Semantic fitting and reconstruction
Journal on Computing and Cultural Heritage (JOCCH)
Fitting sharp features with loop subdivision surfaces
SGP '08 Proceedings of the Symposium on Geometry Processing
A comparison of sampling strategies for computing general sweeps
Computer-Aided Design
SMI 2012: Short A revisit to fitting parametric surfaces to point clouds
Computers and Graphics
Fitting polynomial volumes to surface meshes with Voronoï squared distance minimization
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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We present a complete framework for computing a subdivision surface to approximate unorganized point sample data, which is a separable nonlinear least squares problem. We study the convergence and stability of three geometrically motivated optimization schemes and reveal their intrinsic relations with standard methods for constrained nonlinear optimization. A commonly used method in graphics, called point distance minimization, is shown to use a variant of the gradient descent step and thus has only linear convergence. The second method, called tangent distance minimization, which is well known in computer vision, is shown to use the Gauss-Newton step and, thus, demonstrates near-quadratic convergence for zero residual problems but may not converge otherwise. Finally, we show that an optimization scheme called squared distance minimization, recently proposed by Pottmann et al., can be derived from the Newton method. Hence, with proper regularization, tangent distance minimization and squared distance minimization are more efficient than point distance minimization. We also investigate the effects of two step-size control methods - Levenberg-Marquardt regularization and the Armijo rule-on the convergence stability and efficiency of the above optimization schemes.