This chapter first demonstrates the results of our algorithm. We implement our algorithm on a desktop PC with Intel Core2 Extreme CPU X9650, 8G RAM, and NVIDIA GeForce 8800 GTS 512 video card. We use several measured BRDF data from MERL and Cornell libraries and complex HDR environment maps for rendering.
Each viewing direction of the materials is fit into 20 SRBFs and the environment maps are represented by 100 SRBFs.
In the following, we will compare our results with SRBFs-based product importance sampling presented by Tsai et al. [27]. These results are compared in equal-sample or equal-time manners. We use the Uffizi Gallery environment map (Figure 6.1) as light source and four different testing scenes (Figures 6.2 ~ 6.5). All the scenes are rendered with 5 shadow rays.
Figure 6.1: The Uffizi Gallery environment map
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Figure 6.2: “Buddh and Car” Scene: “Mystique” Buddha, “GarnetRed” Car, and Cayman Walls
Figure 6.3: “Bathroom” Scene: “OrangePaint” Basket, “Teflon” Bathtub, and
“WhitePaint” Walls
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Figure 6.4: “Meeting Room” Scene: All the objects in the scene use
“Fruitwood241” from MERL library as material
Figure 6.5: “Restroom” Scene: “Cayman” Bed, “GarnetRed” Closet, and “Teflon”
Walls
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We first compare the rendered results of “Buddha and Car” Scene. Figures 6.6 ~ 6.7 show the comparison of equal-samples results. We can find that our results are much brighter than the ones rendered with previous method. The reason is that shadow rays are concentrated along the visible directions. More of them pass the visibility test and contribute to the outgoing radiance.
Figure 6.6: Rendered results of “Buddha and Car” Scene using 200 samples/pixel
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Figure 6.7: Rendered results of “Buddha and Car” Scene using 400 samples/pixel
Figures 6.8 ~ 6.10 show the closer-look of the results. We can obviously find the reduction of noise in the two regions by comparing the images with the referenced image.
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Figure 6.8: Referenced image of the two zoom-in regions (“Buddha And Car”
Scene)
Figure 6.9: Comparison of the first zoom-in region (“Buddha And Car” Scene)
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Figure 6.10: Comparison of the second zoom-in region (“Buddha And Car”
Scene)
Then we compute the root mean square (RMS) error and variance with the referenced image. The results are displayed in Figure 6.11 and Table 6.1. In Figure 6.11, we use different colors to represent the error. Red means high error and blue means low. We can obviously find the decrease of red and yellow regions. Another important point we can find is that although we increase the number of samples per pixel from 200 to 400, the overall error does not decrease as expected in the Tsai’s results. The reason is most of the samples failed in the visibility tests and do not contribute to the final image. Our algorithm does not suffer this bottleneck and successfully reduces the error as the number of samples increases.
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Figure 6.11: RMS Error of the “Buddha And Car” Scene. Red represents high error and blue represents low error. The higher-error regions (red and yellow) are reduced by using our approach
Tsai et al.[2008] Our method
200 samples/pixel 0.149487 0.081025
400 samples/pixel 0.139078 0.058851
Table 6.1: Variance comparison of “Buddha And Car” Scene
Then we compare the rendered results of the “Bathroom” Scene. In this scene, we use the measured BRDF data from MERL library for rendering. The scene is composed of an “OrangePaint” basket, a “Teflon” basetub, and “WhitePaint” Walls.
Figure 6.12 shows the rendered results using different number of samples per pixel and 5 shadow rays per camera ray.
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Figure 6.12: Rendered results of “Bathroom” Scene
Figure 6.13 and Table 6.2 shows the RMS error and variance of the “Bathroom”
Scene. We can find the error near the bathtub and the entire variance is reduced.
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Figure 6.13: RMS Error of the “Bathroom” Scene
Tsai et al.[2008] Our method
200 samples/pixel 0.155543 0.139747
400 samples/pixel 0.124805 0.103070
Table 6.2: Variance comparison of “Bathroom” Scene
Figure 6.14 shows the rendered results of “Meeting Room Scene” using Tsai’s and ours approach with 200 ~ 800 samples per pixel. The number of shadow rays generated for each camera ray is fixed to 5.
