Curve reconstruction from unorganized points

Abstract

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.

Interpolating an unorganized 2D point cloud with a single closed shape

“…If the noise is such that the point spacing gets unreasonably non-uniform, then the algorithm will terminate with an incomplete or incorrect result. For such noisy data an approximation algorithm like the one presented in [26] should be preferred. If one looks closely at the statistics in Table 4, those point sets which are densely sampled (Figure 12e) are relatively less complex to reconstruct than sparsely sampled sets.…”

Generating parametric models of tubes from laser scans

“…Reconstruction of pipe surfaces from unorganized points has been investigated by Lee in [5] and later extended to canal surfaces in [6]. The methods there are based on translating surface samples along the estimated normal direction.…”

“…In the aforementioned article, Lee [5] also proposed the use of the moving least squares approximation technique for smoothing a noisy point cloud of a curve. This method has later gained much attention in the context of computing surfaces approximating a point cloud, and several variants are proposed in [7,2] and references therein.…”

Scale Selection for the Analysis of Point-Sampled Curves

“…A popular first step in the analysis for many of these problems is the computation of first-order or tangent information at each point [3,4,6,10]. One objective of this step is to reasonably capture the underlying curvilinear geometry of the point set, so as to be amenable to shape reconstruction and feature extraction.…”

“…There are several approaches in the literature, both non-parametric (tensor voting [6], radial basis functions, etc.) and parametric [5] (moving least-squares approximations [4], implicit parabolic fitting, b-splines, etc. ).…”