Compression Algorithm for Implicit 3D B-Spline Solids

• Published in: Communications in mathematics and statistics Vol. 6; no. 2; pp. 119 - 140
• Main Authors: Song, Yanzhi, Luo, Yixin, Liu, Yuan, Deng, Jiansong, Yang, Zhouwang
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2018; Springer Nature B.V
• Subjects: Algorithms; Coding; Coefficients; Discrete Wavelet Transform; Mathematics; Mathematics and Statistics; Preprocessing; Random access; Redundancy; Representations; Solid modelling; Statistics; Tensors; Three dimensional printing; Wavelet transforms; Compression; Progressive transmission; 94A24; 3D discrete wavelet transform; Implicit tensor-product B-spline; 65D17; Additive manufacturing; 3D SPIHT
• ISSN: 2194-6701; 2194-671X
• DOI: 10.1007/s40304-018-0128-y

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.