiance-field hierarchy is tightly coupled with monocular depth prediction and pose refinement—a core factor in achieving drift-free reconstructions:

• Depth is predicted by a Vision Transformer (ViT) network trained for metric scale; pose is refined by multi-scale feature bundle adjustment (FBA), operating in learned descriptor space to overcome sparse-keypoint brittleness (Syed et al., 20 Dec 2025).
• The optimization objective integrates:

$$\mathcal{L} = \lambda_p \mathcal{L}_{\text{photo}} + \lambda_d \mathcal{L}_{\text{depth}} + \lambda_b\mathcal{L}_{\text{FBA}} + \lambda_f(\mathcal{L}^{\mathrm{fwd\_flow}} + \mathcal{L}^{\mathrm{bwd\_flow}})$$

where losses enforce photometric consistency (via current local RF output), depth alignment, pose coherence, and optical flow consistency (RAFT).

• Progressive training alternates depth warm-up, pose optimization, and radiance-field fine-tuning, ensuring mutual consistency among all components (Syed et al., 20 Dec 2025).
• Sliding temporal supervision windows and spatial field freezing ensure local pose errors do not propagate globally.

A similar progressive optimization strategy with pose initialization from previous frames, local windowed refinement, and coarse-to-fine grid upsampling is used in (Meuleman et al., 2023).

6. Memory Efficiency and Computational Scalability

Incremental hierarchies bound computational and memory overhead:

• Each hash-grid field has limited parameter count and VRAM footprint ($<$7 GB for up to $K\approx5–8$ fields on an A100; a monolithic NeRF would require $>$20 GB) (Syed et al., 20 Dec 2025).
• Only the (small) active field and its window need backward-pass activation storage and optimizer state at any time. Freezing reduces activation and moment buffer memory by ∼60 %.
• In (Meuleman et al., 2023), the core capacity and grid resolution of each TensoRF is reused for each local block, rendering the system’s per-frame memory demand almost constant even for long trajectories.
• Reconstruction proceeds without any need for global bundle adjustment or loop closure.

7. Empirical Performance and Comparative Analysis

Evaluations on large-scale datasets illustrate the practical impact:

• On Tanks and Temples, the hierarchy in (Syed et al., 20 Dec 2025) achieves Absolute Trajectory Error of 0.001–0.021 m (up to 18× lower than BARF and 2× lower than NoPe-NeRF) and sub-pixel Relative Pose Error, with photorealistic novel-view synthesis from an uncalibrated monocular RGB camera.
• In (Meuleman et al., 2023), local-field hierarchies outperform single-field and globally optimized methods by large margins, improving PSNR from 9.6 dB (BARF) to 22.85 dB (LocalRF) on registered poses, and from 11.8 dB to ≈20.4 dB when starting poses from scratch.
• Ablations confirm the necessity of both progressive optimization and field locality: removing progression or locality significantly degrades image fidelity and robustness to pose drift.

Incremental local-radiance-field hierarchies thus provide an effective, memory-bounded, and scalable solution for city-scale or long-trajectory 3D reconstruction in monocular video pipelines (Syed et al., 20 Dec 2025, Meuleman et al., 2023).