Variational shape approximation of point set surfaces

Skrodzki, Martin; Zimmermann, Eric; Polthier, Konrad

doi:10.1016/j.cagd.2020.101875

Cited by 8 publications

(3 citation statements)

References 9 publications

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“…Variational shape approximation [8,50] minimizes an approximation error between the input data and a set of primitives using Lloyd's clustering algorithm [25]. This approach can be combined with sequences of splitting and merging of primitives so that the number of primitives has not to be constant and fixed a priori by the user [44]. Input data are however supposed to be free of outliers, leading to good results on synthetic data only.…”

Section: Related Workmentioning

confidence: 99%

Finding Good Configurations of Planar Primitives in Unorganized Point Clouds

Mulin¹,

Lafarge²

2022

2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

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We present an algorithm for detecting planar primitives from unorganized 3D point clouds. Departing from an initial configuration, the algorithm refines both the continuous plane parameters and the discrete assignment of input points to them by seeking high fidelity, high simplicity and high completeness. Our key contribution relies upon the design of an exploration mechanism guided by a multiobjective energy function. The transitions within the large solution space are handled by five geometric operators that create, remove and modify primitives. We demonstrate the potential of our method on a variety of scenes, from organic shapes to man-made objects, and sensors, from multiview stereo to laser. We show its efficacy with respect to existing primitive fitting approaches and illustrate its applicative interest in compact mesh reconstruction, when combined with a plane assembly method.

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Section: Related Workmentioning

confidence: 99%

Finding Good Configurations of Planar Primitives in Unorganized Point Clouds

Mulin¹,

Lafarge²

2022

2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

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show abstract

“…To fit candidate primitive surface patches to the input shape discretized as a point cloud or polygonal mesh, early works apply probabilistic search like RANSAC [Schnabel et al 2009[Schnabel et al , 2007 or solve variational optimizations [Cohen-Steiner et al 2004;Skrodzki et al 2020;Yan et al 2012] that iterate between primitive fitting and segmentation. Subsequent works apply global optimization over structural constraints to enhance the local primitive fitting as well as the overall model structural regularity [Li et al 2011;Nan and Wonka 2017].…”

Section: Related Workmentioning

confidence: 99%

ComplexGen: CAD Reconstruction by B-Rep Chain Complex Generation

Guo¹,

Liu²,

Pan³

et al. 2022

Preprint

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“…This paper is an extension of a chapter in a PhD thesis (Skrodzki, 2019, Chapter 5). Some results of the paper have been presented as a poster at the International Geometry Summit 2019 in Vancouver, Canada and have been published in the corresponding poster proceedings, see Skrodzki et al (2019).…”

Section: Introductionmentioning

confidence: 99%

Variational Shape Approximation of Point Set Surfaces

Skrodzki,

Zimmermann,

Polthier

2020

Preprint

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In this work, we present a translation of the complete pipeline for variational shape approximation (VSA) to the setting of point sets. First, we describe an explicit example for the theoretically known non-convergence of the currently available VSA approaches. The example motivates us to introduce an alternate version of VSA based on a switch operation for which we prove convergence. Second, we discuss how two operations-split and merge-can be included in a fully automatic pipeline that is in turn independent of the placement and number of initial seeds. Third and finally, we present two approaches how to obtain a simplified mesh from the output of the VSA procedure. This simplification is either based on simple plane intersection or based on a variational optimization problem. Several qualitative and quantitative results prove the relevance of our approach.

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Variational shape approximation of point set surfaces

Cited by 8 publications

References 9 publications

Finding Good Configurations of Planar Primitives in Unorganized Point Clouds

Finding Good Configurations of Planar Primitives in Unorganized Point Clouds

ComplexGen: CAD Reconstruction by B-Rep Chain Complex Generation

Variational Shape Approximation of Point Set Surfaces

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