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AdaGaR: Adaptive Gabor Representation for Dynamic Scene Reconstruction

Jiewen Chan, Zhenjun Zhao, Yu-Lun Liu

arXiv:2601.00796v1cs.CV

TL;DR

Monocular dynamic-scene reconstruction must capture detailed appearance while preserving continuous motion, but Gaussian detail limits, Gabor energy instability, and insufficient temporal constraints complicate this goal. AdaGaR combines adaptive Gabor primitives, spline-based temporal regularization, and adaptive initialization; it reports state-of-the-art Tap-Vid performance and generalization across several tasks.

  • Problem

    Monocular dynamic-scene reconstruction must capture high-frequency appearance while maintaining temporal continuity, challenges existing methods face through Gaussian low-pass filtering, Gabor energy instability, and missing temporal constraints.

    Source: §1 · pp. 1–2

  • Method

    AdaGaR combines learnable Adaptive Gabor Representation, Cubic Hermite Splines with Temporal Curvature Regularization, and initialization using depth, tracking, and foreground masks.

    Source: §1 · p. 2

  • Results

    AdaGaR achieves state-of-the-art video reconstruction on Tap-Vid and generalizes to frame interpolation, depth consistency, video editing, and stereo view synthesis.

    Source: §1 · p. 2, §6 · p. 8

  • Takeaways & Limitations

    The reported results support AdaGaR as a unified approach to modeling frequency detail and temporal continuity in explicit dynamic representations.

    Source: §1 · p. 2, §6 · p. 8

    Spline-based motion modeling assumes smooth trajectories and may misalign under abrupt or highly nonlinear motion; energy constraints may also produce high-frequency oscillations.

    Source: §6 · p. 8

Abstract

from arXiv · show

Reconstructing dynamic 3D scenes from monocular videos requires simultaneously capturing high-frequency appearance details and temporally continuous motion. Existing methods using single Gaussian primitives are limited by their low-pass filtering nature, while standard Gabor functions introduce energy instability. Moreover, lack of temporal continuity constraints often leads to motion artifacts during interpolation. We propose AdaGaR, a unified framework addressing both frequency adaptivity and temporal continuity in explicit dynamic scene modeling. We introduce Adaptive Gabor Representation, extending Gaussians through learnable frequency weights and adaptive energy compensation to balance detail capture and stability. For temporal continuity, we employ Cubic Hermite Splines with Temporal Curvature Regularization to ensure smooth motion evolution. An Adaptive Initialization mechanism combining depth estimation, point tracking, and foreground masks establishes stable point cloud distributions in early training. Experiments on Tap-Vid DAVIS demonstrate state-of-the-art performance (PSNR 35.49, SSIM 0.9433, LPIPS 0.0723) and strong generalization across frame interpolation, depth consistency, video editing, and stereo view synthesis. Project page: https://jiewenchan.github.io/AdaGaR/

1. Introduction

Monocular dynamic-scene reconstruction must preserve high-frequency appearance while maintaining temporal continuity, but existing representations have limitations in detail, energy stability, or motion continuity. AdaGaR combines frequency-adaptive primitives, spline-based temporal regularization, and adaptive initialization; the paper reports state-of-the-art Tap-Vid results and generalization across several tasks.

Motivation

  • Monocular dynamic-scene reconstruction must jointly preserve high-frequency textures and maintain smooth motion over time.These requirements are presented as the key difficulty of reconstructing real-world scenes from monocular video.Source: §1 · p. 1
  • Gaussian primitives suppress high-frequency detail, Gabor-like modulation can destabilize energy and rendering, and missing temporal constraints can cause discontinuities and geometric tearing.The motion artifacts are especially noted under rapid motion or occlusions.Source: §1 · pp. 1–2

Approach

  • AdaGaR couples learnable Adaptive Gabor Representation with Cubic Hermite Splines and Temporal Curvature Regularization, and uses adaptive initialization to bootstrap stable geometry.The initialization combines depth estimation, point tracking, and foreground masks; the contributions claim it improves training efficiency and final reconstruction quality.Source: §1 · p. 2

Results

  • AdaGaR achieves state-of-the-art video reconstruction on Tap-Vid and generalizes to frame interpolation, depth consistency, video editing, and stereo view synthesis.The introduction identifies these as the evaluation outcomes shown in Fig. 1.Source: §1 · p. 2

2. Related Work

Prior work spans dynamic Gaussian models, frequency-aware rendering, spline-based temporal methods, canonical video representations, and monocular depth and motion priors. AdaGaR differentiates itself by combining adaptive Gabor primitives and temporal regularization with joint depth-, motion-, and segmentation-informed initialization.

