Spherical Harmonics

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4 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

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Latest papers 18

Sep 30, 2026cs.LG

A library for differentiable signal processing and machine learning on the sphere

The two-dimensional sphere embedded in three-dimensional Euclidean space S2, plays a central role in a variety of scientific and engineering domains, including geophysics, planetary science, geodesy, atmospheric physics, quantum chemistry, cosmology, and virtual reality, among many others. As machine learning increasingly permeates these fields, the demand grows for robust tools that process and model functions on the sphere, while respecting the inherent topological and symmetry properties of the domain. We present torch-harmonics, a comprehensive library that offers efficient, differentiable implementations of advanced signal processing and machine learning (ML) methods for spherical data. These include the spherical harmonic transform (SHT), the spherical analogue of the Fourier transform, vector spherical harmonics, discrete-continuous and spectral convolutions, as well as both global and neighborhood spherical attention mechanisms. Beyond traditional representations, torch-harmonics provides the building blocks for state-of-the-art spherical ML architectures such as spherical transformers in order to enable scalable, rotationally-aware learning and inference in modern scientific and engineering applications.

Thorsten Kurth, Max Rietmann, Mauro Bisson +6

NVIDIA Corporation · California Institute of Technology

Spherical Harmonics Sphere Spherical Latent Space Harmonization Graph Signal Processing

Sep 30, 2026cs.CV

Invariant Shape Analysis of Surfaces with Spherical Topology

Spherical harmonic descriptors of closed 3D shapes depend on the parameterization, the pose and the scale of the surface, and the standard rotation-invariant reductions, the power spectrum and the bispectrum, discard the relative orientation of the harmonic bands and cannot distinguish a shape from its mirror image. We construct a descriptor that removes all three dependencies exactly and loses nothing else: a conformal parameterization normalized by its conformal barycenter, followed by polynomial invariants of the rotation group. Identifying each harmonic band with a binary form turns the rotation quotient into classical invariant theory and makes reflections visible as the sign of an invariant, so chirality is recorded. The descriptor is complete for the truncated expansion, stable in the orbit distance, and comes with numerical diagnostics. Benchmarks confirm the guarantees, and on bilateral anatomical structures the descriptor separates mirror-image pairs from asymmetric pairs, which parity-blind descriptors cannot.

T. Shaska, M. -R. Siadat

Spherical Harmonics Statistical Shape Model Symmetry Surface Representation

Sep 28, 2026q-bio.QM

An integrated geometric quantification and shape analysis framework for axillary lymph node metastasis in breast cancer patients

Quantitative characterization of lymph node morphology is important for assessing axillary lymph node metastasis in breast cancer. However, surfaces reconstructed from computed tomography (CT) segmentation may contain geometric and topological defects that compromise subsequent analysis, while conventional shape descriptors predominantly characterize global morphology. To address these issues, we developed an integrated framework combining topology-aware surface processing with multi-resolution spherical harmonic (SH) analysis of CT-derived axillary lymph nodes. The processing pipeline produced topology-valid genus-0 surfaces with improved mesh quality, which were then represented at multiple SH degrees and characterized using 20 predefined geometric feature families. Geometric fidelity increased with SH degree, whereas predictive performance peaked at intermediate resolutions. Preferred SH degree also differed across feature families. A family-specific mixed-resolution model achieved an AUC of 0.918, compared with 0.884 for the conventional PyRadiomics Shape14 baseline, corresponding to an improvement of 0.0344. Controlled perturbation experiments showed that higher SH degrees transmitted more fine-scale geometric variation and yielded lower stability of curvature-based predictions. Representative geometric descriptors provided interpretable characterization of metastasis-associated surface morphology. Independent validation further supported the framework's transportability: label-free replication in a multicenter lymph node cohort reproduced the family-specific resolution effects, while a labeled LIDC-IDRI lung-nodule experiment reproduced the resolution-dependent relationship between SH degree and predictive performance. Altogether, the framework provides a topology-valid basis for quantitative characterization of lymph node morphology and metastasis-associated imaging phenotypes.

