Motion-Adjusted Rendering Module

Updated 23 January 2026

Motion-Adjusted Rendering Module is an algorithmic framework that dynamically modulates rendering based on object, camera, or environmental motion cues.
It integrates techniques like physically-based motion blur, temporal exposure integration, and adaptive sampling to improve visual fidelity and computational efficiency.
Empirical results show significant enhancements in motion fidelity, PSNR, and real-time performance across gaming, neural rendering, SLAM, and VR/AR applications.

A Motion-Adjusted Rendering Module (MARM) is any algorithmic component or pipeline aimed at producing rendered images or video frames in which scene content, visual artifacts, or synthesis parameters are dynamically modulated based on object, camera, or environmental motion cues. In current research, the term encompasses diverse instantiations, from physically motivated motion-blur in rasterization pipelines to explicit bundle-adjusted exposure-path integration in neural and Gaussian representations. Modules in this class correct for motion-induced artifacts, improve motion fidelity, or enable novel control over dynamic visual content across gaming, neural rendering, SLAM, and VR/AR systems (Tan et al., 2022).

1. Architectural Principles and Core Pipeline Stages

The dominant architectural choices for MAVM design depend on the rendering paradigm but generally implement motion awareness in one or more of the following ways:

Physically-based motion blur: In hybrid rasterization/RT engines, real per-pixel velocity vectors $v(x)$ are estimated by differencing world-space geometry over the current and previous frames, projected into the camera plane. This information is stored in G-buffers and used both for spatially accurate post-process blur and for identifying occlusion events, which are then resolved via limited-depth hardware ray tracing to “reveal” background color in the blur cones of foreground objects (Tan et al., 2022).
Temporal exposure integration: Modules targeting photographic realism, such as BAD-NeRF and BAD-Gaussians, encode the real physical image formation process in which blurred pixel values $B(x)$ are integrals over the instantaneous radiance $I_t(x)$ as the camera (or scene) moves during an exposure. Discretizing the process, motion-adjusted rendering samples $n$ virtual sharp camera poses along a continuous SE(3) path within the exposure window, synthesizes sharp images under each, and averages the result (Wang et al., 2022, Zhao et al., 2024).
Explicit deformation or warping: In dynamic human or object modeling, deformation fields (articulated, learned, or ED-graph) transform sample points between canonical and posed or live coordinate frames, ensuring that the radiance query—whether NeRF-based, hash-grid, or 3DGS—is conditioned on correct spatial-temporal positioning (Kim et al., 2024, Jiang et al., 2023).
Spatio-temporal probability modeling: Recent 3DGS extensions employ learnable spatio-temporal masks and separated deformation fields to resolve ambiguity in multi-frame aggregation and to decouple dynamic from static structure at the level of Gaussian primitives (Li et al., 28 May 2025).
Motion-stratified adaptive sampling: Gear-NeRF assigns each (x,t) sample a “gear” level proportional to local motion intensity, and adaptively increases sampling granularity both in time and space in regions of high motion, enabling resource-efficient photo-realistic synthesis without global resolution increases (Liu et al., 2024).

Table 1 summarizes selected modules and their defining methodological attributes:

Module / Paper	Motion Source(s)	Temporal Modeling	Key Adjustment Mechanism(s)
Hybrid MBlur (Tan et al., 2022)	object, camera, silhouettes	G-buffer, velocity	Recursive RT, post-proc blur, compositing
BAD-NeRF (Wang et al., 2022)	camera trajectories	SE(3) keyposes, Lie	Exposure-path integration, BA
BAD-Gaussians (Zhao et al., 2024)	camera trajectories	SE(3) spline	Per-frame GS rendering, bundle-adjustment
MoCo-NeRF (Kim et al., 2024)	skeleton, non-rigid shape	pose sequence	LBS, radiance residual field
STDR (Li et al., 28 May 2025)	3DGS centroids	spatio-temp. mask	Factorized deform, mask, KL reg
Gear-NeRF (Liu et al., 2024)	segmentation + SAM	multi-gear hierarchy	Semantic embedding, adaptive sampling
Instant-NVR (Jiang et al., 2023)	SMPL + ED graph	DQB + MLP	Hybrid canonical-live warp, refinement

2. Mathematical Formulations of Motion Adjustment

Central to modern MARMs is an explicit, often physically motivated, mathematical model coupling image synthesis to scene/camera motion:

Velocity-based sampling: The per-pixel velocity vector is computed as

$v(x) = \frac{p_{\text{cur}} - p_{\text{prev}}}{\Delta t}$

and used both for blur kernel extent and for defining “inner blur” silhouettes, where motion reveals occluded background (Tan et al., 2022, Tan et al., 2022).