Dynamic 3D Gaussian Splatting

  • Dynamic Gaussian methods use deformation models and temporal strategies, while SplineGS applies Cubic Hermite splines in multi-view settings; AdaGaR combines splines and Gabor primitives for monocular video without pose estimation.AdaGaR adds Temporal Curvature Regularization for physically plausible motion.Source: §2 · p. 2

Frequency-Adaptive Rendering

  • Prior Gabor rendering work targets static scenes with fixed frequencies, whereas AdaGaR uses learnable frequency weights in dynamic video and can degrade gracefully to standard Gaussians.Figure 2 illustrates the adaptive Gaussian-to-Gabor progression and its coarse-to-fine reconstruction role.Source: §2 · p. 2, Figure 2 · p. 3

Temporal Modeling and Spline Representations

  • Unlike smoothness implicit in architectures or training, AdaGaR explicitly enforces temporal smoothness through second-order Temporal Curvature Regularization.The related work describes this explicit constraint as supporting physically plausible motion with geometric interpretability.Source: §2 · p. 2

Video Representations and Canonical Spaces

  • Canonical-space methods support temporally consistent processing, while AdaGaR uses orthographic camera coordinates to avoid pose estimation and retains explicit 3D structure.Its Gabor primitives are used for high-frequency preservation and varied applications.Source: §2 · p. 2

Monocular Depth and Motion Estimation

  • Unlike approaches using depth and tracking signals independently, AdaGaR's adaptive initialization jointly reasons about depth, motion, and segmentation.The related-work passage links this joint reasoning to geometrically and temporally consistent initialization.Source: §2 · p. 3

3. Preliminary: 3D Gaussian Splatting

The preliminary section describes 3D Gaussian Splatting as a scene representation built from parameterized Gaussian primitives and rendered by front-to-back blending. It motivates Gabor kernels as a way to address the detail limitation of a single Gaussian.

3D Gaussian Splatting

  • 3D Gaussian Splatting represents a scene as parameterized Gaussian primitives with centers, covariances, opacities, and colors.The passage defines each primitive's center in R^3, covariance in R^3×3, opacity in [0, 1], and color.Source: §3 · p. 3
  • Rendering projects Gaussians onto the image plane and accumulates their colors through front-to-back blending.Source: §3 · p. 3
  • A single Gaussian acts as a low-pass filter that constrains high-frequency texture detail, motivating Gabor kernels as periodic Gaussian extensions.Source: §3 · p. 3

4. Method

AdaGaR represents monocular video with adaptive Gabor primitives and spline-interpolated motion, coupling frequency-adaptive detail with temporal smoothness. Its method also combines multi-objective supervision with an adaptive initialization for temporally coherent geometry.

4.1. Overview

  • AdaGaR models video as dynamic Adaptive Gabor primitives in orthographic camera coordinates, with spline-interpolated motion and frequency-adaptive detail capture.The representation couples learnable frequency weights and energy compensation with temporal curvature regularization.Source: §4.1 · p. 3, §4.2 · pp. 3–4

4.2. Adaptive Gabor Video Representation

  • Weighted sinusoidal waves modulate a Gaussian envelope, allowing primitives to capture directional textures and high-frequency detail.Learnable amplitude weights adjust frequency components, while their directions align with the Gaussian’s spatial orientation.Source: §4.2 · pp. 3–4
  • Adaptive Gabor adjusts intensity using wave energy and degrades naturally to a Gaussian as frequency weights approach zero.A compensation term maintains energy stability during the transition between Gaussian and frequency-modulated Gabor forms.Source: §4.2 · p. 4, Figure 4 · p. 5