Zixi Yi, Limeng Qu, Gary P. T. Choi

School of Mathematics and Statistics, Central South University, Changsha, Hunan, China · Department of General Surgery, The Second Xiangya Hospital, Central South University, Changsha, Hunan, China · Clinical Research Center for Breast Disease in Hunan Province, Changsha, Hunan, China +1

Tumor Morphometric Analysis Multicenter Evaluation Spherical Harmonics

Sep 24, 2026cs.CV

Only What Was Seen: Observation-Gram Compaction of View-Dependent Appearance in 3D Gaussian Splatting

Most of the memory of a 3D Gaussian Splatting model holds spherical-harmonic colour coefficients, yet each Gaussian is seen only from the narrow cone of directions of the training cameras. We turn this into a distortion metric that other compressors can adopt: a per-Gaussian observation Gram matrix, accumulated from viewing directions and blending weights, is the exact first-order map from coefficient changes to squared image error and needs only the model and the camera poses. Under it, degree reduction becomes a closed-form projection that generalises truncation, degree allocation a Lagrangian rate-distortion problem, and vector quantisation the matrix-weighted Lloyd algorithm, of which Compressed3D's quantiser is the scalar case. Swapped into Compressed3D with everything else unchanged, the metric raises PSNR by +0.49 dB before fine-tuning, with SSIM and LPIPS following, and at matched rate still gains +0.32 dB without a single training image. A training-free stack built on the metric alone is 15% smaller than the image-free GSICO at equal quality on Mip-NeRF 360.

Krzysztof Pietroszek

Moholo Inc.

Sparse-View Spherical Harmonics Distortion 3D Generation

Sep 23, 2026cs.CV

GaussPDE: Graph-Based Partial Differential Equation-Driven Rendering for 3D Gaussian Splatting

We present GaussPDE, a framework that injects physically structured partial differential equation (PDE) dynamics into pretrained 3D Gaussian scenes without mesh extraction, voxelization, or retraining. Our key observation is that PDE rendering requires not only accurate appearance, but also a reliable discrete computational domain. We therefore first introduce camera-aware regularization during 3DGS reconstruction to suppress camera-near floaters and oversized primitives that would create unstable graph topology. We then construct an active Gaussian graph using covariance-aware distances and opacity, appearance, and boundary-aware conductance, enabling mass-weighted graph Laplacian PDE evolution directly over Gaussian primitives. The evolving scalar PDE state is coupled back to rendering by modifying the direct-current spherical harmonic color coefficients while preserving geometry, opacity, and view-dependent rendering behavior. Experiments on real and synthetic scenes show that GaussPDE produces stable, controllable, and spatially coherent dynamic visualizations, with reduced cross-boundary leakage compared with baselines.

Haoyuan Yue, Fengyuan Ye, Ziyin Li

Department of Physics, Westlake University, Hangzhou, China · The Chinese University of Hong Kong, Shenzhen, China · Department of Accounting, Xi’an Jiaotong-Liverpool University, Suzhou, China

3D Gaussian Differentiable Rendering Spherical Harmonics Partial Differential Equations Visual Analytics

Sep 21, 2026cs.SD

Fast Time-Varying Exponentiated Convolution Methods for Generative Direction Dependent Reverberation

Spherical harmonic encoded acoustic sound-fields capture directional characteristics of room impulse responses that are useful for accurate spatial audio reproduction. However, high costs of multi-microphone measurements and numerical simulations motivate alternative data-set augmentation and synthetic data generation methods that supplement small collections. This paper introduces time-varying exponentiated convolution methods that transform both Gaussian noise and impulse responses into reverberation and modified spectral-decay fields respectively. We derive two recursive and fast convolution algorithms that extend into the spherical harmonic domain, model smooth reverberation time distributions with non-stationary Gaussian processes, and realize an optimal filter design. Experiments evaluate computational performance, and validate out-of-distribution generated impulse responses.

Yuancheng Luo

NuSpace Audio, Cambridge, MA, USA

Reverberation Spatial Audio Acoustic Spherical Harmonics Modern Generative Audio Models Convolutional

Sep 14, 2026cs.CV

NOVA-GS: Noise-Aware View-Consistent Gaussian Splatting for Low-Light Novel View Synthesis

Reconstructing 3D scenes under real-world low-light conditions remains challenging due to severe sensor noise, low signal-to-noise ratios, and degraded photometric consistency, which destabilize geometry estimation and novel view synthesis. Existing approaches often rely on well-lit reference data for reliable Structure-from-Motion (SfM) initialization under degraded inputs or apply per-view enhancement methods that introduce cross-view inconsistencies. To address these limitations, we propose \textbf{NOVA-GS}, a unified noise-aware framework for low-light 3D Gaussian Splatting that subsumes enhancement, denoising, and geometry optimization within a single process. Our method leverages VGGT-based feed-forward estimation to obtain robust camera poses and geometry directly from degraded inputs, eliminating the need for SfM. Building on this initialization, NOVA-GS integrates three coupled components: a structure-aware enhancement module for exposure correction, a self-supervised denoising module with blind-spot masking for pseudo-supervision, and a consistency-driven Gaussian Splatting optimization enforcing cross-view geometric coherence. We further introduce a noise-guided spherical harmonic regularization to suppress view-dependent artifacts in noisy regions. Extensive experiments on diverse real-world low-light datasets demonstrate improved geometric fidelity, color consistency, and robustness without requiring paired supervision or well-lit references. https://shaurya2524.github.io/nova-gs/

