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    Noise-induced bias in digital image correlation (DIC) affects accuracy, especially with low contrast. This study introduces a general formula for convolution-based interpolation, improving bias estimation for various methods.

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    Area of Science:

    • * Optical Metrology
    • * Image Analysis
    • * Computational Mechanics

    Background:

    • * Digital Image Correlation (DIC) is sensitive to noise-induced bias, particularly with low image contrast.
    • * Existing bias estimation methods are limited to traditional interpolation techniques (linear, cubic) and exclude generalized methods (BSpline, OMOMS).
    • * Both traditional and generalized interpolation methods rely on convolution-based approaches.

    Purpose of the Study:

    • * To theoretically analyze noise-induced bias in convolution-based interpolation for DIC.
    • * To develop a generalized and accurate method for estimating noise-induced bias applicable to various interpolation techniques.
    • * To reveal how advanced interpolation methods mitigate noise-induced bias.

    Main Methods:

    • * Developed a theoretical framework for analyzing noise-induced bias in convolution-based interpolation.
    • * Derived a sinusoidal approximate formula for quantifying noise-induced bias.
    • * Validated the formula through numerical simulations and experimental subpixel translation tests.

    Main Results:

    • * A novel, general formula for estimating noise-induced bias in convolution-based interpolation was derived.
    • * The proposed formula is simpler, briefer, and more widely applicable than existing methods.
    • * The study provides a quantitative explanation for the position-dependent nature of noise variability.

    Conclusions:

    • * The derived sinusoidal formula offers a fast, easy, and accurate strategy for estimating noise-induced bias.
    • * The theoretical analysis elucidates the mechanism by which sophisticated interpolation methods reduce bias.
    • * This work enhances the reliability of DIC measurements by providing a more robust bias estimation technique.