Technical SectionView-dependent level-of-detail abstraction for interactive atomistic visualization of biological structures☆
Graphical abstract
Introduction
Biologists have started to rely significantly on biological visualization and simulation to understand the molecular machinery of life. In coarse-grained (the so-called mesoscopic) particle-based simulations, biological structures often consist of millions to billions of atoms. Real-time atomistic rendering is a challenging task as it incorporates a large number of particles.
On the other hand, biological data sets consist of only a few individual molecules with a large number of instances. To take advantage of the repetitive nature, many instances can be rendered using the same building block. To reduce the geometric complexity of rendering a biological scene, hierarchical geometrical representations are often used to simplify unnecessary model details. Particle-based data reduction and data simplification are the main approaches of molecular hierarchical abstraction. As the work of Parulek et al. [1] shows that fast hierarchical clustering (FHC) [2] is an available simplification approach to abstract various levels of detail. However, the utilization of FHC brings two major limitations. First, it is difficult to find the most suitable parameters for evaluating the clustering method. Second, utilizing hierarchical abstraction is necessary to perform sequential clustering.
For interactively rendering large biological scenes, we need to overcome these limitations. Our main focus lies in the hierarchical geometry abstraction of large biomolecular data sets on PCs. The contributions of this paper can be summarized as follows:
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With a volume-based distance metric (VDM), we propose sophisticated molecular hierarchical representations by hierarchical clustering. Our distance metric achieves a better quality of clustering and an outstanding performance.
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We define an approximate metric to quantitatively evaluate the object space error, and we also use this error metric for adaptive LOD selection.
Our main motivation is to help scientists to see the big biological structure interactively in a level-of-detail way, and achieve atomistic visualizations of mesoscopic simulations which can have above billions of atoms. We organize the rest of the paper as follows. After presenting the related works on large biological visualization (Section 2), we illustrate the framework of our view-dependent macromolecule rendering (Section 3). We present the details of molecular hierarchical representation (Section 4), in which surface representation (Section 4.1) and the hierarchical clustering method (Section 4.2) are explained. Consequently, we present the view-dependent LOD rendering algorithm (Section 5), including our object space error metric (Section 5.1) and LOD selection algorithm (Section 5.2). A discussion of the results is provided in Section 6. Section 7 provides discussion and outlines the limitations of our work. Conclusions and future work are presented in Section 8.
Section snippets
Related work
Because data sets consist of a large number of particles, some parallel visualization systems, such as ParaView and VMD, are developed for clusters of workstations. As noted in the Introduction section, our main focus is hierarchical geometry abstraction of large biomolecular data sets on current desktop PCs. Our approach builds on several aspects of previous work on large biological structure visualization, in particular with respect to molecular surface representation, LOD approaches and
Overview
Motivated by the need for the visualization of large molecular systems, we design a view-dependent macromolecule rendering framework as shown in Fig. 1. Our framework consists of four steps. The first two steps are data processing. The models of building blocks with various LODs are prepared for rendering, and the matrix list is prepared for assembling. The last two steps are at run time, i.e., the LOD selection runs on the CPU, and the real-time renders on the GPU.
In the LOD model preparing
Molecule surface representation method
In the spirit of focus and context visualization, we abstract several geometry levels from molecule surfaces of building blocks. As shown in Fig. 2, the hierarchy contains three constant biological levels: atom, residue and molecule. The focus level is used to provide useful information about a local molecular detail. Except for the focus level, the successive levels are spherical space-filling to provide a gross structural context. This is the fastest representation to render. Therefore, we
Approximate object space error metric
To evaluate the error caused by hierarchical clustering quantitatively, we define an approximate object space error metric. Fig. 7 shows that, because the cluster A represents a set of atoms, the object space error is anisotropic and difficult to compute. After using clustering the method, these atoms for the most part gather densely around the centre of bounding sphere. Let “big atom” approximate these atoms. Fig. 7 shows that the “big atom” has the same centre as the bounding sphere, and
Result analysis
We measured the performance of clustering, as well as the performance of LOD rendering. The data sets are from the RCSB Protein Data Bank [32]. The test platform is a Windows 7 PC with an Intel Core i7 and Nvidia Geforce GTX 780Ti. We use Megamol [29] as our ray-casting rendering engine, and the window size was set to 1920×1080 pixels for all measurements.
Discussions and limitations
The utilization of our LOD abstraction has two major limitations.
The shape of hierarchical abstraction: In our current work, each formed cluster is represented by a sphere, which bounds all child elements within this cluster. It is easy and fast to use hierarchical clustering for spheres. However, when the abstraction level becomes high, the object space error of the cluster will be amplified. Although we can control the screen space error threshold τ to guarantee the quality of output image,
Conclusion and future work
In this paper, we have demonstrated an LOD representation for atomistic visualization of biological structures. We fulfilled the promise of fast molecular hierarchical abstraction by developing a residue-considered multi-levels method. With the volume-based distance metric, the time consumption of our method is two orders of magnitude shorter than previous atom-based clustering. Our VDM can also effectively reduce space error caused by abstraction. Moreover, based on the approximate error
Acknowledgements
We would like to thank the anonymous reviewers for their help in improving the paper, and BenZhuo Lu, Michael Krone and Julius Parulek for helpful discussions. This work was partially supported by 863 Program, and the National Science Foundation of China (Grant no. 61071199).
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This article was recommended for publication by Stefan Bruckner.