Inverse Geometric Reconstruction Based on MW-NURBS Curves

Musrrat Ali (), Deepika Saini and Sanoj Kumar ()
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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, SOCS, UPES, Dehradun 248007, Uttarakhand, India

Mathematics, 2024, vol. 12, issue 13, 1-20

Abstract: Currently, rational curves such as the Non-Uniform Rational B-Spline (NURBS) play a significant role in both shape representation and shape reconstruction. NURBS weights are often real in nature and are referred to as challenging to assign, with the exception of conics. ‘Matrix Weighted Rational Curves’ are the expanded form of rational curves that result from replacing these real weights with matrices, or matrix weights. The only difference between these curves and conventional curves is the geometric definition of the matrix weights. In this paper, MW-NURBS curves are used to reconstruct space curves from their stereo perspectives. In particular, MW-NURBS fitting is carried out in stereo views, and the weight matrices for the MW-NURBS curves are produced using the normal vectors provided at the control points. Instead of needing to solve a complicated system, the MW-NURBS model can reconstruct curves by choosing control points and control normals from the input data. The efficacy of the proposed strategy is verified by using many examples based on both synthetic and real images. The various error types are compared to those of conventional methods like point-based and NURBS-based approaches. The results demonstrate that the errors acquired from the proposed approach are much fewer than those obtained from the point-based method and the NURBS-based method.

Keywords: curve-fitting; inverse reconstruction; MW-NURBS; stereo images (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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