Growing Least Squares for the Analysis of Manifolds in Scale‐Space

Mellado, Nicolas; Guennebaud, Gaël; Barla, Pascal; Reuter, Patrick; Schlick, Christophe

doi:10.1111/j.1467-8659.2012.03174.x

Cited by 32 publications

(59 citation statements)

References 34 publications

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“…As future work, it might be beneficial Table 1: sheet of paper 1 (left), and half-cylinder (right) with both the input and the PC-MLS reconstruction. to study whether some kind of multi-scale analysis [17] could allow to resolve some of the ambiguous cases as this might allow to produce even more developable reconstructions. Our approach could also be easily adapted to fall back to a full quadratic approximation instead of a linear one.…”

Section: Resultsmentioning

confidence: 99%

“…Given an unstructured and possibly noisy point cloud, MLS define a continuous surface by means of a continuously moving surface proxy approximating the input points nearby the considered evaluation point and some weight functions playing the role of a low-pass filter. By adjusting the support size of the weight functions, smoothness can be traded for proximity to the data [17].…”

Section: Motivationmentioning

confidence: 99%

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Parabolic-cylindrical moving least squares surfaces

Ridel

Guennebaud

Reuter

et al. 2015

Computers & Graphics

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a b s t r a c tMoving least squares (MLS) surface approximation is a popular tool for the processing and reconstruction of non-structured and noisy point clouds. This paper introduces a new variant improving the approximation quality when the underlying surface is assumed to be locally developable, which is often the case in point clouds coming from the acquisition of manufactured objects. Our approach follows Levin's classical MLS procedure: the point cloud is locally approximated by a bivariate quadratic polynomial height-field defined in a local tangent frame. The a priori developability knowledge is introduced by constraining the fitted polynomials to have a zero-Gaussian curvature leading to the actual fit of the so-called parabolic cylinders. When the local developability assumption cannot be made unambiguously, our fitted parabolic cylinders seamlessly degenerate to linear approximations. We show that our novel MLS kernel reconstructs more locally developable surfaces than previous MLS methods while being faithful to the data.

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Section: Resultsmentioning

confidence: 99%

Section: Motivationmentioning

confidence: 99%

Parabolic-cylindrical moving least squares surfaces

Ridel

Guennebaud

Reuter

et al. 2015

Computers & Graphics

Self Cite

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show abstract

“…For each direction, a 1D relief function was obtained by cubic polynomial fitting at multiple scales. Mellado et al [24] built a scale-space through least-square fits of a low-degree algebraic surface onto neighborhoods of continuously increasing size, and proposed a local geometric variation by combining the curvature, the normal and the distance to 0-isosurface. All these multiscale features can only be evaluated at a relative small scale since they are local properties.…”

Section: Related Workmentioning

confidence: 99%

Polynomial local shape descriptor on interest points for 3D part-in-whole matching

Quan

Tang

2015

Computer-Aided Design

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“…As shown in the experiments, this technique is very sensitive and does not provide sufficiently robust results on digital surfaces. Mellado et al [10] have introduced a fast least square spherical fitting approach to a point cloud to create a multi-scale feature score. Again, the scale-space parameter is the neighborhood size considered in the fitting.…”

Section: Introductionmentioning

confidence: 99%

Scale-space feature extraction on digital surfaces

Levallois

Cœurjolly

Lachaud

2015

Computers & Graphics

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a b s t r a c tA classical problem in many computer graphics applications consists in extracting significant zones or points on an object surface, like loci of tangent discontinuity (edges), maxima or minima of curvatures, inflection points, etc. These places have specific local geometrical properties and often called generically features. An important problem is related to the scale, or range of scales, for which a feature is relevant. We propose a new robust method to detect features on digital data (surface of objects in Z 3 , which exploits asymptotic properties of recent digital curvature estimators. In Coeurjolly et al.[1] and Levallois et al. [1,2], authors have proposed curvature estimators (mean, principal and Gaussian) on 2D and 3D digitized shapes and have demonstrated their multigrid convergence (for C 3 -smooth surfaces). Since such approaches integrate local information within a ball around points of interest, the radius is a crucial parameter. In this paper, we consider the radius as a scale-space parameter. By analyzing the behavior of such curvature estimators as the ball radius tends to zero, we propose a tool to efficiently characterize and extract several relevant features (edges, smooth and flat parts) on digital surfaces.

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Growing Least Squares for the Analysis of Manifolds in Scale‐Space

Cited by 32 publications

References 34 publications

Parabolic-cylindrical moving least squares surfaces

Parabolic-cylindrical moving least squares surfaces

Polynomial local shape descriptor on interest points for 3D part-in-whole matching

Scale-space feature extraction on digital surfaces

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