Shaurya Pavan A, Vemunuri Divya Madhuri, Yash Pradeep Gawande +1

Indian Institute of Technology Madras

Novel View Synthesis Gaussian Splatting Spherical Harmonics

Jul 16, 2026cs.CV

Compression of 3D Gaussian Splatting Data Using GPU-friendly Graphics Texture Coding

Techniques for modeling 3D scenes from image collections, such as 3D Gaussian Splatting (3DGS), are capable of generating high-quality novel views by leveraging graphics primitives with view-dependent appearance. In 3DGS, spherical harmonic (SH) are employed to model view-dependent color, resulting in a large number of SH coefficients per primitive and large memory requirements. While compression approaches have been proposed to mitigate this problem, they do not exploit the capabilities of modern Graphics Processing Units (GPUs) for parallel decoding and rendering. In this paper, we propose a method for compressing SH color coefficients using texture compression schemes specifically designed for efficient parallel GPU decoding and supported by dedicated hardware acceleration. It is shown that those methods can compress color coefficients more effectively than 2D textures by exploiting the fact that primitives can be locally grouped and reordered according to color. Furthermore, we introduce a bit-rate control strategy that preserves random access, enabling large-scale parallelization without compromising rendering performance. Experimental results using BC1 and BC7 texture compression formats show that GPU-based decompression can be achieved with negligible or imperceptible degradation in the visual quality of rendered 3DGS scenes.

Amir Said, Randall Rauwendaal

Qualcomm AI Research San Diego, CA, USA · Qualcomm Graphics Research Boulder, CO, USA

Spherical Harmonics Cpu-Gpu Hybrid Designs Data Compression Methods

Jul 7, 2026cs.RO

EAGOR: Embodied Reasoning in Omni-direction

Omni-directional (360°) cameras provide embodied agents with a holistic view of their surroundings, making them suited for directional reasoning in tasks such as navigation and object search. Existing Vision Language Models (VLMs) project 360° observations to 2D equirectangular projection (ERP) images and process them using architectures designed for perspective images. However, they ignore the spherical nature of 360° observations, where each pixel represents a viewing direction relative to the agent. Consequently, their direction estimates often become inconsistent under camera view transformations caused by agent motion. This limitation is particularly critical for map-free navigation, where the agent must continuously estimate the target direction in its egocentric frame. We propose EAGOR, a training-free, geometry-aware framework for embodied 360° directional reasoning. Instead of predicting target directions as ERP image coordinates, EAGOR formulates directional reasoning as recursive Bayesian estimation directly on the sphere. It maintains a continuous belief over target directions and propagates it equivariantly under agent motion without training the backbone VLMs. To achieve this, we introduce the Spherical Harmonic Belief Field (SH-BF), whose spherical harmonic representation provides a globally defined, rotation-aware basis for directional estimation on the spherical manifold. This formulation eliminates ERP seam discontinuities, latitude distortions, and interpolation errors. We evaluate EAGOR on two benchmark datasets and real-world experiments with a legged robot across directional reasoning tasks. EAGOR consistently outperforms existing methods, achieving average relative gains of +34.4% and +45.6% on HOS and OSR-Bench, respectively, while improving navigation success by +14.6%, reducing step count by 17.7%, and lowering mean angular error by 24.5%.

