3D Field of Junctions: A Noise-Robust, Training-Free Structural Prior for Volumetric Inverse Problems

2026-03-02

AI Summary

This work addresses the challenge of severe noise interference and poor preservation of sharp edges and corners in low signal-to-noise ratio 3D imaging inverse problems by proposing a training-free 3D structural prior termed 3D Field of Junctions (3D FoJ). Extending the Field of Junctions concept to full 3D for the first time, the method models volumetric patches using local 3D wedge-like junction structures and enforces inter-patch consistency constraints within a projection/proximal gradient optimization framework to achieve high-quality reconstruction. Being entirely unsupervised and free from hallucination risks inherent in learning-based approaches, 3D FoJ consistently outperforms both conventional and deep learning methods across diverse applications—including low-dose CT, cryo-electron tomography, and LiDAR point cloud denoising under adverse weather—demonstrating superior capability in preserving geometric features such as edges and corners.

Technology Category

• Computer Vision: 3D Computer Vision
• Machine Learning: Structured Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Volume denoising is a foundational problem in computational imaging, as many 3D imaging inverse problems face high levels of measurement noise. Inspired by the strong 2D image denoising properties of Field of Junctions (ICCV 2021), we propose a novel, fully volumetric 3D Field of Junctions (3D FoJ) representation that optimizes a junction of 3D wedges that best explain each 3D patch of a full volume, while encouraging consistency between overlapping patches. In addition to direct volume denoising, we leverage our 3D FoJ representation as a structural prior that: (i) requires no training data, and thus precludes the risk of hallucination, (ii) preserves and enhances sharp edge and corner structures in 3D, even under low signal to noise ratio (SNR), and (iii) can be used as a drop-in denoising representation via projected or proximal gradient descent for any volumetric inverse problem with low SNR. We demonstrate successful volume reconstruction and denoising with 3D FoJ across three diverse 3D imaging tasks with low-SNR measurements: low-dose X-ray computed tomography (CT), cryogenic electron tomography (cryo-ET), and denoising point clouds such as those from lidar in adverse weather. Across these challenging low-SNR volumetric imaging problems, 3D FoJ outperforms a mixture of classical and neural methods.

Problem

• volume denoising
• volumetric inverse problems
• low SNR
• 3D imaging
• noise-robust

Innovation

• 3D Field of Junctions
• training-free prior
• volumetric denoising
• low-SNR reconstruction
• structural prior