# SpectralSplats: Robust Differentiable Tracking via Spectral Moment Supervision

arXiv: https://arxiv.org/abs/2603.24036 · HTML: https://mlsanity.com/paper/2603.24036/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 41 references that are in the map.
- First posted on arXiv 25 Mar 2026.

## Builds on (most cited first, 30 of 34)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [Deformable 3D Gaussians for High-Fidelity Monocular Dynamic Scene Reconstruction](https://mlsanity.com/paper/2309.13101/) (2023)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [Dynamic 3D Gaussians: Tracking by Persistent Dynamic View Synthesis](https://mlsanity.com/paper/2308.09713/) (2023)
- [BARF: Bundle-Adjusting Neural Radiance Fields](https://mlsanity.com/paper/2104.06405/) (2021)
- [HexPlane: A Fast Representation for Dynamic Scenes](https://mlsanity.com/paper/2301.09632/) (2023)
- [Real-time Photorealistic Dynamic Scene Representation and Rendering with 4D Gaussian Splatting](https://mlsanity.com/paper/2310.10642/) (2023)
- [Soft Rasterizer: A Differentiable Renderer for Image-based 3D Reasoning](https://mlsanity.com/paper/1904.01786/) (2019)
- [DrivingGaussian: Composite Gaussian Splatting for Surrounding Dynamic Autonomous Driving Scenes](https://mlsanity.com/paper/2312.07920/) (2023)
- [SC-GS: Sparse-Controlled Gaussian Splatting for Editable Dynamic Scenes](https://mlsanity.com/paper/2312.14937/) (2023)
- [Spacetime Gaussian Feature Splatting for Real-Time Dynamic View Synthesis](https://mlsanity.com/paper/2312.16812/) (2023)
- [3D Menagerie: Modeling the 3D shape and pose of animals](https://mlsanity.com/paper/1611.07700/) (2016)
- [Street Gaussians: Modeling Dynamic Urban Scenes with Gaussian Splatting](https://mlsanity.com/paper/2401.01339/) (2024)
- [OmniRe: Omni Urban Scene Reconstruction](https://mlsanity.com/paper/2408.16760/) (2024)
- [3DGStream: On-the-Fly Training of 3D Gaussians for Efficient Streaming of Photo-Realistic Free-Viewpoint Videos](https://mlsanity.com/paper/2403.01444/) (2024)
- [HUGS: Holistic Urban 3D Scene Understanding via Gaussian Splatting](https://mlsanity.com/paper/2403.12722/) (2024)
- [Consistent4D: Consistent 360deg Dynamic Object Generation from Monocular Video](https://mlsanity.com/paper/2311.02848/) (2023)
- [DynMF: Neural Motion Factorization for Real-time Dynamic View Synthesis with 3D Gaussian Splatting](https://mlsanity.com/paper/2312.00112/) (2023)
- [GART: Gaussian Articulated Template Models](https://mlsanity.com/paper/2311.16099/) (2023)
- [FreGS: 3D Gaussian Splatting with Progressive Frequency Regularization](https://mlsanity.com/paper/2403.06908/) (2024)
- [SC4D: Sparse-Controlled Video-to-4D Generation and Motion Transfer](https://mlsanity.com/paper/2404.03736/) (2024)
- [SAPE: Spatially-Adaptive Progressive Encoding for Neural Optimization](https://mlsanity.com/paper/2104.09125/) (2021)
- [DeformGS: Scene Flow in Highly Deformable Scenes for Deformable Object Manipulation](https://mlsanity.com/paper/2312.00583/) (2023)
- [DynOMo: Online Point Tracking by Dynamic Online Monocular Gaussian Reconstruction](https://mlsanity.com/paper/2409.02104/) (2024)
- [6DOPE-GS: Online 6D Object Pose Estimation using Gaussian Splatting](https://mlsanity.com/paper/2412.01543/) (2024)

## Abstract (arXiv)

3D Gaussian Splatting (3DGS) enables real-time, photorealistic novel view synthesis, making it a highly attractive representation for model-based video tracking. However, leveraging the differentiability of the 3DGS renderer "in the wild" remains notoriously fragile. A fundamental bottleneck lies in the compact, local support of the Gaussian primitives. Standard photometric objectives implicitly rely on spatial overlap; if severe camera misalignment places the rendered object outside the target's local footprint, gradients strictly vanish, leaving the optimizer stranded. We introduce SpectralSplats, a robust tracking framework that resolves this "vanishing gradient" problem by shifting the optimization objective from the spatial to the frequency domain. By supervising the rendered image via a set of global complex sinusoidal features (Spectral Moments), we construct a global basin of attraction, ensuring that a valid, directional gradient toward the target exists across the entire image domain, even when pixel overlap is completely nonexistent. To harness this global basin without introducing periodic local minima associated with high frequencies, we derive a principled Frequency Annealing schedule from first principles, gracefully transitioning the optimizer from global convexity to precise spatial alignment. We demonstrate that SpectralSplats acts as a seamless, drop-in replacement for spatial losses across diverse deformation parameterizations (from MLPs to sparse control points), successfully recovering complex deformations even from severely misaligned initializations where standard appearance-based tracking catastrophically fails.