# A Robust Skeletonization Method for High-Density Fringe Patterns in Holographic Interferometry Based on Parametric Modeling and Strip Integration

## TL;DR

This paper introduces a new method for analyzing high-density fringe patterns in holographic interferometry, improving accuracy and reliability in noisy conditions.

## Contribution

The novel skeletonization method combines parametric modeling, noise-robust strip integration, and sub-pixel accuracy for reliable fringe analysis.

## Key findings

- The method achieves topology preservation and noise suppression in fringe pattern analysis.
- It demonstrates sub-pixel accuracy without phase extraction, enhancing contour localization.
- Validation on synthetic and real interferograms confirms lower error and practical utility.

## Abstract

Accurate displacement field measurement by holographic interferometry requires robust analysis of high-density fringe patterns, which is hindered by speckle noise inherent in any interferogram, no matter how perfect. Conventional skeletonization methods, such as edge detection algorithms and active contour models, often fail under these conditions, producing fragmented and unreliable fringe contours. This paper presents a novel skeletonization procedure that simultaneously addresses three fundamental challenges: (1) topology preservation—by representing the fringe family within a physics-informed, finite-dimensional parametric subspace (e.g., Fourier-based contours), ensuring global smoothness, connectivity, and correct nesting of each fringe; (2) extreme noise robustness—through a robust strip integration functional that replaces noisy point sampling with Gaussian-weighted intensity averaging across a narrow strip, effectively suppressing speckle while yielding a smooth objective function suitable for gradient-based optimization; and (3) sub-pixel accuracy without phase extraction—leveraging continuous bicubic interpolation within a recursive quasi-optimization framework that exploits fringe similarity for precise and stable contour localization. The method’s performance is quantitatively validated on synthetic interferograms with controlled noise, demonstrating significantly lower error compared to baseline techniques. Practical utility is confirmed by successful processing of a real interferogram of a bent plate containing over 100 fringes, enabling precise displacement field reconstruction that closely matches independent theoretical modeling. The proposed procedure provides a reliable tool for processing challenging interferograms where traditional methods fail to deliver satisfactory results.