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Optimization-Driven Reconstruction of 3D Space Curves from Two Views Using NURBS

Author

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  • Musrrat Ali

    (Department of Basic Sciences, Preparatory Year, King Faisal University, Al-Ahsa 31982, Saudi Arabia
    Department of Mathematics and Statistics, College of Science, King Faisal University, Al Ahsa 31982, Saudi Arabia)

  • Deepika Saini

    (Department of Mathematics, Graphic Era (Deemed to be University), Dehradun 248002, Uttarakhand, India)

  • Sanoj Kumar

    (Data Science Cluster, School of Computer Science, UPES, Dehradun 248007, Uttarakhand, India)

  • Abdul Rahaman Wahab Sait

    (Department of Archives and Communication, Center of Documentation and Administrative Communication, King Faisal University, Al-Ahsa 31982, Saudi Arabia)

Abstract

In the realm of 3D curve reconstruction, Non-Uniform Rational B-Splines (NURBSs) offer a versatile mathematical tool due to their ability to precisely represent complex geometries. However, achieving high fitting accuracy in stereo-based applications remains challenging, primarily due to the nonlinear nature of weight optimization. This study introduces an enhanced iterative strategy that leverages the geometric significance of NURBS weights to incrementally refine curve fitting. By formulating an inverse optimization problem guided by model deformation principles, the proposed method progressively adjusts weights to minimize reprojection error. Experimental evaluations confirm the method’s convergence and demonstrate its superiority in fitting accuracy when compared to conventional optimization techniques.

Suggested Citation

  • Musrrat Ali & Deepika Saini & Sanoj Kumar & Abdul Rahaman Wahab Sait, 2025. "Optimization-Driven Reconstruction of 3D Space Curves from Two Views Using NURBS," Mathematics, MDPI, vol. 13(14), pages 1-18, July.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:14:p:2256-:d:1700249
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