Shriram Damodaran, Soumyaratna Debnath, Yan Wu +2

EmPACT Lab, NTU Singapore · Institute for Infocomm Research, A*STAR Singapore

Egocentric Vision Spherical Harmonics

Jul 1, 2026cs.LG

Spin-Weighted Spherical Harmonics Enable Complete and Scalable $\mathrm{E}(3)$ -Equivariant Networks

\mathrm{E}(3)

-equivariant networks are promising for 3D atomistic system modeling, yet their scalability is limited by the

O(L^6)

complexity of the Clebsch-Gordan Tensor Product (CGTP). The recently proposed Gaunt Tensor Product (GTP) reduces the complexity but is unable to capture the antisymmetric paths, resulting in incomplete expressivity. In this work, we present SpinGTP, an approach to overcome the GTP incompleteness by generalizing from scalar functions to Spin-Weighted Spherical Harmonics (SWSH). By relying on the algebraic properties of SWSH, SpinGTP recovers the missing antisymmetric interactions while maintaining the asymptotic efficiency of GTP. It also allows for a more expressive equivariant basis that naturally accounts for the parity-odd components of tensor products. We evaluate SpinGTP across diverse benchmarks, including Tetris, 3BPA, SPICE-MACE-OFF, and OC20. Our results show that SpinGTP achieves accuracies comparable to full CGTP. Notably, by explicitly capturing antisymmetric paths, SpinGTP exhibits superior performance in tasks involving chiral materials and non-centrosymmetric geometries. This work provides a complete, scalable, and mathematically rigorous path toward high-order equivariance in large-scale 3D atomistic system simulations.

Chenxing Liang, Yuchao Lin, Andrii Kryvenko +5

Department of Computer Science and Engineering, Texas A&M University · Lambda, Inc. · Department of Materials Science and Engineering, Texas A&M University +3

Spherical Harmonics Equivariant Neural Networks Molecular Dynamics

Jun 8, 2026cs.CV

Beyond Spherical Harmonics: Rethinking Appearance Models for Radiance Reconstruction

View-dependent appearance modeling remains a challenging problem in novel-view synthesis and reconstruction. Accurately representing complex angular effects often requires substantial memory and computational resources. For new learning-based methods, a common approach is to rely on SH. However, capturing high-frequency phenomena such as specular reflections demands high-order expansions, which increase memory usage and computational cost. Consequently, most methods employ low-order SH, which limits the ability to model complex view-dependent effects, resulting in overly smooth or diffuse representations. To address these limitations, we systematically evaluate a wide range of spherical functions in the context of scene reconstruction. Some of them are introduced to graphics and computer vision for the first time in this paper. Based on the insights from the experiment, we develop a novel spherical formulation, the Normalized Anisotropic Spherical Gabor function that enables efficient modeling and learning of high-frequency appearance effects while maintaining compact representation. Compared to existing approaches, our function achieves higher-quality reconstruction of view-dependent phenomena such as glints, while being up to five times more memory-efficient and more efficient to evaluate. We validate its performance in radiance-field reconstruction tasks.

Ewa Miazga, Jorge Condor, Piotr Didyk

1École Polytechnique Fédérale de Lausanne, Switzerland · 2Università della Svizzera Italiana, Lugano, Switzerland

Spherical Harmonics Surface Reconstruction Appearance High-Frequency Reconstruction

Jun 3, 2026cs.SD

SHB-AE: Spherical harmonic beamforming based Ambisonics encoding and upscaling method for smartphone microphone array

With the rapid development of virtual reality (VR) and augmented reality (AR), spatial audio recording and reproduction have gained increasing research interest. Higher Order Ambisonics (HOA) stands out for its adaptability to various playback devices and its ability to integrate head orientation. However, current HOA recordings often rely on bulky spherical microphone arrays (SMA), and portable devices like smartphones are limited by array configuration and number of microphones. We propose SHB-AE, a spherical harmonic beamforming based method for Ambisonics encoding using a smartphone microphone array (SPMA). By designing beamformers for each order of spherical harmonic functions based on the array manifold, the method enables Ambisonics encoding and up-scaling. Validation on a real SPMA and its simulated free-field counterpart in noisy and reverberant conditions showed that the method successfully encodes and up-scales Ambisonics up to the fourth order with just four irregularly arranged microphones.

Yuhuan You, Yufan Qian, Tianshu Qu +2

Peking University · Beijing Xiaomi Mobile Software Co., Ltd · Xiaomi Communications Co., Ltd

Microphone Array Spatial Audio Spherical Harmonics

May 28, 2026cs.CV

Uncertainty-driven 3D Gaussian Splatting Active Mapping via Anisotropic Visibility Field

We present Gaussian Splatting Anisotropic Visibility Field (GAVIS), a novel framework for uncertainty quantification and active mapping in 3DGS. Our key insight is that regions unseen from the training views yield unreliable predictions from the 3DGS. To address this, we introduce a principled and efficient method for quantifying the visibility field in 3DGS, defined as the anisotropic visibility of each particle with respect to the training views, and represented using spherical harmonics. The resulting visibility field is integrated into a Bayesian Network-based uncertainty-aware 3DGS rasterizer, enabling real-time (200 FPS) uncertainty quantification for synthesized views. Active mapping is further performed within a maximum information gain framework building on this formulation. Extensive experiments across diverse environments demonstrate that GAVIS consistently and significantly outperforms prior approaches in both accuracy and efficiency. Moreover, beyond standalone use, our method can be applied post-hoc to improve the performance of existing approaches.

