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

TL;DR

This work proposes 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.

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.

Figures (5)

• Figure 1: Our 3D Field of Junctions (3D FoJ) is an effective volumetric denoiser across diverse inverse problems: low-dose computed tomography (top row), cryogenic electron tomography (middle row), and point cloud denoising (bottom row). Our cryo-ET experiment uses real data for which noiseless ground truth is not available. Only 3D FoJ successfully captures both the top and side handles of the teapot in low-dose CT.
• Figure 2: Junction schematics for Field of Junctions (FoJ) in 2D (left) and our 3D FoJ (right).(a) In 2D, verbin2021field models each patch as an $M$-junction: a vertex and $M$ angles define $M$ uniform-color wedges. Allowing the vertex to lie inside or outside the patch enables a unified representation of edges, corners, junctions, and homogeneous regions. (b) In 3D, we visualize the two-region case ($M{=}2$) with different configurations of intersecting planes inside a volumetric patch. We show $M{=}2$ for visual clarity; our experiments use $M{=}3$ regions.
• Figure 3: Comparison of unseen projection views synthesized from reconstructed 3D volumes (top) and slice views of reconstructed 3D volumes (bottom) for the engine dataset under low-SNR (P50) conditions.
• Figure 4: Visual denoising results for the real cryo-ET centriole volume, sliced in each dimension. 3D FoJ preserves fine structural details that are overly smoothed by NLM.
• Figure 5: Denoising results for the dragon point cloud with 60% outlier noise and 500k random spread points. Slices show that 3D FoJ effectively removes noise both inside and outside the object surface. At this extreme level of spread noise, PointCVaR rejects nearly all points as outliers.