Fitting unorganized point clouds with active implicit B-spline curves

Yang, Zhouwang; Deng, Jiansong; Chen, Falai

doi:10.1007/s00371-005-0340-0

Cited by 55 publications

(28 citation statements)

References 20 publications

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“…2(right) depicts how an IBS provides a more flexible representation than an IP. Moreover, since it is linear with respect to its coefficient vector it is appropriate for linear fitting [20] as well as the non-linear ones [21], [22].…”

Section: A Solution Spacementioning

confidence: 99%

Implicit B-Spline Surface Reconstruction

Rouhani

Sappa

Boyer

2015

IEEE Trans. on Image Process.

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Abstract-This paper presents a fast and flexible curve, and surface reconstruction technique based on implicit B-spline. This representation does not require any parameterization and it is locally supported. This fact has been exploited in this paper to propose a reconstruction technique through solving a sparse system of equations. This method is further accelerated to reduce the dimension to the active control lattice. Moreover, the surface smoothness and user interaction are allowed for controlling the surface. Finally, a novel weighting technique has been introduced in order to blend small patches and smooth them in the overlapping regions. The whole framework is very fast and efficient and can handle large cloud of points with very low computational cost. The experimental results show the flexibility and accuracy of the proposed algorithm to describe objects with complex topologies. Comparisons with other fitting methods highlight the superiority of the proposed approach in the presence of noise and missing data.

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Section: A Solution Spacementioning

confidence: 99%

Implicit B-Spline Surface Reconstruction

Rouhani

Sappa

Boyer

2015

IEEE Trans. on Image Process.

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“…In [31] the reconstruction of implicit surfaces from given polygonal models is considered. Active implicit B-spline curves for fitting unorganized point clouds were used in [41], extending the geometric distance minimization in the case of implicitly defined curves using a trust-region algorithm.…”

Section: Surface Fittingmentioning

confidence: 99%

Robust fitting of implicitly defined surfaces using Gauss–Newton-type techniques

Aigner

Jüttler

2009

Vis Comput

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We describe Gauss-Newton type methods for fitting implicitly defined curves and surfaces to given unorganized data points. The methods are suitable not only for leastsquares approximation, but they can also deal with general error functions, such as approximations to the ℓ 1 or ℓ ∞ norm of the vector of residuals. Two different definitions of the residuals will be discussed, which lead to two different classes of methods: direct methods and data-based ones. In addition we discuss the continuous versions of the methods, which furnish geometric interpretations as evolution processes.It is shown that the data-based methods -which are less costly, as they work without the computation of the closest points -can efficiently deal with error functions that are adapted to noisy and uncertain data. In addition, we observe that the interpretation as evolution process allows to deal with the issues of regularization and with additional constraints.

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“…The representation of planar object in terms of curve has many advantages, for example, scaling, shearing, translation, rotation and clipping operations can be performed. Although a good amount of work has been done in the area [10][11][12][13][14][15][16], it is still desired to proceed further. Most of the research has tackled this kind of problem by curve subdivision or curve segmentation.…”

Section: Introductionmentioning

confidence: 98%

“…Curve reconstruction problem is also solved by approximating the point clouds using implicit B-spline curve [12]. The authors, in [12], have used trust region algorithm in optimization theory as minimization heuristics.…”

Section: Introductionmentioning

confidence: 99%

Capturing Outlines of Planar Images by Cubic Spline using Stochastic Evolution

Sarfraz

Parvez

Rizvi

2007

Computer Graphics, Imaging and Visualisation (CGIV 2007)

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This paper is concerned with a new technique of curve fitting. The technique has various phases including extracting outlines of images, detecting corner points from the detected outline, addition of extra knot points if needed. The last phase makes a significant contribution by making the technique automated. It uses the idea of Stochastic Evolution to optimize the shape parameters in the description of the generalized cubic spline. It ultimately produces optimal results for the approximate vectorization of the digital contour obtained from the planar images.

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Fitting unorganized point clouds with active implicit B-spline curves

Cited by 55 publications

References 20 publications

Implicit B-Spline Surface Reconstruction

Implicit B-Spline Surface Reconstruction

Robust fitting of implicitly defined surfaces using Gauss–Newton-type techniques

Capturing Outlines of Planar Images by Cubic Spline using Stochastic Evolution

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