4.3. Temporally Dynamic Adaptive Gabor

  • Cubic Hermite splines interpolate primitive motion between keyframes; an auto-slope monotone gate and curvature penalty constrain temporal changes.The curvature term penalizes second-order energy over time, while the interpolation smoothness coefficient controls curve flatness and prevents reverse oscillations at keyframes.Source: §4.3 · pp. 4–5

4.4. Optimization

  • Optimization combines RGB reconstruction, optical-flow consistency, depth supervision, and temporal curvature regularization.Flow supervision aligns projected primitives with tracked 2D trajectories using visibility-weighted L1 loss; depth estimates provide scale- and shift-invariant geometric priors.Source: §4.4 · pp. 5–6

4.5. Adaptive Initialization

  • Adaptive initialization fuses cues to create a dense, temporally coherent point cloud, adjusting sampling to scene motion and depth distribution.Grid coverage and boundary-aware compensation complement temporal-spatial sampling; the resulting initialization reduces early-stage flickering.Source: §4.5 · p. 6

5. Experiment

On Tap-Vid DAVIS, AdaGaR outperforms baselines across PSNR, SSIM, and LPIPS, with further evaluations covering depth consistency, interpolation, editing, and stereo synthesis. Ablations compare its Adaptive Gabor Representation, spline interpolation, curvature regularization, and initialization.

5.1. Evaluation

  • Evaluation uses Tap-Vid DAVIS [65] with PSNR, SSIM, and LPIPS; training takes 500 warm-up iterations plus 10K main iterations and 90 minutes per video sequence on an RTX 4090.Control points are updated every 100 iterations.Source: §5.1 · p. 6
  • AdaGaR improves PSNR by 6.86 dB over the previous best method [76] and outperforms baselines across PSNR, SSIM, and LPIPS on Tap-Vid DAVIS [65].The visual comparison also reports sharper textures and coherent motion than MLP-based representations.Source: Table 1 · p. 6, §5.1 · p. 6

5.2. Applications

  • Depth remains stable across frames, while Hermite-spline interpolation preserves texture and avoids boundary artifacts in intermediate frames.The depth comparison reports reduced flicker and boundary misalignment versus per-frame optimizers; interpolation queries splines at fractional timestamps.Source: §5.2 · p. 6, Figure 6 · p. 7, Figure 7 · p. 8
  • Canonical-space editing remains temporally coherent, and the explicit 3D representation supports stereo synthesis from monocular input with plausible geometry.The editing comparison describes reduced style drift and flicker; stereo synthesis is reported with improved disparity consistency.Source: §5.2 · p. 6, Figure 8 · p. 8, Figure 9 · p. 8

5.3. Ablation Study

  • With the same 1M primitives, Adaptive Gabor Representation gives the best PSNR, SSIM, and LPIPS among Gaussian, standard Gabor, and adaptive Gabor configurations.The ablation reports improved high-frequency detail and energy stability; Table 2 attributes the Gabor comparison to the compensation term b.Source: §5.3 · p. 6, Table 2 · p. 7
  • Cubic Hermite Splines outperform B-Spline and Cubic Spline across metrics, with smoother trajectories and preserved dynamic details.The table caption notes that standard Cubic Spline suffers from trajectory oscillations and identifies explicit velocity control as essential for smooth motion.Source: §5.3 · pp. 6–7, Table 3 · p. 7
  • Without temporal curvature regularization, interpolation shows motion artifacts and tearing; with it, interpolation is smoother and more stable.The comparison is reported as confirming the necessity of explicit curvature control.Source: §5.3 · pp. 7–8
  • Compared with random initialization, adaptive initialization produces denser, temporally coherent initial geometry, reducing flicker and improving early reconstruction quality.Source: §5.3 · p. 8

6. Conclusion

AdaGaR combines adaptive Gabor primitives with spline-based curvature control to capture detail and maintain continuity; the conclusion also reports ablation outcomes and notes motion and frequency limitations.

