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A mathematical approach to best luminance maps.

Ali Alsam, Hans Jakob Rivertz

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    Summary

    This study introduces an algorithm for optimal color-to-grayscale conversion, minimizing image tensor differences. The new method significantly reduces errors in color gradients compared to traditional techniques.

    Area of Science:

    • Computer Vision
    • Image Processing
    • Color Science

    Background:

    • Accurate color-to-grayscale conversion is crucial for various image processing applications.
    • Conventional methods like luminance transformation often fail to preserve local image structure and color gradients effectively.

    Purpose of the Study:

    • To develop a novel algorithm for optimal global color-to-grayscale mapping.
    • To minimize the difference between multi-channel local tensors and mono-chromatic image tensors.

    Main Methods:

    • Representing grayscale images as weighted sums of RGB channels, including linear, polynomial, and root polynomial functions.
    • Employing an optimization process to find the best weights for combining these functions.
    • Incorporating squared and root squared channels for further refinement.

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    Main Results:

    • The proposed algorithm significantly reduces the root mean square difference in color gradients by up to 50% compared to conventional luminance transformation.
    • Optimal weights were found to effectively combine linear, polynomial, and root polynomial functions.
    • Visual inspection confirmed the improvements in grayscale image quality.

    Conclusions:

    • The developed algorithm provides a superior method for color-to-grayscale mapping.
    • Minimizing tensor differences offers a more robust approach to preserving image information.
    • The method demonstrates significant quantitative and qualitative improvements over existing techniques.