3.2 Fourier Volume Rendering
3.2.5 Results of FVR
We developed a GUI (Graphical User Interface) software system with the proposed trans-fer function for FVR. Using the developed software system, users can easily modify the transfer function and change the view direction. Our implementation environment was as follows:
• CPU: Pentium 4, 2.4 GHz,
• Memory: 2 GB,
• GPU: nVidia GeForce 8800 GT,
• Video memory: 768 MB,
• Viewport size: 512 × 512 pixel.
To evaluate the performance, we used two sets of volume data of different size, 1283 and 2563, with the B-spline transfer functions defined by one, four, and six control points.
We measured the rendering time and the pre-processing time, which included computing a 3D FFT. The performance of different cases is shown in Table 3.1. Because modern GPUs support parallel computing, increasing the volume size and number of control points slightly affect the frame rate. However, the pre-processing time is linearly proportional to the volume size and the number of control points.
This study presents the rendered results using several data sets. The first data set was CT-scan human chest volume data. The volume size was 2563 voxels. The rendered results obtained using the B´ezier curve and the B-spline transfer functions defined by six control points are shown in Figs. 3.7 and 3.8. In both Figs. 3.7 and 3.8, the images on the left show the rendered result obtained by applying the transfer functions that are shown on the right. The transfer functions in the first and second rows of both figures were designed to depict lung and bone structure, respectively. As shown in Fig. 3.8, using B-spline as the transfer function can significantly enhance lung capillaries. The result in Fig. 3.9 show that using a transfer function with greater control points can achieve better rendering. This study used a B-spline transfer function with 20 control points clustered into six groups. A comparison of the images shown in Figs. 3.8 and 3.9, the lung capillaries were significantly enhanced.
We also tested two volume data sets of HeLa cells, HeLa1 and HeLa2 (see Section 4.1.3). These data sets were reconstructed from the synchrotron radiation images aligned by the proposed alignment method(see Ch. 4). The size of HeLa1 and HeLa2 is 2563 voxels. Fig. 3.10 shows the results of HeLa1. The results were obtained using the B-spline transfer function of 25 control points. Among these control points, three control points, P0 to P2, were used to adjust the weights of membrane voxels. The cluster G0 contained first two control points to adjust the background voxels. The cluster G1 contained middle six control points to adjust the weights of the voxels which contain the intensities between membrane and particles. The cluster G2 contained the remained 11 control points to adjust the weights of particle voxels. In the top row, we mainly enhanced the weights of P1 and P2 to render the membrane of cell. The bottom row shows the results of the particles. The gray scales of particles are between 0.5 to 1.0, the weight of
G2 was enhanced to render the particles.
Fig. 3.11 shows the results of HeLa2. The results were obtained using the B-spline transfer function of 50 control points. Among these control points, three control points, P0 to P2, were used to adjust the weights of membrane voxels. The cluster G0 contained first two control points to adjust the background voxels. The cluster G1 contained middle seven control points to adjust the weights of the voxels which contain intensities between membrane and particles. The cluster G2 contained the remained 38 control points to adjust the weights of particle voxels. In the top row, we mainly enhanced the weights of P1 and P2 to render the membrane of cell. The bottom row shows the results of the particles. The gray scales of particles are between 0.5 to 1.0, the weight of G2 was enhanced to render the particles.
One disadvantage of the proposed method is the significant amount of memory re-quired. A user can more easily design a curve shape if more control points are used.
However, the memory required increases in linear proportion to the number of control points, and the GPU memory is limited. Currently, commercially available GPUs can process a volume of 2563 if six control points are used. When additional control points are required, the control points can be clustered into groups if they possess the same weight or their weight can be obtained through interpolation. Each group requires a copy of the volume to ensure the required memory can be maintained at a manageable size.
One limitation of the proposed method is that transfer functions containing a negative value are not allowed. This issue is the future research. Additionally, another future works is designing an efficient sampling method for extracting a slice of the frequency domain volume because the computing time required for sampling a slice of the frequency domain data is longer than that required to perform the inverse 2D Fourier transform. A more efficient sampling method is required to improve the overall performance.
Figure 3.7: The results of FVR with B´ezier curve transfer function(CT chest).
The rendered results that were obtained using the B´ezier curve transfer function. The data set was the CT-scan human chest of 2563 voxels. The left image in the first row depicted lung structure. The image in the right shows the transfer function. We tried to enhance the gray scales between 0.4 and 0.65. But the gray scales between 0.25 and 0.8 are also enhanced so that the lung capillaries were blurred. The left image in the second row shows the bone structures through enhancing the gray scales between 0.9 and 1.0.
Figure 3.8: The results of FVR with B-spline transfer function(CT chest). The same volume data used as Fig. 3.7. The rendered results that were obtained using the B-spline transfer function. The first row shows lung structure and the second row shows the bone structure. Using the B-spline transfer function was easier to control the curve shape. The lung capillaries were more clearly shown in the rendered result compared to the result in Fig. 3.7.
G0
G1
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G3
G0 G4
G5
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Figure 3.9: The results of FVR with B-spline transfer function(CT chest).
The same volume data used as Fig. 3.7. The rendered results were obtained using the B-spline transfer function defined by 20 control points. The control points were clustered into six groups, G0∼5. The first row shows lung structure, the gray scales between 0.4 and 0.65 were enhanced. The second row shows bone structure, the gray scales between 0.7 and 1.0 were enhanced. Compared to the results that are shown in Fig. 3.8, the lung capillaries and backbone structure were further enhanced.
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Figure 3.10: The results of FVR with B-spline transfer function(HeLa1). This is the volume of HeLa cell with 2563 voxels. The results were obtained using the B-spline transfer function of 25 control points. P0 to P2, were used to adjust the weights of membrane voxels. The cluster G2 contained the final 11 control points to adjust the weights of particle voxels. In the top row, the weights of P1 and P2 were enhanced to render the membrane of cell. In the bottom row, the weights of G2 is enhanced to render the particles.
G2 G1
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Figure 3.11: The results of FVR with B-spline transfer function(HeLa2). This is the volume of HeLa cell with 2563 voxels. The results were obtained using the B-spline transfer function of 50 control points. P0 to P2, were used to adjust the weights of membrane voxels. The cluster G2 contained the final 11 control points to adjust the weights of particle voxels. In the top row, the weights of P1 and P2 were enhanced to render the membrane of cell. In the bottom row, the weights of G2 is enhanced to render the particles.
Table 3.1: The computing time of two cases using the B-spline as a transfer function.
Data size
(voxel) 1283 2563
The number of
the control points 6 4 1 6 4 1
Memory required
(MB) 96 64 16 768 512 128
Pre-processing
(second) 18.1 12.1 3 167.4 109 8.7
Frame rate
(FPS) 64.1 65.8 66.46 59.2 62.41 66.26