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Figure 6.14: Rendered results of “Meeting Room” Scene
As shown in Figure 6.14, the results rendered with our algorithm are much brighter across the entire image. Moreover, Figures 6.15 ~ 6.17 show that our approach keeps more high-frequency details than previous method. Figure 6.15 shows the referenced image of the two zoom-in regions, and Figures 6.16 ~ 6.17 compares the rendered
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results.
Figure 6.15: Referenced image of the two zoom-in regions (“Meeting Room”
Scene).
Figure 6.16: Comparison of the first zoom-in region (“Meeting Room” Scene)
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Figure 6.17: Comparison of the second zoom-in region (“Meeting Room” Scene)
The RMS and variance of these two approaches are displayed in Figure 6.18 and Table 6.3. We can find the great reduction of variance from Table 6.3. Even with one-fourth samples, our proposed algorithm still produces less variance than the previous method. In the next scene, we will compare the equal-time rendered results of our approach and the one proposed by Tsai et al. [24].
Tsai et al.[2008] Our method
200 samples/pixel 0.127465 0.091346
400 samples/pixel 0.118740 0.068415
800 samples/pixel 0.106096 0.045513
Table 6.3: Variance Comparison of “Meeting Room” Scene
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Figure 6.18: Root Mean Square (RMS) Error Comparison of “Meeting Room”
Scene
Finally consider the “Restroom” Scene. We first compare the equal-samples results as above. The rendered images are illustrated in Figure 6.19 and the zoom-in details are shown in Figures 6.20 ~ 6.22. The RMS error and variance are shown in Figure 6.23 and Table 6.4.
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Figure 6.19: Equal-samples rendered results of “Restroom” Scene
Figure 6.20: Referenced image of the two zoom-in regions (“Restroom” Scene)
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Figure 6.21: Equal-samples Comparison: The first zoom-in region (“Restroom”
Scene)
Figure 6.22: Equal-samples Comparison: The second zoom-in region (“Restroom” Scene)
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Figure 6.23: Equal-samples Comparison: Root Mean Square (RMS) Error of
“Restroom Scene”
Tsai et al.[2008] Our method
200 samples/pixel 0.125262 0.062662
400 samples/pixel 0.118084 0.047234
Table 6.4: Equal-samples Comparison: Variance Comparison of “Restroom” Scene
Then we use Figures 6.24 ~ 6.27 to show the equal-time results. Although our algorithm spends more time on each sample, we can obtain higher-quality images by using much fewer samples. The enhancement of performance is obvious as follows.
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Figure 6.24: Equal-time rendered results of “Restroom” Scene
Figure 6.25: Equal-time Comparison: The first zoom-in region (“Restroom”
Scene)
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Figure 6.26: Equal-time Comparison: The second zoom-in region (“Restroom”
Scene)
Figure 6.27: Equal-time Comparison: Root Mean Square (RMS) Error of
“Restroom” Scene
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The major overhead of our algorithm is the increase of frequency to reconstruct the CDF. However, it is interesting that the enhancement of quality is also positively proportional to the number of reconstruction. Since we only reconstruct the CDF when there is a new invisible direction recorded in the visibility cache, it seems that we can avoid the invisible directions more accurately if we have more contents in the cache. For general scenes which have little occlusion, our algorithm is as fast as Tsai et al. [27]. Because most of the time the visibility cache is empty, our algorithm works similarly as Tsai’s algorithm. We will have a little enhancement along the shadowed regions by spending a little more time (2% overhead). For the scenes like Figures 6.2
~ 6.5, our algorithm increase 40% ~ 50% computation time compared with Tsai’s approach. However, as seen from Figures 6.24 ~ 6.27, we can obtain much better results by using the same time. Therefore, our proposed algorithm greatly improves the sampling efficiency.
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