The voxel visibility model: An efficient framework for transfer function design

https://doi.org/10.1016/j.compmedimag.2014.11.014Get rights and content

Highlights

  • We propose the voxel visibility model for transfer function in volume rendering.

  • We propose an optimization algorithm for automatic transfer function design.

  • The voxel visibility model is a feature- and voxel-level model.

  • The voxel visibility model can be efficiently used by users.

  • The voxel visibility model provides an importance-based strategy.

Abstract

Volume visualization is a very important work in medical imaging and surgery plan. However, determining an ideal transfer function is still a challenging task because of the lack of measurable metrics for quality of volume visualization. In the paper, we presented the voxel vibility model as a quality metric to design the desired visibility for voxels instead of designing transfer functions directly. Transfer functions are obtained by minimizing the distance between the desired visibility distribution and the actual visibility distribution. The voxel model is a mapping function from the feature attributes of voxels to the visibility of voxels. To consider between-class information and with-class information simultaneously, the voxel visibility model is described as a Gaussian mixture model. To highlight the important features, the matched result can be obtained by changing the parameters in the voxel visibility model through a simple and effective interface. Simultaneously, we also proposed an algorithm for transfer functions optimization. The effectiveness of this method is demonstrated through experimental results on several volumetric data sets.

Introduction

Volume visualization is an effective and flexible technique for exploring meaningful structures in 3D scalar fields. It is often used in medical imaging and surgery plan. The key to comprehensible volume visualization still lies in the design of effective transfer functions. A transfer function provides a map for the attributes in volume space to the attributes in visual space. It plays an important role in the understanding of the overall volumetric data and the individual features contained within the volume space. However, an effective transfer function design is difficult and time-consuming, as witnessed by the large amounts of literature on transfer function designs.

Several problems prevent users from effectively obtaining satisfactory rendered images of volumes. First, the domain of the transfer function space is too large. In traditional 1D or multi-dimensional transfer functions, users design transfer functions through trial-and-error modifications of opacity and color values to obtain accurately identifying and visually distinguishing various objects in a volume. However, there are more than 104 different transfer functions for trials when the step is 0.1 in the domain and range, even in 1D transfer function space, which causes the transfer function design to be ineffective. To improve efficiency, two types of strategy are proposed. The traditional strategy is to reduce the domain of the transfer function space using a feature cluster approach[1], [2]. Recently, a semi-automatic transfer function design based on a visibility metric [3], [4], [5] was proposed. In the visibility histogram [3], the metric is defined on bins of volume data sets, and users can design visibility at the voxel level. However, the influence of each feature on the rendered image, which is of greater concern to users, is not considered. In feature visibility [4], the metric is defined directly on the features. It is efficient for users to adjust the visibility of different features. However, feature visibility is designed at the feature level. The visibility of voxels in the same feature, which represents greater detail, cannot be adjusted.

In this paper, a new concept, i.e. the voxel visibility model, is proposed to automate transfer function design. The voxel visibility model is a mapping function from voxels feature attributes to their visibility attributes, which allows users to directly adjust the visibility of each voxel. Additionally, feature information is contained in the model. Thus, users can design a visibility metric at both the feature and voxel levels simultaneously. Based on the voxel visibility model, an energy function is defined to model the mismatch between the actual projected visibility distribution and the desired visibility distribution. The opacity is automatically obtained by an optimization process of the energy function. In this paper, we provide two distribution models: the average distribution model and the accumulated distribution model. The voxel visibility model is provided by the Gaussian mixture model (GMM). Different desired visibility distributions can be obtained by manipulating the shape, size and orientation of the voxel visibility model for flexible volume exploration. Fig. 1. provides a two-step exploration procedure.

Section snippets

Related work

Generally, transfer function is categorized as data-centric method and image-centric method. In this section, we mainly review a few recent data-centric methods for transfer function design. At the same time, these methods are categorized as attributes-space method, cluster-space method and goal-oriented method. Here, attributes-space method means that the feature attributes of voxels are directly mapped to opacities and colors. Cluster-space method means that voxels are first clustered by the

Methodology

In this section, we first introduce our framework for transfer function design based on the voxel visibility model. In the second part, we describe the voxel visibility model in the detail. Then, the objective function and the optimizer is constructed. At last, GPU-assisted computation is discussed.

Experiments and results

In this section, we present several experiments that were conducted to evaluate the proposed approach. Used data sets are described in Table 1. All of the experiments were conducted on a PC equipped with an Intel Core 2 Xeon E5503 CPU, 2 GB of RAM and a Nvidia GeForce GTX 280 graphics card. By default, the average visibility distribution function, β = 0, and 6 uniformly distributed viewpoints are used in the following experiments.

Fig. 3 compared the rendering result on the Gaussian transfer

Conclusion

In this paper, we presented a new visibility metric, i.e., the voxel visibility model, as a framework for automatic transfer function design. Based on the voxel visibility model, users can design the desired voxel visibility distribution using a few parameters. The opacity transfer function is obtained by minimizing the distance between the desired voxel visibility distribution and the actual projected voxel visibility distribution. To help users understand the data systematically, we proposed

Acknowledgments

This work was partly supported by the National Natural Science Foundation of China (61100113, U1401252), Chongqing Research Program of Application Foundation and Advanced Technology (cstc2013jcyjA40062), the Scientific Research Foundation for the Returned Overseas Chinese Scholars (2012-940). The volume data are download from the Volume Library(http://www9.informatik.-uni-erlangen.de/External/vollib/) and VolVis Data Sets(http://www.volvis.org/).

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