# On Detection of Faint Edges in Noisy Images

arXiv: https://arxiv.org/abs/1706.07717 · HTML: https://mlsanity.com/paper/1706.07717/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jun 2017.

## Built on by (most cited first, 5 of 5)

- [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)
- [Automatic defect segmentation by unsupervised anomaly learning](https://mlsanity.com/paper/2202.02998/) (2022)
- [Classic versus deep learning approaches to address computer vision challenges](https://mlsanity.com/paper/2101.09744/) (2021)
- [Rate-optimal neural boundary detection from unlabeled noisy images](https://mlsanity.com/paper/2606.00715/) (2026)

## Abstract (arXiv)

A fundamental question for edge detection in noisy images is how faint can an edge be and still be detected. In this paper we offer a formalism to study this question and subsequently introduce computationally efficient multiscale edge detection algorithms designed to detect faint edges in noisy images. In our formalism we view edge detection as a search in a discrete, though potentially large, set of feasible curves. First, we derive approximate expressions for the detection threshold as a function of curve length and the complexity of the search space. We then present two edge detection algorithms, one for straight edges, and the second for curved ones. Both algorithms efficiently search for edges in a large set of candidates by hierarchically constructing difference filters that match the curves traced by the sought edges. We demonstrate the utility of our algorithms in both simulations and applications involving challenging real images. Finally, based on these principles, we develop an algorithm for fiber detection and enhancement. We exemplify its utility to reveal and enhance nerve axons in light microscopy images.