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    Area of Science:

    • Computer Vision
    • 3D Reconstruction
    • Photogrammetry

    Background:

    • Lambertian surface reflectance is a common assumption in Shape from Shading (SFS).
    • Existing SFS methods often require multiple images or specific lighting conditions.
    • Accurate 3D shape measurement is crucial for various industrial and scientific applications.

    Purpose of the Study:

    • To develop a novel scaled Shape from Shading (SFS) method for precise 3D dimensional measurement of Lambertian surfaces.
    • To improve the accuracy of SFS by incorporating a more refined light source model and camera matrix.
    • To enable 3D surface reconstruction from a single image.

    Main Methods:

    • A new scaled SFS algorithm was developed, utilizing a refined point light source model.
    • The relationship between surface depth and image grayscale was established by integrating the camera matrix.
    • Constraints including brightness, smoothness, and integrability were applied for shape recovery.
    • The method was validated using algorithm simulations and experimental measurements.

    Main Results:

    • Algorithm simulations demonstrated a perfect match between simulated and reconstructed structures.
    • The rebuilding root mean square error (RMSE) achieved was below 0.6mm.
    • Experimental measurement of a PVC tube's internal surface yielded an overall error below 2%.

    Conclusions:

    • The novel scaled SFS method enables accurate and dimensioned 3D shape measurement of Lambertian surfaces from a single image.
    • The integration of an improved light source model and camera matrix enhances reconstruction accuracy.
    • The method shows practical applicability with low measurement errors in real-world scenarios.