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

Musrrat Ali (), Deepika Saini, Sanoj Kumar () and Abdul Rahaman Wahab Sait
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Musrrat Ali: Department of Basic Sciences, Preparatory Year, 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

Mathematics, 2025, vol. 13, issue 14, 1-18

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.

Keywords: two-view geometry; iterative optimization; curve fitting; geometric optimization; reprojection error minimization; NURBS (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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