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    This study introduces a full-vector gradient for multispectral sensors, improving accuracy in metrological applications like vision-based quality control. The method accounts for non-orthogonal channels, offering enhanced gradient calculation for various sensors.

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    Area of Science:

    • Metrology
    • Image Processing
    • Computer Vision

    Background:

    • Gradient extraction is crucial for metrological applications, particularly in vision-based quality control.
    • Existing methods may not fully address the complexities of multispectral sensor data.

    Purpose of the Study:

    • To propose a novel full-vector gradient for multispectral sensors.
    • To enhance the accuracy of gradient calculations in metrology.

    Main Methods:

    • Extended the Di Zenzo expression to incorporate a Gram matrix, accounting for non-orthogonal acquisition channels.
    • Developed a generic expression independent of channel count.
    • Tested the method on color and multispectral snapshot sensors.

    Main Results:

    • Demonstrated improved accuracy in gradient calculation compared to standard methods.
    • Validated the approach using both objective tests and real-world image data.
    • The full-vector gradient method proved effective across different sensor types.

    Conclusions:

    • The proposed full-vector gradient offers a more accurate approach for multispectral sensor data.
    • This advancement has significant implications for metrological applications relying on precise image analysis.