NURBS-based geometric inverse reconstruction of free-form shapes

Abstract

In this study, a geometric inverse algorithm is proposed for reconstructing free-form shapes (curves and surfaces) in space from their arbitrary perspective images using a Non-Uniform Rational B-Spline (NURBS) model. In particular, NURBS model is used to recover information about the required shape in space. An optimization problem is formulated to fit the NURBS to the digitized data in the images. Control points and weights are treated as the decision variables in the optimization process. The 3D shape reconstruction problem is reduced to a problem that comprises stereo reconstruction of control points and computation of the corresponding weights. The correspondence between the control points in the two images is obtained using a third image. The performance of the proposed algorithm was validated by taking several examples based on the synthetic and real images. Comparisons were made with a point-based method in terms of various types of errors.

Keywords

• 3D reconstruction
• Free-form shapes
• Non-Uniform Rational B-Spline (NURBS)
• Perspective projection
• Quadratic programing problem (QPP)