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Biorthogonal Wavelet Surface Reconstruction Using Partial Integrations
Xiaohua Ren1; Luan Lyu1; Xiaowei He2; Wei Cao1; Zhixin Yang3; Bin Sheng6; Yanci Zhang5; Enhua Wu1,2,4
Source PublicationComputer Graphics Forum

We introduce a new biorthogonal wavelet approach to creating a water-tight surface defined by an implicit function, from a finite set of oriented points. Our approach aims at addressing problems with previous wavelet methods which are not resilient to missing or nonuniformly sampled data. To address the problems, our approach has two key elements. First, by applying a three-dimensional partial integration, we derive a new integral formula to compute the wavelet coefficients without requiring the implicit function to be an indicator function. It can be shown that the previously used formula is a special case of our formula when the integrated function is an indicator function. Second, a simple yet general method is proposed to construct smooth wavelets with small support. With our method, a family of wavelets can be constructed with the same support size as previously used wavelets while having one more degree of continuity. Experiments show that our approach can robustly produce results comparable to those produced by the Fourier and Poisson methods, regardless of the input data being noisy, missing or nonuniform. Moreover, our approach does not need to compute global integrals or solve large linear systems.

KeywordCcs Concepts •computing Methodologies → Mesh Geometry Models •mathematics Of Computing → Computation Of Transforms
URLView the original
Indexed BySCI
WOS Research AreaComputer Science
WOS SubjectComputer Science, Software Engineering
WOS IDWOS:000448166700002
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Document TypeJournal article
CollectionFaculty of Science and Technology
Corresponding AuthorEnhua Wu
Affiliation1.FST, University of Macau
2.State Key Lab. of CS, ISCAS & Univ. of CAS
3.FST, University of Macau State Key Lab. of Internet of Things for Smart City, Univ. of Macau
4.Zhuhai-UM S&T Research Institute
5.Sichuan University
6.Shanghai Jiao Tong University
First Author AffilicationUniversity of Macau
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Xiaohua Ren,Luan Lyu,Xiaowei He,et al. Biorthogonal Wavelet Surface Reconstruction Using Partial Integrations[J]. Computer Graphics Forum,2018,37(7):13-24.
APA Xiaohua Ren.,Luan Lyu.,Xiaowei He.,Wei Cao.,Zhixin Yang.,...&Enhua Wu.(2018).Biorthogonal Wavelet Surface Reconstruction Using Partial Integrations.Computer Graphics Forum,37(7),13-24.
MLA Xiaohua Ren,et al."Biorthogonal Wavelet Surface Reconstruction Using Partial Integrations".Computer Graphics Forum 37.7(2018):13-24.
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