Compression Algorithm for Implicit 3D B-Spline Solids

Compression Algorithm for Implicit 3D B-Spline Solids Due to advantages in solid modeling with complex geometry and its ideal suitability for 3D printing, the implicit representation has been widely used in recent years. The demand for free-form shapes makes the implicit tensor-product B-spline representation attract more and more attention. However, it is an important challenge to deal with the storage and transmission requirements of enormous coefficient tensor. In this paper, we propose a new compression framework for coefficient tensors of implicit 3D tensor-product B-spline solids. The proposed compression algorithm consists of four steps, i.e., preprocessing, block splitting, using a lifting-based 3D discrete wavelet transform, and coding with 3D set partitioning in hierarchical trees algorithm. Finally, we manage to lessen the criticism of the implicit tensor-product B-spline representation of surface for its redundancy store of 3D coefficient tensor. Experimental results show that the proposed compression framework not only achieves satisfactory reconstruction quality and considerable compression ratios, but also supports progressive transmissions and random access by employing patch-wise coding strategy. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications in Mathematics and Statistics Springer Journals

Compression Algorithm for Implicit 3D B-Spline Solids

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Publisher
Springer Journals
Copyright
Copyright © 2018 by School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Mathematics, general; Statistics, general
ISSN
2194-6701
eISSN
2194-671X
D.O.I.
10.1007/s40304-018-0128-y
Publisher site
See Article on Publisher Site

Abstract

Due to advantages in solid modeling with complex geometry and its ideal suitability for 3D printing, the implicit representation has been widely used in recent years. The demand for free-form shapes makes the implicit tensor-product B-spline representation attract more and more attention. However, it is an important challenge to deal with the storage and transmission requirements of enormous coefficient tensor. In this paper, we propose a new compression framework for coefficient tensors of implicit 3D tensor-product B-spline solids. The proposed compression algorithm consists of four steps, i.e., preprocessing, block splitting, using a lifting-based 3D discrete wavelet transform, and coding with 3D set partitioning in hierarchical trees algorithm. Finally, we manage to lessen the criticism of the implicit tensor-product B-spline representation of surface for its redundancy store of 3D coefficient tensor. Experimental results show that the proposed compression framework not only achieves satisfactory reconstruction quality and considerable compression ratios, but also supports progressive transmissions and random access by employing patch-wise coding strategy.

Journal

Communications in Mathematics and StatisticsSpringer Journals

Published: May 16, 2018

References

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