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 polygonINSTIC

Parametric curve reconstruction from point clouds using minimization techniques

Curve reconstruction from noisy point samples is central to surface reconstruction and therefore to reverse engineering, medical imaging, etc. Although Piecewise Linear (PL) curve reconstruction plays an important role, smooth (C1-, C2-,?) curves are needed for many applications. In reconstruction of parametric curves from noisy point samples there remain unsolved issues such as (1) high computational expenses, (2) presence of artifacts and outlier curls, (3) erratic behavior of self-intersecting curves, and (4) erratic excursions at sharp corners. Some of these issues are related to non-Nyquist (i.e. sparse) samples. In response to these shortcomings, this article reports the minimization-based fitting of parametric curves for noisy point clouds. Our approach features: (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

Publicaciones, ponencias, patentes, registros y emprendimientos 2011

Este documento presenta la relación de publicaciones, ponencias, patentes, registros y emprendimientos realizados por la Universidad EAFIT en el año 2011. La información está organizada por Grupos de Investigación dentro de cada una de las Escuelas. En la parte final, de manera repetida, se indican los productos en los que han participado estudiantes tanto de posgrado como de pregrado. Estos autores se indican en subrayado. Cada contribución aparece en orden alfabético dentro de la correspondiente categoría de la siguiente secuencia: publicaciones internacionales, ublicaciones nacionales, ponencias internacionales, ponencias nacionales, patentes, registros y emprendimientos. En las publicaciones están comprendidos los libros, capítulos de libros y artículos de revista. Las ponencias relacionan las presentaciones en conferencias, congresos y eventos de divulgación. La mayoría de estas presentaciones figuran, tal como se indica en cada caso, publicadas como parte de las memorias del evento respectivo