Background Complexity

We first show the disparity maps that use images of textureless background.

Ground truth disparity map WTA

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DERS GC-NS

Figure 43: Disparity maps on the simple background test images

Figure 44 shows the disparity maps on the complex background test images (Figure 32).

Ground truth disparity map WTA

DERS GC-NS

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Figure 44: Disparity on complex background test images

Table 2 and Table 3 compare BPR and MSE of all methods on these test images. Note that the error metrics are calculated only on the foreground region or only on the background region, which are marked in the “Region” column (as explained in sec. 4.5).

Table 2: BPR of disparity maps on simple and complex background test images

Table 3: MSE of disparity map on smiple and complex background test images

Examining the above images and tables, we have a few observation. For WTA, its BPR and MSE in foreground and background both decrease from the simple background image to the complex background image. For DERS, BPR and MSE decrease from the simple background to complex in background, but increase in foreground. For GC-NS, BPR shows no increasing and decreasing in foreground from simple to complex background, but BPR in background and MSE in both foreground and background decrease. In the following discussions, we focus on the foreground. When the background is simple, WTA has the worst result in BPR. However, when the simple background changes to the complex background, the result of DERS becomes worse than that of WTA. WTA improves estimation results the most among the three methods from the simple to the complex background.

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The design principles of these disparity estimating algorithms may help explaining their behaviors. Although WTA and GC-NS do not use image segmentation explicitly, their grouping method is very similar to that of image segmentation. As a result, the edge can be preserve better, and the estimated disparity in the foreground can also benefit from it. For DERS, it does not use any concept of grouping, so the foreground get worse when the background become complex.

Next, we want to see whether the results will be better if we cut off the textureless regions.

Figure 45 shows that we first cut off the left part of image, and we call it CUT1 (Figure 33).

Figure 46 are the images cutting off the left and top parts, and we call it CUT2 (Figure 33).

Table 4 and Table 5 are the comparisons of full background, CUT1 and CUT2 in BPR and MSE.

Ground truth disparity map WTA

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DERS GC-NS

Figure 45: Disparity maps on CUT1 images

Ground truth disparity map WTA

DERS GC-NS

Figure 46: Disparity maps on CUT2 images

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Table 4: Compison of BPR of computed disparity maps on different size of background

Table 5: Compison of MSE of computed disparity maps on different size of background

For WTA, cutting off textureless background does not change the disparity results in the foreground, but it helps to decrease the BPR and MSE in the background. The black regions in the depth maps become less in CUT1 and CUT2. For DERS, there is an obvious improvement in the background in BPR and MSE when the full size background changes is reduced to CUT1. There are still some errors on the left side. This is because the pixels on the picture left border of the left image have no corresponding pixels on the right image. For GC-NS, the accuracy improves the most among the three methods in the background when the full size background is reduced to CUT2. For all of these three methods, cutting off the textureless does not affect the foreground much.

We thus conclude that cutting off the textureless region can improve the performance of stereo matching algorithms as we expect. We found that estimation error of DERS on the left side of image is caused not by both the textureless region and the missing part on the right

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view. But why we do not see this phenomenon in the other two methods? The reason is that the two methods do cross checking between left and right estimated disparity. In fact, DERS does cross checking by using three input images, but our modification uses only two input images.

Next, we look at repeated-pattern background. Tables 6~9 show BPR and MSE comparison between the repeated-pattern background and the textureless background, and between the complex and the textureless background.

WTA has better disparity estimation results when the texture is full of repeated pattern or the texture is complex. The BPR and MSE of DERS indicate that it cannot handle the repeated-pattern area well. But when the texture is complex, DERS performs better than when the texture is simple. The performance of GC-NS, the performance improves when the background contains repeated pattern or complex pattern.

WTA and GC-NS use adaptive windowing in their grouping methods. In contrast, DERS uses a fixed window. We believe this explains why DERS has poor performance in the repeated-pattern area.

Table 6: BPR focusing on the repeated-pattern area

Table 7: MSE focusing on the repeated-pattern area

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Table 8: BPR focusing on the complex area

Table 9: MSE focusing on the complex area