Set Of Unorganized Points Research Articles

Curve reconstruction from unorganized points

We present an algorithm to approximate a set of unorganized points with a simple curve without self-intersections. The moving least-squares method has a good ability to reduce a point cloud to a thin curve-like shape which is a near-best approximation of the point set. In this paper, an improved moving least-squares technique is suggested using Euclidean minimum spanning tree, region expansion and refining iteration. After thinning a given point cloud using the improved moving least-squares technique we can easily reconstruct a smooth curve. As an application, a pipe surface reconstruction algorithm is presented.

Implicit simplicial models for adaptive curve reconstruction

Parametric deformable models have been extensively and very successfully used for reconstructing free-form curves and surfaces, and for tracking nonrigid deformations, but they require previous knowledge of the topological type of the data, and good initial curve or surface estimates. With deformable models, it is also computationally expensive to check for and to prevent self-intersections while tracking deformations. The implicit simplicial models that we introduce in this paper are implicit curves and surfaces defined by piecewise linear functions. This representation allows for local deformations, control of the topological type, and prevention of self-intersections during deformations. As a first application, we also describe an algorithm for 2D curve reconstruction from unorganized sets of data points. The topology, the number of connected components, and the geometry of the data are all estimated using an adaptive space subdivision approach. The main four components of the algorithm are topology estimation, curve fitting, adaptive space subdivision, and mesh relaxation.

A Graph–Based Approach to Surface Reconstruction

AbstractA new approach to the reconstruction of a surface from an unorganized set of points in space is presented. The point set may for example be obtained with a laser scanner or a manual digitizing tool, and is the only source of information about the shape of the acquired object. The basic idea is to calculate the Euclidean minimum spanning tree (EMST) of the given points. The EMST is then augmented to the so‐called surface description graph (SDG). Finally the wire frame defined by the SDG are filled with triangles. The advantage of our approach is that also highly non‐convex and even disconnected surfaces are reconstructed quite reliably. This is demonstrated for a variety of data sets.

Surface reconstruction from unorganized points

We describe and demonstrate an algorithm that takes as input an unorganized set of points {x l , . . . . x n } ⊂ R 3 on or near an unknown manifold M, and produces as output a simplicial surface that approximates M. Neither the topology, the presence of boundaries, nor the geometry of M are assumed to be known in advance - all are inferred automatically from the data. This problem naturally arises in a variety of practical situations such as range scanning an object from multiple view points, recovery of biological shapes from two-dimensional slices, and interactive surface sketching.