Elsevier

Computers & Graphics

Volume 52, November 2015, Pages 62-71
Computers & Graphics

Technical Section
View-dependent level-of-detail abstraction for interactive atomistic visualization of biological structures

https://doi.org/10.1016/j.cag.2015.06.008Get rights and content

Highlights

  • A view-dependent macromolecule rendering framework has been designed.

  • Several geometry levels from molecule surfaces of building block were abstracted.

  • A volume-based distance metric was proposed for hierarchical clustering.

  • Approximate object space error metric was proposed for LOD rendering.

  • The view-dependent approach provides valid results in large biological scene with more than 10 billion atoms.

Abstract

The visualization of biological structures is a challenging task because it requires rendering millions to billions of atoms in real time. In this paper, we propose a view-dependent approach by which a large biological scene can be visualized interactively. In this scheme, we first extract several levels of building blocks of biological structures from a molecular abstraction based on hierarchical clustering. We then define a volume-based distance metric for the clustering process to reduce “inflation” error and propose a quantitative error metric for the object space error evaluation. Finally, we utilize an adaptive screen-space level-of-detail selection with the error metric at run time. Empirical results demonstrate that our molecular hierarchical abstraction method achieves high quality rendering results and performs better than other existing methods. Moreover, our result also shows that the view-dependent approach provides valid results in a large biological scene with more than 10 billion elements.

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:

  • 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.

  • 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” A 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).

References (32)

  • A.N. Raposo et al.

    3d molecular assembling of b-dna sequences using nucleotides as building blocks

    Graph Models

    (2012)
  • J. Parulek et al.

    Continuous levels-of-detail and visual abstraction for seamless molecular visualization

    Comput Graph Forum

    (2014)
  • D. Müllner

    fastclusterfast hierarchical, agglomerative clustering routines for r and python

    J Stat Softw

    (2013)
  • B. Lee et al.

    The interpretation of protein structuresestimation of static accessibility

    J Mol Biol

    (1971)
  • F.M. Richards

    Areas, volumes, packing, and protein structure

    Annu Rev Biophys Bioeng

    (1977)
  • Greer J, Bush BL. Macromolecular shape and surface maps by solvent exclusion. Proc Natl Acad Sci USA...
  • J.F. Blinn

    A generalization of algebraic surface drawing

    ACM Trans Graph

    (1982)
  • N. Lindow et al.

    Ligand excluded surfacea new type of molecular surface

    IEEE Trans Vis Comput Graph

    (2014)
  • M. Tarini et al.

    Ambient occlusion and edge cueing for enhancing real time molecular visualization

    IEEE Trans Vis Comput Graph

    (2006)
  • M. Krone et al.

    Interactive visualization of molecular surface dynamics

    IEEE Trans Vis Comput Graph

    (2009)
  • N. Lindow et al.

    Accelerated visualization of dynamic molecular surfaces

    Comput Graph Forum

    (2010)
  • Chavent, Matthieu and Lévy, Bruno and Krone, Michael and Bidmon, Katrin and Nominé, Jean-Philippe and Ertl, Thomas and...
  • Parulek J, Viola I. Implicit representation of molecular surfaces. In: Proceedings of the IEEE Pacific visualization...
  • Y. Kanamori et al.

    Gpu-based fast ray casting for a large number of metaballs

    Comput Graph Forum

    (2008)
  • Krone M, Grottel S, Ertl T. Parallel contour-buildup algorithm for the molecular surface. In: 2011 IEEE symposium on...
  • Szcsi L, Ills D. Real-time metaball ray casting with fragment lists. In: Andújar C, Puppo E, editors. Eurographics...
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