Shutter integration (BAD-NeRF, BAD-Gaussians): The observed color is modeled as

$B(x) = \frac{1}{\tau} \int_{0}^{\tau} I_t(x) \, dt \approx \frac{1}{n} \sum_{i=0}^{n-1} I_i(x)$

with each $I_i(x)$ generated by rendering under the interpolated camera pose $T_i$ over the exposure (Wang et al., 2022, Zhao et al., 2024).

Canon-to-live deformation for dynamic humans (MoCo-NeRF): A 3D world point $x_c$ in canonical space is mapped to live space at pose $\theta_t$ by LBS; the rendered radiance at each ray sample is then

$C_{\mathrm{final}}(r) = \sum_{m=1}^M w_m \left[c_m + \Delta c_m\right]$

with $w_m$ based on transmittance and $\Delta c_m$ produced by a radiance-residual field (Kim et al., 2024).

Spatio-temporal masks in dynamic 3DGS (STDR): Each Gaussian $i$ at $(x,t)$ is given a spatio-temporal weight

$M_i(x,t) = p_s^i(x)\, p_t^i(t)$

controlling its effective opacity and participation in each frame (Li et al., 28 May 2025).

Motion-adaptive sampling (Gear-NeRF): Given a motion score $g(x,t)$ , gear assignment $p(x,t)$ modulates the density of sub-samples per ray and the temporal granularity of features, with high-motion regions afforded exponentially higher sample rates (Liu et al., 2024).

3. Implementation Trade-offs and Integration

Engineering design of MARMs must balance quality versus latency, particularly in real-time applications:

Hybrid MBlur achieves high-fidelity motion blur in games at ~150–200 fps (RTX 2080Ti), with the ray-reveal pass raising per-frame cost by only ∼0.9 ms over pure post-processing (Tan et al., 2022).
BAD-Gaussians' explicit splatting and motion-blur exposure integration attains real-time synthesis (200+ FPS), outperforming NeRF-style methods by orders of magnitude in training speed and enabling real novel-view exploration (Zhao et al., 2024).
3DGS-based MARMs such as STDR and DynaGSLAM exploit separable MLPs, spatio-temporal masks, and Hermite motion splines to maintain both accuracy and interactive speed in complex, dynamic scenes (e.g., DynaGSLAM: ~347 ms mapping per frame, PSNR up to +4 dB over prior SLAM) (Li et al., 15 Mar 2025, Li et al., 28 May 2025).
Multi-entity scalability is addressed in frameworks such as MoCo-NeRF by leveraging shared multi-resolution hash encodings, identity codes, and global–local parameter partitioning, achieving efficient joint training over multiple dynamic subjects (Kim et al., 2024).

Critical settings—such as sample count $N$ , tile size $m$ , edge sensitivity, recursion depth for RT, opacities and mask regularization amplitudes, or per-gear step granularity—are scene-dependent and typically determined by empirical quality/speed balancing.

4. Applications and Empirical Outcomes

MARMs are deployed across distinct application domains:

Real-time game rendering: Hybrid MBlur eliminates post-process inner-blur artifacts and achieves near–ground-truth quality at interactive rates, especially in complex scenes with high object velocities (Tan et al., 2022, Tan et al., 2022).
3D scene reconstruction and deblurring: BAD-NeRF and BAD-Gaussians demonstrate robust recovery from severely motion-blurred input, yielding substantial gains in PSNR/SSIM and accurate pose recovery (ATE reduced by 60–80% compared to COLMAP) (Wang et al., 2022, Zhao et al., 2024).
Dynamic human and object modeling: In dynamic NeRF systems, MARM strategies capture fine-grained non-rigid deformations and motion-conditioned appearance (SurMo, MoCo-NeRF, H-NeRF), enabling temporally coherent, sharp, and physically plausible renderings of humans with clothing and hair (Kim et al., 2024, Hu et al., 2024, Xu et al., 2021).
Dynamic SLAM and online mapping: DynaGSLAM's motion-reconciled Gaussian management produces clean dynamic maps with far fewer “ghost” artifacts and high frame-level tracking accuracy versus anti-dynamic GS-SLAM alternatives (Li et al., 15 Mar 2025).
Adaptive resource allocation: Gear-NeRF's stratified sampling realizes state-of-the-art rendering and tracking accuracy while controlling computational load, supporting prompt-based object tracking and temporal upscaling across arbitrary views (Liu et al., 2024).

