Real-time Volume Shading for Deformable Model　（sap＿ 0482）

Satoshi Yano † ∗ Megumi Nakao † Kotaro Minato †

Fig. 1: Lung volume deformation with GPU-based shading

This presentation proposes real-time volume shadingmethods for deformable modeling. Although several vol-ume manipulation techniques1 have been developed, volumeshading on time-varying, volumetrically rendered imageswas still difficult problem. In order to perform volume defor-mation, we apply FEM-based modeling of tetrahedral gridsand visualize deformation results by using texture-based vol-ume rendering. The proposed approach does not update 3Dtexture or voxels, and achieves fast volume shading by per-grid gradient estimation and interpolation on GPUs.　 A normal vector is needed for the shading. Generally, agray-level gradient method defines gradient voxels from 3Dtexture, which are used for normal vectors. However, sincereconstructing voxels takes high computational costs, themethod is not available for interactive volume deformation.In our framework, two data structures; initial volume dataand its tetrahedral grid, are prepared. Next, gradient vol-ume texture is created. This process is pre-computationallydone. In real-time simulation stage, interactive volume de-formation is performed through the following algorithms.

1. Grid deformation and update vertex position.

2. Define the difference of gradient at each vertex of thegrid.

3. Create proxy geometry with interpolated gradient dif-ference from the grid.

4. Render shaded volume deformation results by gradientinterpolation and shading on GPUs.

Without reconstructing 3D texture, the gradient of eachvertex of the grid is calculated and interpolated betweenthe vertices fast on GPUs. We approximate a virtual planeat each vertex and estimate per-vertex gradient using theLeast-Square method (See a Fig.2). Before and after thedeformation, the per-vertex gradients are calculated. Thegradient difference ∆N is utilized as change of normal vec-tor and interpolate them between vertices on GPUs.　We confirmed volume visualization results of time-varyinggradient difference via volume deformation. (see Fig. 3)

†Graduate School of Information Science, Nara Institute ofScience and Technology. Nara, Japan

∗satoshi-y@is.naist.jp

We employed texture-based volume rendering of tetrahe-dral grid based on [2]. The results show that our frameworkallows real-time volume shading by adding interpolated gra-dient difference to the initial gradient volume on GPUs. Weare still exploring better per-vertex gradient formulation inorder to perform stable volume shading independent to gridtopology.

Fig. 2: Virtual plane definition per vertex using Least-squaresmethod. The gradient difference ∆N = (N ′x − Nx, N ′y −Ny, N ′z − Nz) is utilized for transformation of normal vectorand interpolated on GPU.

Fig. 3: Volume visualization of gradient difference. The vector isrepresented using RGB color value and overlaid on the volumet-rically rendered image. (a) Volume deformation of left-side lungand (b) volumetrically rendered gradient difference, (c) anotherdeformation and (d) its rendered gradient.

References［1］C. D. Correa, D. Silver, M. Chen, ”Discontinuous Dis-placement Mapping for Volume Graphics”, Proc. VolumeGraphics, pp. 9-16, 2006.［2］M. Nakao, T. Kuroda, K. Minato, ”Volume Interac-tion with Voxels by Manipulating 3D General Grids”, ACMSIGGRAPH Poster, 2005.

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