# Edge, Ridge, and Blob Detection with Symmetric Molecules

## TL;DR

This paper introduces a new multiscale, symmetry-based method for detecting and characterizing edges, ridges, and blobs in images, demonstrating robustness to noise and invariance to contrast changes.

## Contribution

The paper presents a novel symmetry-based approach using alpha-molecules for feature detection, providing comprehensive geometric characterization and improved robustness over existing methods.

## Key findings

- High accuracy in synthetic image detection tasks
- Robustness to noise and contrast variations demonstrated
- Effective in real-world applications like blood vessel and cell colony analysis

## Abstract

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.