Parametric Curve Reconstruction from Point Clouds using Minimization Techniques

Smooth (C1-, C2-,...) curve reconstruction from noisy point samples is central to reverse engineering, medical imaging, etc. Unresolved issues in this problem are (1) high computational expenses, (2) presence of artifacts and outlier curls, (3) erratic behavior at self-intersections and sharp corners. Some of these issues are related to non-Nyquist (i.e. sparse) samples. Our work reconstructs curves by minimizing the accumulative distance curve cs. point sample. We address the open issues above by using (a) Principal Component Analysis (PCA) pre-processing to obtain a topologically correct approximation of the sampled curve. (b) Numerical, instead of algebraic, calculation of roots in point-to-curve distances. (c) Penalties for curve excursions by using point cloud to curve and curve to point cloud. (d) Objective functions which are economic to minimize. The implemented algorithms successfully deal with self intersecting and / or non-Nyquist samples. Ongoing research includes self-tuning of the algorithms and decimation of the point cloud and the control polygon.