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Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics
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Antiderivative of gradient data by spline model integration.

Irfan Badar, Liangxin Yang, Christian Hellmann

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
    |October 6, 2021
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    Summary
    This summary is machine-generated.

    This study introduces a spline model integration technique to reconstruct original functions from gradient data. This method accurately recovers functions from irregular measurements, overcoming limitations of slope-only optical techniques.

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    Area of Science:

    • Numerical analysis
    • Applied mathematics
    • Computational geometry

    Background:

    • Optical techniques often provide function gradients (slopes) at discrete points, not the functions themselves.
    • Retrieving original functions from gradient data typically requires integration, which can be complex and inaccurate with irregular data.

    Purpose of the Study:

    • To develop and present a novel spline model function-based integration technique.
    • To enable accurate reconstruction of original functions from irregularly measured gradient data.
    • To address limitations of existing methods in retrieving full functions from slope data.

    Main Methods:

    • Utilizing a spline model to represent and integrate gradient information.
    • Developing an integration process for irregularly sampled data points.
    • Applying the technique to general shape domains.

    Main Results:

    • High accuracy in reconstructing original functions from gradient data.
    • Efficient and fast computation of the integration process.
    • Successful application to irregularly measured data over general domains.

    Conclusions:

    • The spline model function-based integration technique offers a robust solution for function reconstruction from gradient data.
    • This method enhances the utility of optical measurements by enabling the recovery of complete functions.
    • The approach provides a significant advancement for applications requiring accurate function retrieval from slope information.