# Field of Junctions: Extracting Boundary Structure at Low SNR

arXiv: https://arxiv.org/abs/2011.13866 · HTML: https://mlsanity.com/paper/2011.13866/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Nov 2020.

## Built on by (most cited first, 6 of 6)

- [Blurry-Edges: Photon-Limited Depth Estimation from Defocused Boundaries](https://mlsanity.com/paper/2503.23606/) (2025)
- [CT-Bound: Robust Boundary Detection From Noisy Images Via Hybrid Convolution and Transformer Neural Networks](https://mlsanity.com/paper/2403.16494/) (2024)
- [2D Neural Fields with Learned Discontinuities](https://mlsanity.com/paper/2408.00771/) (2024)
- [Boundary Attention: Learning curves, corners, junctions and grouping](https://mlsanity.com/paper/2401.00935/) (2024)
- [3D Field of Junctions: A Noise-Robust, Training-Free Structural Prior for Volumetric Inverse Problems](https://mlsanity.com/paper/2603.02149/) (2026)
- [Non-Learning Low-Light Stereo Vision](https://mlsanity.com/paper/2606.00379/) (2026)

## Abstract (arXiv)

We introduce a bottom-up model for simultaneously finding many boundary elements in an image, including contours, corners and junctions. The model explains boundary shape in each small patch using a 'generalized M-junction' comprising M angles and a freely-moving vertex. Images are analyzed using non-convex optimization to cooperatively find M+2 junction values at every location, with spatial consistency being enforced by a novel regularizer that reduces curvature while preserving corners and junctions. The resulting 'field of junctions' is simultaneously a contour detector, corner/junction detector, and boundary-aware smoothing of regional appearance. Notably, its unified analysis of contours, corners, junctions and uniform regions allows it to succeed at high noise levels, where other methods for segmentation and boundary detection fail.