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    New hyper-objective measures for vector fields ensure measurements are independent of observer movement. This allows for the extraction of deforming vortices, improving scientific measurements.

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    Area of Science:

    • Fluid dynamics
    • Computational mathematics
    • Scientific visualization

    Background:

    • Vector field properties like magnitude and vorticity change with observer movement.
    • Existing invariance conditions (Galilean, objectivity) are insufficient for all physical measurements.
    • Need for robust measures invariant to broader reference frame transformations.

    Purpose of the Study:

    • Introduce new invariance conditions: similarity and affine transformations.
    • Develop hyper-objective measures for vector fields.
    • Enable extraction of vortices that deform or change volume.

    Main Methods:

    • Define and implement similarity and affine invariance for vector fields.
    • Develop a generic method to transform existing vortex measures into hyper-objective ones.
    • Apply methods to 2D and 3D vector field vortex extraction.

    Main Results:

    • Demonstrated hyper-objective measures invariant under similarity and affine transformations.
    • Successfully extracted deforming vortices using the new measures.
    • Analyzed numerical robustness, extraction time, and minimization residuals.

    Conclusions:

    • Hyper-objective measures provide a more robust framework for analyzing vector fields.
    • The developed methods enhance vortex extraction capabilities, especially for dynamic vortices.
    • This work offers a significant advancement in invariant physical property measurement.