An Improved Method for NURBS Free-Form Surface Based on Discrete Stationary Wavelet Transform

Kong, Deming; Tian, Xiaoqiang; Kong, Dehan; Zhang, Xiaodan; Li, Yuan

doi:10.1109/access.2020.2986607

Cited by 4 publications

(5 citation statements)

References 17 publications

(22 reference statements)

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“…Compared with Shannon-Cosine interpolation wavelet method, the interval wavelet constructed in this paper reduces the boundary effect and avoids the phenomenon of infinite oscillation. (2) The wavelet multi-scale interpolation operator constructed in this paper is sensitive to the change of the gradient. According to this character, sparse feature interpolation points can be obtained adaptively.…”

Section: Discussionmentioning

confidence: 99%

“…Then, we prove the continuity of the functions S c (x) at the endpoints x = ±N/2. To the Equation (2) proposed in this paper is obvious. To the function S c (x) in Reference [20], we also give its proof as follows.…”

Section: Shannon-cosine Interpolation Waveletmentioning

confidence: 92%

“…In modern industrial manufacturing technology, curve and surface modeling technology is one of the very important technologies, and its plays an important role in numerical fitting and approximation; computer vision; streamlined design of crafts, outline design of aircraft, automobiles and ships; restoration of cultural relics; geological surface interpolation [1]; reverse engineering [2,3]; and other fields. Besides, it is the core of computer-aided geometric design (CAGD) [4].…”

Section: Introductionmentioning

confidence: 99%

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Hermite Interpolation Based Interval Shannon-Cosine Wavelet and Its Application in Sparse Representation of Curve

Wang

Mei

et al. 2020

Mathematics

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Using the wavelet transform defined in the infinite domain to process the signal defined in finite interval, the wavelet transform coefficients at the boundary are usually very large. It will bring severe boundary effect, which reduces the calculation accuracy. The construction of interval wavelet is the most common method to reduce the boundary effect. By studying the properties of Shannon-Cosine interpolation wavelet, an improved version of the wavelet function is proposed, and the corresponding interval interpolation wavelet based on Hermite interpolation extension and variational principle is designed, which possesses almost all of the excellent properties such as interpolation, smoothness, compact support and normalization. Then, the multi-scale interpolation operator is constructed, which can be applied to select the sparse feature points and reconstruct signal based on these sparse points adaptively. To validate the effectiveness of the proposed method, we compare the proposed method with Shannon-Cosine interpolation wavelet method, Akima method, Bezier method and cubic spline method by taking infinitesimal derivable function cos(x) and irregular piecewise function as an example. In the reconstruction of cos(x) and piecewise function, the proposed method reduces the boundary effect at the endpoints. When the interpolation points are the same, the maximum error, average absolute error, mean square error and running time are 1.20 × 10−4, 2.52 × 10−3, 2.76 × 10−5, 1.68 × 10−2 and 4.02 × 10−3, 4.94 × 10−4, 1.11 × 10−3, 9.27 × 10−3, respectively. The four indicators mentioned above are all lower than the other three methods. When reconstructing an infinitely derivable function, the curve reconstructed by our method is smoother, and it satisfies C2 and G2 continuity. Therefore, the proposed method can better realize the reconstruction of smooth curves, improve the reconstruction efficiency and provide new ideas to the curve reconstruction method.

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Section: Discussionmentioning

confidence: 99%

Section: Shannon-cosine Interpolation Waveletmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

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Hermite Interpolation Based Interval Shannon-Cosine Wavelet and Its Application in Sparse Representation of Curve

Wang

Mei

et al. 2020

Mathematics

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“…Kong et al adopted the discrete stationary wavelet transform method to extract the feature points of the surface to be reconstructed, which are the input data of the NURBS equation. Compared with the traditional NURBS surface reconstruction method, the root mean square error of the fitting result is reduced to 77.64% [129].…”

Section: Parametric Shape Representation Methodsmentioning

confidence: 99%

High-Precision 3D Reconstruction for Small-to-Medium-Sized Objects Utilizing Line-Structured Light Scanning: A Review

2021

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Three-dimensional reconstruction technology has demonstrated broad application potential in the industrial, construction, medical, forestry, agricultural, and pastural sectors in the last few years. High-quality digital point cloud information exists to help researchers to understand objects and environments. However, current research mainly focuses on making adaptive adjustments to various scenarios and related issues in the application of this technology rather than looking for further improvements and enhancements based on technical principles. Meanwhile, a review of approaches, algorithms, and techniques for high-precision 3D reconstruction utilizing line-structured light scanning, which is analyzed from a deeper perspective of elementary details, is lacking. This paper takes the technological path as the logical sequence to provide a detailed summary of the latest development status of each key technology, which will serve potential users and new researchers in this field. The focus is placed on exploring studies reconstructing small-to-medium-sized objects, as opposed to performing large-scale reconstructions in the field.

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“…More advanced approximation methods have therefore been proposed, e.g. by adding additional criteria [5], using discrete stationary wavelet transform [6], genetic algorithms [7], evolutionary strategies [8], [9], combinations of hybrid optimization algorithms and iterative schemes [10], [11], subdivision methods [12], reparametrization [13]. However, in general these methods also suffer from not fitting the mesh vertices and many of them also over parametrizes the surface.…”

Section: Introductionmentioning

confidence: 99%

A New Method for Generating Work Piece Surface Representations for Robotic Machining

Leth

Petersen

2021

2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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Execution of automatically generated programs for accurate robotic machining requires the generated trajectories to be not only accurate with respect to the work piece, but also that the trajectories are continuous differentiable (C 1 ) while avoiding unnecessary large curvatures leading to large accelerations that could compromise machining quality or speed. A widely used work piece representation is 3D triangle meshes as they can be easily generated in any CAD representations and from surface scans, and they are also very suitable for robotics applications. However, they lack the C 1 property across the triangle edges.In this paper, a new method for generating C 1 surfaces based on 3D triangle meshes is presented. It will be shown by an example that the method is as good as existing methods with respect to the accuracy of the generated surface, and that the problem with large curvatures is much smaller than for existing methods. Moreover, the difficult input specification of derivatives at the vertices is avoided with this method.

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An Improved Method for NURBS Free-Form Surface Based on Discrete Stationary Wavelet Transform

Cited by 4 publications

References 17 publications

Hermite Interpolation Based Interval Shannon-Cosine Wavelet and Its Application in Sparse Representation of Curve

Hermite Interpolation Based Interval Shannon-Cosine Wavelet and Its Application in Sparse Representation of Curve

High-Precision 3D Reconstruction for Small-to-Medium-Sized Objects Utilizing Line-Structured Light Scanning: A Review

A New Method for Generating Work Piece Surface Representations for Robotic Machining

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