# Shearlet-Based Detection of Flame Fronts

arXiv: https://arxiv.org/abs/1511.03753 · HTML: https://mlsanity.com/paper/1511.03753/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Nov 2015.

## Built on by (most cited first, 2 of 2)

- [Extracting Complex Topology from Multivariate Functional Approximation: Contours, Jacobi Sets, and Ridge-Valley Graphs](https://mlsanity.com/paper/2508.07637/) (2025)
- [The Mathematics of Artificial Intelligence](https://mlsanity.com/paper/2203.08890/) (2022)

## Abstract (arXiv)

Identifying and characterizing flame fronts is the most common task in the computer-assisted analysis of data obtained from imaging techniques such as planar laser-induced fluorescence (PLIF), laser Rayleigh scattering (LRS), or particle imaging velocimetry (PIV). We present a novel edge and ridge (line) detection algorithm based on complex-valued wavelet-like analyzing functions -- so-called complex shearlets -- displaying several traits useful for the extraction of flame fronts. In addition to providing a unified approach to the detection of edges and ridges, our method inherently yields estimates of local tangent orientations and local curvatures. To examine the applicability for high-frequency recordings of combustion processes, the algorithm is applied to mock images distorted with varying degrees of noise and real-world PLIF images of both OH and CH radicals. Furthermore, we compare the performance of the newly proposed complex shearlet-based measure to well-established edge and ridge detection techniques such as the Canny edge detector, another shearlet-based edge detector, and the phase congruency measure.