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

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 overcomes these limitations through a threefold approach: (1) representation of the entire fringe family within a physics-informed, finite-dimensional parametric subspace (e.g., a collection of Fourier-based contours), ensuring global smoothness and connectivity of each fringe; (2) introduction of a robust strip-integration functional, which replaces noisy point sampling with a Gaussian-weighted intensity integral across a narrow strip, yielding a smooth objective function, which is convenient to optimize with standard gradient-based techniques; and (3) a recursive quasi-optimization algorithm that takes into account fringe similarity for efficient and stable identification. The method's efficiency is quantitatively validated on synthetic interferograms with controlled noise, demonstrating significantly lower error compared to baseline techniques. Its practical utility is confirmed by successful processing of a real, interferogram of a bent plate containing over 100 fringes, enabling precise reconstruction of the displacement field that closely matches result of independent theoretical modelling. The proposed procedure provides a reliable tool for processing challenging interferograms where traditional methods may fail to obtain satisfactory result.