Shangjie Xue, Jesse Dill, Dhruv Ahuja +3

Georgia Institute of Technology

3D Gaussian Gaussian Splatting 3D Mapping Spherical Harmonics Anisotropic

May 26, 2026cs.CV

Rotation-Invariant Spherical Watermarking via Third-Order SO(3) Representation Coupling

Reliable watermarking of panoramic imagery is fundamentally challenged by arbitrary 3D rotations. As panoramas are defined on the sphere, they naturally transform under the action of

SO(3)

, rendering conventional planar representations and augmentation-based robustness strategies inadequate and devoid of theoretical guarantees. To address this, we formulate panoramas as spherical signals and leverage

SO(3)

representation theory to derive provably rotation-invariant descriptors. While spherical harmonic coefficients transform equivariantly under rotations, the natural invariant constructions are typically limited to zeroth-order statistics which eliminate directional information and severely constrain embedding capacity. In this work, we introduce a principled third-order invariant construction by coupling higher-order

SO(3)

irreducible representations via tensor products and projecting onto the trivial representation. This yields a spherical invariant bispectrum that preserves phase information while remaining strictly rotation-invariant. Leveraging this property, we embed watermarks into higher-order spherical harmonic coefficients and recover them from invariant bispectral scalars, enabling reliable extraction under arbitrary 3D rotations. We provide a theoretical proof of

SO(3)

invariance for it and demonstrate experimentally its near-perfect robustness to continuous rotations while maintaining high visual fidelity.

Pengzhen Chen, Yanwei Liu, Xiaoyan Gu +3

Institute of Information Engineering, Chinese Academy of Sciences · School of Cyber Security, University of Chinese Academy of Sciences · State Key Laboratory of Cyberspace Security Defense +2

Watermarks Spherical Harmonics Watermarking Omnidirectional Images Lie Group Higher-Order Structures

May 18, 2026stat.ML

Shallow ReLU $^s$ Networks in $L^p$ -Type and Sobolev Spaces: Approximation and Path-Norm Controlled Generalization

This paper studies approximation by shallow ReLU

^s

networks,

σ_s(t)=\max\{0,t\}^s

, together with their generalization behavior under

\ell_1

path-norm control. For the

L^p

-type integral spaces

\widetilde{\mathcal{F}}_{p,τ_d,s}

,

1\le p\le2

, spherical harmonic analysis yields approximation bounds for shallow networks. In particular, when

τ_d

is the uniform measure and

1\le p<2

, the approximation rate is

O\!\left(m^{-\frac{p(2s+2d+1)-2d}{2dp}}\right)

for

1\le p\le p^*

and

O\!\left(m^{-\frac{p(4s+3d-1)-2d+2}{4dp}}\right)

for

p^*<p<2

, where

p^*=\frac{2d+2}{d+3}

. Approximation bounds for Sobolev spaces

W^{α,p}

,

1\le p<2

, are obtained through embeddings into spectral Barron spaces. For nonparametric regression with sub-Gaussian noise, path-norm-regularized shallow ReLU

^s

networks achieve minimax-optimal rates

O\!\left(n^{-\frac{d+2s+1}{2d+2s+1}}\log n\right)

over

\mathscr{B}_s

and

O\!\left(n^{-\frac{2α}{2α+d}}\log n\right)

over

W^{α,\infty}

, with matching lower bounds up to logarithmic factors.

Weizhao Li, Fanghui Liu, Lei Shi

School of Mathematical Sciences Fudan University Shanghai, China · School of Mathematical Sciences Institute of Natural Sciences and MOE-LSC2026 Shanghai Jiao Tong University Shanghai, China · School of Mathematical Sciences Shanghai Key Laboratory for Contemporary Applied Mathematics25 Fudan University Shanghai, China

Logarithmic Sobolev Inequalities Rectified Linear Unit Networks Approximation Spherical Harmonics

