# Edge, Ridge, and Blob Detection with Symmetric Molecules

arXiv: https://arxiv.org/abs/1901.09723 · HTML: https://mlsanity.com/paper/1901.09723/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jan 2019.

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

- [Sequential vessel segmentation via deep channel attention network](https://mlsanity.com/paper/2102.05229/) (2021)
- [Explaining Image Classifiers with Multiscale Directional Image Representation](https://mlsanity.com/paper/2211.12857/) (2022)
- [Robust PCA Unrolling Network for Super-resolution Vessel Extraction in X-ray Coronary Angiography](https://mlsanity.com/paper/2204.08466/) (2022)
- [CoShNet: A Hybrid Complex Valued Neural Network using Shearlets](https://mlsanity.com/paper/2208.06882/) (2022)
- [Extracting Complex Topology from Multivariate Functional Approximation: Contours, Jacobi Sets, and Ridge-Valley Graphs](https://mlsanity.com/paper/2508.07637/) (2025)
- [Dynamic Atomic Column Detection in Transmission Electron Microscopy Videos via Ridge Estimation](https://mlsanity.com/paper/2302.00816/) (2023)

## Abstract (arXiv)

We present a novel approach to the detection and characterization of edges, ridges, and blobs in two-dimensional images which exploits the symmetry properties of directionally sensitive analyzing functions in multiscale systems that are constructed in the framework of alpha-molecules. The proposed feature detectors are inspired by the notion of phase congruency, stable in the presence of noise, and by definition invariant to changes in contrast. We also show how the behavior of coefficients corresponding to differently scaled and oriented analyzing functions can be used to obtain a comprehensive characterization of the geometry of features in terms of local tangent directions, widths, and heights. The accuracy and robustness of the proposed measures are validated and compared to various state-of-the-art algorithms in extensive numerical experiments in which we consider sets of clean and distorted synthetic images that are associated with reliable ground truths. To further demonstrate the applicability, we show how the proposed ridge measure can be used to detect and characterize blood vessels in digital retinal images and how the proposed blob measure can be applied to automatically count the number of cell colonies in a Petri dish.