一种多分辨率体绘制中张量分解最佳秩选取算法

An Algorithm for Choosing Optimal Rank in Tensor Approximation of Multi-Resolution Volume Rendering

采用多分辨率体绘制是解决海量数据体绘制的一种有效方法,但是基于信息熵的多分辨率体绘制在解决信噪比低、细微结构复杂的物探领域内体数据时存在较大的缺陷。而数据的张量近似是通过高阶奇异值分解提取数据的特征基,并通过特征基的线性组合来近似包含细微结构的低信噪比体数据。因此可以在保证数据压缩率的情况下,保留数据的细微构造信息。本文针对基于张量近似的多分辨率体绘制中秩的选取问题开展研究,低秩实现了高的数据压缩,但峰值信噪比低;高秩实现了较好的绘制效果,但数据压缩率低。本文提出了一种张量近似中最佳秩的选取算法。其基本思想是在高秩分解的基础上,通过二分搜索选取满足误差门限的最佳秩。并且,数据分块处理,不同分块采用不同秩,实现了在满足数据压缩率的情况下,保证有较好的绘制效果。通过仿真结果表明,相比于统一秩的高秩分解而言,提升了数据压缩率,而整体绘制效果基本与高秩分解相当;相比于统一秩的中低秩分解而言,在增加少量的压缩率的情况下,提升了绘制效果。

Multi-resolution volume rendering is an effective method to solve the problem of massive data volume rendering. The comentropy based multi-resolution volume rendering has an obvious limitation when handling data of geophysical field which have a low SNR and complex microstructure characteristics. Tensor approximation can extract the characteristic bases of the data, and gain the data approximation with microstructure characteristics by means of the linear combination of the characteristic bases. We made a research about how to choose the rank in tensor approximation multi-resolution volume rendering. Low rank gained a high compression ratio, but low PSNR. High rank gained an ideal rendering effect, but low compression ratio. In this paper, we presented a method that could find the best rank adaptively for every block. Based on high rank decomposition, we did binary search to find the optimal rank which will exactly meet the error threshold. Mean-while, data were separated into blocks, different blocks have different ranks. Experimental results show that our method has a higher compression ratio and similar render result in comparison with high rank decomposition and our method has a significant better rendering result and a slightly lower compression ratio.