5. Limitations, Open Challenges, and Future Directions

Limitations common to current MARMs include:

Layer limitations: Most hybrid RT approaches recurse one or two layers only. Deep occlusion stacks (thin multi-layered geometry) are not fully resolved, and transparent/translucent media are not robustly handled (Tan et al., 2022).
Assumption of linear or low-order motion: Exposure-path integration models assume linear or cubic spline camera trajectories; aggressive or abrupt motion, nonrigid scene deformation, or rolling-shutter effects are more difficult to model (Wang et al., 2022, Zhao et al., 2024).
Parameter sensitivity and scene dependency: Edge thresholds, neighborhood dilation, blur radii, or sample counts require tuning for each scene type to avoid performance pathologies (oversmoothness, ringing, or excessive cost) (Tan et al., 2022).
Physical realism versus computational cost: High-fidelity reconstructions (e.g., full distributed RT motion-blur ground truth at 200 spp) remain out of reach for interactive pipelines; MARMs trade sharpness and semi-transparency for interactive performance (Tan et al., 2022).

Emerging research seeks to address these with:

More expressive motion priors and deformation fields, potentially learned end-to-end from video (Guo et al., 7 Nov 2025, Hu et al., 2024).
Integration of semantic cues (segmentations, object classes, interactions) to further guide adaptive sampling and mask stratification (Gear-NeRF, STDR) (Liu et al., 2024, Li et al., 28 May 2025).
Physically-based handling of transparency and complex BRDF interactions, as in Gaussian Splashing with per-kernel normals and surface-aligned material attributes (Feng et al., 2024).
Efficient multi-layer and volumetric RT, and higher-order motion models for immersive VR/AR content with reduced artifacting under extreme motion.

6. Representative Performance Metrics

Evaluations are task-dependent but center on photometric and perceptual fidelity, pose/trajectory accuracy, and computational efficiency:

Paper	Task	Notable Metrics	Baseline	With Module
(Tan et al., 2022)	Game motion blur	FPS (PP/Hybrid): 295/205; Ray cost: ∼0.9ms	Post-proc.	Hybrid MBlur
(Zhao et al., 2024)	Deblur 3DGS	PSNR: 36.95, SSIM +0.04, LPIPS halved vs BAD-NeRF	BAD-NeRF	BAD-Gaussians
(Li et al., 15 Mar 2025)	SLAM-mapping	PSNR+3–4dB, DynaPSNR+15, SSIM→0.95+	Static/anti-	DynaGSLAM
(Li et al., 28 May 2025)	Dynamic 3DGS	PSNR +0.68 (D-NeRF), +0.26 (SC-GS), SSIM +, LPIPS–	DeformGS etc.	+STDR
(Kim et al., 2024)	Dynamic human NeRF	Multi-sbj.: 6 in ~2 hrs, 1–2 hr per subject	HumanNeRF	MoCo-NeRF
(Liu et al., 2024)	Free-viewpoint NeRF	Technicolor PSNR: 32.21 (SOTA), mIoU: 97.4	HyperReel	Gear-NeRF

Combined, these demonstrate the capacity of state-of-the-art MARMs to bridge the divide between fast but artifact-prone postprocessing and slow, physically accurate but impractical all-ray solutions, yielding both rapid and high-fidelity results adaptable to a variety of 3D and video synthesis settings.

References:

(Tan et al., 2022, Wang et al., 2022, Zhao et al., 2024, Kim et al., 2024, Li et al., 28 May 2025, Li et al., 15 Mar 2025, Xu et al., 2021, Tan et al., 2022, Jiang et al., 2023, Liu et al., 2024, Feng et al., 2024, Hu et al., 2024, Guo et al., 7 Nov 2025).