May 18, 2026cs.LG

Spherical Harmonic Optimal Transport: Application to Climate Models Comparisons

Optimal transport provides a powerful framework for comparing measures while respecting the geometry of their support, but comes with an expensive computational cost, hindering its potential application to real world use cases. On manifolds, convolutional algorithms based on the heat kernel have been proposed to alleviate this cost, but their theoretical properties remain largely unexplored. We establish that the heat kernel cost converges to the optimal transport cost as time vanishes in the balanced and unbalanced cases. In the specific case of the 2-sphere

\mathbb{S}^2

, we ensure that the associated Sinkhorn divergences retains the desirable geometric and analytic properties of classical optimal transport discrepancies. Moreover, we leverage the harmonic structure of the sphere to derive a fast Sinkhorn algorithm, requiring only

\mathcal{O}(n)

memory and

\mathcal{O}(n^{3/2})

time per iteration, with fully dense GPU-friendly operations. We validate its computational efficiency on synthetic data, and discuss its potential use in the evaluation of global climate models, providing both spatial and seasonal insights into models performances.

Pierre Houédry, Iskander Legheraba, Léo Buecher +1

INRIA Rennes · LPHI, UMR 5294, CNRS, INSERM · IRISA, UMR 6074, CNRS

Differentiable Optimal Transport Optimal Transport Approach Fused Sinkhorn-Localized Similarity Spherical Harmonics Sphere Global Climate Models

Apr 29, 2026cs.CV

MesonGS++: Post-training Compression of 3D Gaussian Splatting with Hyperparameter Searching

3D Gaussian Splatting (3DGS) achieves high-quality novel view synthesis with real-time rendering, but its storage cost remains prohibitive for practical deployment. Existing post-training compression methods still rely on many coupled hyperparameters across pruning, transformation, quantization, and entropy coding, making it difficult to control the final compressed size and fully exploit the rate-distortion trade-off. We propose MesonGS++, a size-aware post-training codec for 3D Gaussian compression. On the codec side, MesonGS++ combines joint importance-based pruning, octree geometry coding, attribute transformation, selective vector quantization for higher-degree spherical harmonics, and group-wise mixed-precision quantization with entropy coding. On the configuration side, it treats the reserve ratio and bit-width allocation as the dominant rate-distortion knobs and jointly optimizes them under a target storage budget via discrete sampling and 0--1 integer linear programming. We further propose a linear size estimator and a CUDA parallel quantization operator to accelerate the hyperparameter searching process. Extensive experiments show that MesonGS++ achieves over 34

\times

compression while preserving rendering fidelity, outperforming state-of-the-art post-training methods and accurately meeting target size budgets. Remarkably, without any training, MesonGS++ can even surpass the PSNR of vanilla 3DGS at a 20

\times

compression rate on the Stump scene. Our code is available at https://github.com/mmlab-sigs/mesongs_plus

Shuzhao Xie, Junchen Ge, Weixiang Zhang +10

Shenzhen International Graduate School, Tsinghua University, Shenzhen, China · The Hong Kong University of Science and Technology, Hong Kong SAR, China · Harbin Institute of Technology, Shenzhen, China +6

3D Gaussian Large-Scale 3D Editing Dataset Spherical Harmonics Mixed-Precision Quantization Hyperparameter

Apr 1, 2026cs.CV

Neural Harmonic Textures for High-Quality Primitive Based Neural Reconstruction

Primitive-based methods such as 3D Gaussian Splatting have recently become the state-of-the-art for novel-view synthesis and related reconstruction tasks. Compared to neural fields, these representations are more flexible, adaptive, and scale better to large scenes. However, the limited expressivity of individual primitives makes modeling high-frequency detail challenging. We introduce Neural Harmonic Textures, a neural representation approach that anchors latent feature vectors on a virtual scaffold surrounding each primitive. These features are interpolated within the primitive at ray intersection points. Inspired by Fourier analysis, we apply periodic activations to the interpolated features, turning alpha blending into a weighted sum of harmonic components. The resulting signal is then decoded in a single deferred pass using a small neural network, significantly reducing computational cost. Neural Harmonic Textures yield state-of-the-art results in real-time novel view synthesis while bridging the gap between primitive- and neural-field-based reconstruction. Our method integrates seamlessly into existing primitive-based pipelines such as 3DGUT, Triangle Splatting, and 2DGS. We further demonstrate its generality with applications to 2D image fitting and semantic reconstruction.

Jorge Condor, Nicolas Moenne-Loccoz, Merlin Nimier-David +3

NVIDIA · Università della Svizzera italiana, Lugano, Switzerland

Neural Reconstruction Novel View Synthesis Texture Spherical Harmonics High-Frequency Reconstruction