VOILA Lab @ GT ECCV 2026

3D Field of Junctions

A Noise-Robust, Training-Free Structural Prior
for Volumetric Inverse Problems

Namhoon Kim* Narges Moeini* Justin Romberg Sara Fridovich-Keil

Georgia Institute of Technology * Equal contribution; order determined by coin flip

Interactive demo Watch talk Paper PDF arXiv Code BibTeX
Comparison of 3D FoJ against baselines for low-dose CT, cryo-electron tomography, and point-cloud denoising.
Results on low-dose CT, real cryo-ET, and point-cloud denoising. All experiments use the same training-free 3D FoJ representation.

Interactive demo

Noise robustness on an engine CT volume

Move from the clean engine volume to P100, P50, and P20 Poisson observations while keeping every 3D FoJ setting fixed. The linked XY, YZ, and XZ views show how the fitted regions and global boundaries change as measurements get noisier.

Structural robustness · fixed FoJ settings Engine CT · 3D junction field
256³ native voxels 4 noise states 0 training volumes
Poisson noise level Clean reference

No added noise; the experiment volume is shown as the reference state.

Linked voxel (128, 128, 128)
Drag crosshair · Scroll through depth
Loading the engine CT and fitted junction field…
Input Noise-free CT
Clean reference
Local model Junction regions
28.99 dB vs clean
Global structure Junction boundaries
Continuous global contour map
XY axial z = 128
Noise-free CT · XY
Junction regions · XY
Junction boundaries · XY
YZ sagittal x = 128
Noise-free CT · YZ
Junction regions · YZ
Junction boundaries · YZ
XZ coronal y = 128
Noise-free CT · XZ
Junction regions · XZ
Junction boundaries · XZ
Paper CT. Actual fitted junctions.

Every state uses the same 256³ source, dense overlapping 6³ patches, stride 2, search schedule, and random seed. Only the expected photon count changes; each noisy result is precomputed by the repository's actual 3D FoJ optimizer.

x y z

Video

ECCV 2026 presentation

Paper

3D Field of Junctions

Abstract

Volume denoising is a foundational problem in computational imaging, where many 3D inverse problems face severe measurement noise. We introduce a fully volumetric 3D Field of Junctions (3D FoJ): an explicit representation that fits junctions of 3D wedges to overlapping patches while encouraging global consistency.

3D FoJ requires no training data, preserves sharp edges and corners under low signal-to-noise ratio, and acts as a drop-in denoising representation for projected or proximal gradient methods. Across low-dose X-ray CT, cryogenic electron tomography, and noisy point clouds, it outperforms the evaluated classical, untrained neural, and noisy-example-trained denoisers.

Training-free by design

An explicit geometric prior avoids the need for clean training volumes and reduces the risk of learned hallucination.

Boundary preserving

Intersecting planes model sharp corners, straight or bent boundaries, curved surfaces, and constant regions in one representation.

Inverse-problem ready

Use 3D FoJ directly as a denoiser or as a projected/proximal step in a wider volumetric reconstruction loop.

Method

Junction representation

Each overlapping 3D patch is divided by intersecting planes into uniform-valued wedges. Joint optimization aligns both geometry and appearance across neighboring patches.

Three-dimensional junction representing a sharp corner inside a volume patch.
Sharp corner
Three-dimensional junction whose vertex lies on a patch boundary.
Bent boundary
Plane configuration representing an edge through a volume patch.
Planar edge
Junction vertex outside the patch representing a uniform region.
Uniform region

Moving the shared vertex and plane orientations gives one model enough flexibility to represent corners, edges, bends, and homogeneous regions.

  1. 1

    Partition

    Represent the volume as overlapping 3D patches.

  2. 2

    Initialize

    Fit each patch's junction geometry and wedge values.

  3. 3

    Refine

    Jointly encourage boundary and color consistency.

  4. 4

    Reconstruct

    Average overlapping predictions into a clean volume.

Results

Experimental results

Low-dose CT comparison showing input, 3D FoJ, R-squared Gaussian, NAF, Filter2Noise, 3D total variation, and ground truth projection views.
Low-dose X-ray CT. Under extreme P50 shot noise, 3D FoJ recovers coherent internal structure while retaining sharper boundaries than the evaluated baselines.

Citation

BibTeX

BibTeX 
@inproceedings{kim2026three,
  title     = {3D Field of Junctions: A Noise-Robust, Training-Free
               Structural Prior for Volumetric Inverse Problems},
  author    = {Kim, Namhoon and Moeini, Narges and Romberg, Justin
               and Fridovich-Keil, Sara},
  booktitle = {European Conference on Computer Vision (ECCV)},
  year      = {2026}
}