Compact implicit surface reconstruction via low-rank tensor approximation

Pan, Maodong; Tong, Weihua; Chen, Falai

doi:10.1016/j.cad.2016.05.007

Cited by 25 publications

(9 citation statements)

References 22 publications

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“…[23,24] consider compactly supported RBF to reduce the computational cost and improve the efficiency of the reconstruction process. Pan et al [25] incorporated a low-rank tensor approximation technique and reduced the storage requirement efficiently. 2…”

Section: Related Workmentioning

confidence: 99%

Implicit progressive-iterative approximation for curve and surface reconstruction

Hamza

Lin

2020

Computer Aided Geometric Design

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Implicit curve and surface reconstruction attracts the attention of many researchers and gains a wide range of applications, due to its ability to describe objects with complicated geometry and topology. However, extra zero-level sets or spurious sheets arise in the reconstruction process makes the reconstruction result challenging to be interpreted and damage the final result. In this paper, we proposed an implicit curve and surface reconstruction method based on the progressive-iterative approximation method, named implicit progressive-iterative approximation (I-PIA). The proposed method elegantly eliminates the spurious sheets naturally without requiring any explicit minimization procedure, thus reducing the computational cost greatly and providing high-quality reconstruction results. Numerical examples are provided to demonstrate the efficiency and effectiveness of the proposed method.

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Section: Related Workmentioning

confidence: 99%

Implicit progressive-iterative approximation for curve and surface reconstruction

Hamza

Lin

2020

Computer Aided Geometric Design

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“…The details of low-rank tensor approximation and its applications have been discussed in depth in [9]. Recently, the low-rank tensor optimization has been applied in graphics and geometric modeling community, e.g., in finding the upright orientation of 3D shapes [30] and in compact implicit surface reconstructions [27]. For other applications of low-rank tensors in geometric modeling and processing, please refer to [38] and references therein.…”

Section: Applications Of Low-rank Tensor Approximationmentioning

confidence: 99%

“…The above algorithm iteratively solves two sub-problems to obtain two sequences of complex functions {ν k } and {f k }. In order to accelerate the convergence of the algorithm, we add a weight into the second term of problem (16) after t 0 iterations, where t 0 satisfies µ(f t0 ) ∞ − 1 < 0 for a threshold 0 , which leads to the following problem arg min (27) where the weight ω = 1/((1 − |µ(f t0 )|) 2 + δ) and δ is a threshold which helps to avoid division by zero. The problem ( 27) can be solved in the same way as the problem (16).…”

Section: Post-processingmentioning

confidence: 99%

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A Low-rank Spline Approximation of Planar Domains

Pan,

Chen

2017

Preprint

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Construction of spline surfaces from given boundary curves is one of the classical problems in computer aided geometric design, which regains much attention in isogeometric analysis in recent years and is called domain parameterization. However, for most of the state-of-the-art parameterization methods, the rank of the spline parameterization is usually large, which results in higher computational cost in solving numerical PDEs. In this paper, we propose a low-rank representation for the spline parameterization of planar domains using low-rank tensor approximation technique, and apply quasi-conformal map as the framework of the spline parameterization. Under given correspondence of boundary curves, a quasi-conformal map with low rank and low distortion between a unit square and the computational domain can be modeled as a nonlinear optimization problem. We propose an efficient algorithm to compute the quasi-conformal map by solving two convex optimization problems alternatively. Experimental results show that our approach can produce a bijective and low-rank parametric spline representation of planar domains, which results in better performance than previous approaches in solving numerical PDEs.

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“…Besides, the implicit surfaces possess the robustness for collision detections [6] and Boolean operations [7], which are appreciated by the techniques of solid modeling [8]. They are also suitable for reconstructing surfaces from datasets of noisy, incomplete or non-uniformly distributed [9], [10].…”

Section: Introductionmentioning

confidence: 99%

Detailed Voxel-Based Implicit Modeling With Local Boolean Composition of Discrete Level Sets

et al. 2020

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Compared with the functionally-based implicit models, the level set models are usually defined by discretely sampling the implicit function values over the volume grid to represent the shapes, which are suitable for scientific computing and engineering. However, the voxel-based level set methods usually lose some features and details to represent the solids due to the finite grid resolutions. In this paper, we propose a more accurate voxel-based implicit modeling method based on discrete level sets. Compared with the traditional level set methods, more than one level set function can be defined in an implicit model with our approach by classifying the cells of the volume grid. The local Boolean compositions conducted over the compound cells are used to depict the interactions of different implicit surfaces represented by corresponding level set functions, and the sharp and thin details caused by Boolean operations are preserved owing to the definition of the compound cells. We show in our experiments that our method is robust to provide the more detailed implicit description of the shapes with less loss of the features than the conventional voxel-based level set methods. INDEX TERMS Compound cells, discrete level sets, local Boolean composition, voxel-based implicit modeling.

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Compact implicit surface reconstruction via low-rank tensor approximation

Cited by 25 publications

References 22 publications

Implicit progressive-iterative approximation for curve and surface reconstruction

Implicit progressive-iterative approximation for curve and surface reconstruction

A Low-rank Spline Approximation of Planar Domains

Detailed Voxel-Based Implicit Modeling With Local Boolean Composition of Discrete Level Sets

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