Application of Particle Based Rendering to Slice Image withOpacity Map
Kyoko Hasegawa 1, Saori Ojima 2, and Satoshi Tanaka １121

College of Information Science and Engineering, Ritsumeikan University, Japan
Graduate School of Science and Engineering, Ritsumeikan University, Japan

Introduction

In medical, scientific, and other fields, transparent surface
visualization is used to investigate inner 3D structures. Usually,
this type of visualization uses polygon graphics, where thepolygons must be sorted along the line of sight. The sorting,however, takes a long computation time for large-scale data.
Besides, the order of polygons in the sorting often becomesindefinite, especially for intersecting surfaces.
Recently, Koyamada et al. proposed the particle-based
volume rendering (PBVR) even though [1], which uses tiny
particles as rendering primitives. This method does not require
any sorting and applicable to large-scale data. It also enables
natural volume fusion [2]. We extend PBVR such that it
becomes applicable to surfaces as well as volumes [3]. We callthis method "particle-based rendering (PBR)". A great
advantage of this extension is that 3D fused visualization ofdifferent volume/surface/slice objects becomes possible simply
by merging particles prepared for each element to be fused. Inthe PBR, surface is visualized at constant opacity by applying
the uniform sampling method. In this research, the slice image isrendered with the opacity map using the transfer function, that iscolor and opacity map, same as the volume rendering. Therefor,
we propose the sampling technique in order to execute renderingsame as volume.
2

Creating SliceRendering

ImageUsing

Particle(b)(c)
Fig. 1. Schematic View of the PBR. (a) LR sets of particles,(b) LR images, (c) Final image.
In order to visualize a surface, we stochastically generateparticles on the surface. The number of particles is defined by
the following formula:Based

PBR renders 3D scalar fields as particle clouds andincorporates both the emission and absorption effects. The
particle density depends on the transfer function and is used toevaluate the number of particles to be generated in the volumedata. Because the particles can be considered opaque, novisibility sorting processing is required. PBR has three
processes: particle generation, particle projection onto the image,and ensemble averaging of particle luminosities. The firstprocess stochastically generates particles according to the formof transfer function. We repeat to create such particle
distribution until LR statistically independent particle sets areprepared (See Fig. 1(a)). Below we call LR the ‘repeat level’.
Such particle projection with the occlusion effect is executed foreach particle set prepared in the first process. As the result, LR
similar images are created (See Fig. 1(b)). The second process
projects particles onto an image plane. The third process
calculates the ensemble average of the LR images created in thesecond process (See Fig. 1(c)), which realizes transparent
images.

,(1)where α, sp and sa are the opacity, the area of the particle and thesurface, respectively[3]. The slice plane is drawn same as above
technique.
We suggest the technique that applies not only the color but
also the opacity to the slice image. In this research, threesampling methods are proposed for applied the opacity:
1. Metropolis sampling whole of the plane
2. Uniform sampling at each grid
3. Metropolis sampling at each gridFirst, the Metropolis sampling is adopted same as the particlebased volume rendering. This technique is created the particle
on the slice plane, if the opacity is more than that of one step
before. If that isn't the case, we randomly decide whether or notto create. Second, we assume that the opacity is constant at eachgrid, and the number of particles is decided at each grid. Theopacity at each grid is decided from the center of the grid. Thenthe particles are stochastically uniformly generated at each grid.
Third is the combined with above two technique that uses theMetropolis sampling at each grid. Here, the number of particles
is same as the second technique.
3(a)Experiments

Consider the following the test volume data for simplicity.
The number of grid is, and the scalar value of thisdata is defined as. Fig.2 shows theslice image at z = 2 using three sampling technique: Metropolis

sampling whole of the plane (See Fig. 2(a)), uniform samplingat each grid (See Fig. 2(b)), Metropolis sampling at each grid(See Fig. 2(c)). This figure shows that the pixel color varysmoothly in the case with the technique 1. On the other hand, wehave a clear view of the grid line in Fig. 2(b) since we assume
the opacity is the constant at each grid. And Fig. 2(c) is the same
shown in Fig.2 (b) even though the pixel color vary smoothly inthe each grid. The pixel value at z = y = 2 is shown in Fig. 3.
The pixel value increases linearly with x in the case of thetechnique 1. On the other hand, at the borderline rapid changesin pixel value occur in the case of the technique 2. In thetechnique 3, the pixel value increase linearly with x only if x <310 and then the rapid changes occur. This is because the gap of
the number of the particles between each grid is wide. Thesampling time

(a)

(b)

Fig.4. Slice image at z = 18 using the Metropolis samplingwhole of the plane (Right-had side is the enlarged view).

(c)Fig. 2. Slice image of the test volume data (z = 2). (a)Metropolis sampling, (b) uniform sampling at each grid, (c)Metropolis sampling at each grid.

Fig.5. Slice image at z = 18 using the Uniform sampling at eachgrid (Right-had side is the enlarged view).

Fig.6. Slice image at z = 18 using the Metropolis sampling at
each grid (Right-had side is the enlarged view).
Fig.3 Pixel value on the slice plane at z = 2, y = 2. Red line:
Metropolis sampling, Blue line: uniform sampling at each grid,Black line: Metropolis sampling at each grid.
Fig. 4-6 shows the slice image with color and opacity maps
same as Fig. 1. The technique 1 makes it possible to create thesmooth image shown in Fig. 4. However, the enlarged view isindicated the patchy pattern because the particles dose not tend
to create around the low-opacity area. In the technique 2, theborderline is clearly shown in the low-opacity area (See blue orgreen color area in Fig. 4). On the other hand, in the technique 3,
the borderline is clearly shown in the high-opacity area (See redor yellow color area in Fig. 5).
4

Acknowledgements
The authors wish to thank Prof. Koji Koyamada, Prof. Hiromi T.
Tanaka, Prof. K. Hachimura, Dr. S. Nakata and Dr. Naohisa
Sakommoto for their valuable suggestions.
References
[1]

[2]

Conclusion

We proposed the following three sampling technique todisplay the slice image with opacity map using the PBR: 1.
Metropolis sampling whole of the plane, 2. uniform sampling at
each grid, 3. Metropolis sampling at each grid. The result showthat the technique 1 created the smooth image even though theimage had the patchy pattern at the low-opacity area. The
borderline is clearly shown in the low-opacity area by using thetechnique 2 and is clearly shown in the high-opacity area byusing the technique 3.

[3]

Koyamada, K., Sakamoto, N., Tanaka, S., A Particle Modeling for
Rendering Irregular Volumes, Proceedings of the International
Conference on Computer Modeling and Simulation (UKSIM2008), Cambridge, England, pp.372-377, 2008.
Naohisa Sakamoto, Takuma Kawamura, Koji Koyamada,Improvement of particle-based volume rendering for visualizing
irregular volume data sets, Computers & Graphics, Vol.34, No.1,
pp.34-42, 2010.
S. Tanaka, K. Hasegawa, Y. Shimokubo, T. Kaneko, T. Kawamura,
S. Nakata, S. Ojima, N. Sakamoto, H. T. Tanaka, and K.
Koyamada, “Particle-Based Transparent Rendering of Implicit
Surfaces and its Application to Fused Visualization", EuroVis
2012, Vienna (Austria), June 5–8, 2012 (accepted).