6. Conclusion

  • Curvature regularization produces smooth, artifact-free interpolation, whereas omitting it leads to motion artifacts from trajectory oscillations.The method constrains second-order derivatives for temporal consistency.Source: Figure 10 · p. 8
  • 6.78 dB improvement is reported for adaptive initialization based on depth, tracking, and masks, which yields sharper reconstruction.Without motion-aware initialization, primitives are poorly distributed and details are blurred.Source: Figure 11 · p. 8
  • AdaGaR extends Gaussian primitives to capture high-frequency details while maintaining geometric and motion continuity with Cubic Hermite Splines and Temporal Curvature Regularization.The conclusion reports state-of-the-art performance on Tap-Vid DAVIS and generalization across frame interpolation, depth consistency, video editing, and stereo synthesis.Source: §6 · p. 8
  • The spline-based motion model assumes smooth trajectories and may misalign under abrupt or highly nonlinear motion; frequency constraints may also cause high-frequency oscillations.The authors propose adaptive temporal control points and motion-aware frequency modulation as future work.Source: §6 · p. 8

A.1. Straight-Through Hard Sigmoid for Frequency Weights

  • Frequency weights are clipped to [0, 1] in the forward pass, while a sigmoid gradient surrogate supports backpropagation and stable training.The bounded forward pass prevents unbounded frequency growth that could destabilize energy balance; the backward pass enables gradient-based optimization and avoids exploding gradients.Source: §A.1 · p. 14

B. Proof of Adaptive Degradation to Gaussian

The proof describes Adaptive Gabor representation as naturally reducing to a traditional Gaussian when all frequency weights vanish.

B. Proof of Adaptive Degradation to Gaussian

  • Adaptive Gabor representation naturally degrades to a traditional Gaussian when all frequency weights vanish.This limiting behavior demonstrates its adaptive capability between Gaussian and Gabor modes.Source: B. Proof of Adaptive Degradation to… · p. 14

B.1. Mathematical Formulation

  • The proof recalls the adaptive modulation function from Equations (4) and (5), including a compensation term b.The supplied formulation identifies b as the compensation term but does not state its expression.Source: §B.1 · p. 14
  • The formulation uses γ in [0, 1] to control degradation smoothness and 1/N to normalize a weighted average of multiple waves.Source: §B.1 · p. 14

B.2. Degradation to Gaussian

The section considers the limit in which every frequency weight approaches zero and proceeds through the compensation and modulation terms.

B.2. Degradation to Gaussian

  • The degradation analysis considers the limiting case in which all frequency weights approach zero.Source: §B.2 · p. 14
  • The derivation next substitutes that limiting case into the compensation term.Source: §B.2 · p. 14
  • The derivation then evaluates the modulation term in the same limit.Source: §B.2 · p. 14

B.3. Implication for Opacity

The opacity argument identifies a condition under which the Gabor-modulated opacity recovers the traditional Gaussian primitive.

B.3. Implication for Opacity

  • The section invokes the definition of Gabor-modulated opacity in deriving the recovery result.Source: §B.3 · p. 15
  • When Sadap(x) = 1, the derivation recovers the opacity expression under consideration.Source: §B.3 · p. 15
  • That recovered form is exactly the traditional Gaussian primitive without frequency modulation.Source: §B.3 · p. 15

B.4. Conclusion

The Adaptive Gabor representation transitions from a standard Gaussian when frequency is unnecessary to frequency-enhanced Gabor modes when high-frequency detail is needed, maintaining energy stability across scene regions.

B.4. Conclusion

  • As ω_i approaches 0, the representation degrades to a standard Gaussian; when ω_i > 0, it transitions to frequency-enhanced Gabor modes while maintaining energy stability.The passage describes this adaptation across scene regions with varying frequency characteristics.Source: §B.4 · p. 15

C. Additional Visual Comparisons and Results

Additional visual comparisons report preserved high-frequency textures and temporal consistency across challenging dynamic scenes. Interactive results cover frame interpolation, video editing, and stereo view synthesis.

C. Additional Visual Comparisons and Results

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