ADOPT: Analytical Demodulation of Periodic Textures for In-Plane Wave Tracking

TL;DR

ADOPT is a novel analytical method for tracking in-plane waves from periodic textures in images, offering improved accuracy and efficiency over existing techniques, validated through simulations and experiments.

Contribution

The paper introduces ADOPT, a new analytical demodulation technique based on oriented 2D analytic signals for precise in-plane wave tracking from periodic surface patterns.

Findings

ADOPT outperforms state-of-the-art DIC at high SNRs.

ADOPT provides more accurate displacement estimation for small waves.

The method is computationally more efficient than existing approaches.

Abstract

This paper addresses the problem of tracking in-plane waves from image sequences using periodic surface patterns. Wave-induced deformation is modeled as a spatial phase modulation of a periodic carrier. We propose ADOPT (Analytical Demodulation of Periodic Texture), a method based on an oriented two-dimensional analytic signal to estimate displacement phase and orientation. The approach relies on a physical model describing longitudinal and transverse in-plane waves. Orientation-selective filtering isolates relevant spectral components, and phase extraction provides a stable reconstruction of the displacement field. A theoretical analysis using the Cramer--Rao bound evaluates performance limits of ADOPT. Simulations show that the proposed method outperforms state-of-the-art Digital Image Correlation (DIC) at high signal-to-noise ratios, especially for small displacements where DIC becomes limited. Moreover, ADOPT is more computationally efficient. Experiments on silicone membranes with periodic patterns confirm accurate estimation of wave fields and dispersion curves under impulsive excitation. Overall, the proposed framework provides a robust and efficient solution for wave-induced displacement estimation.