*4.1. Results of CTHW*

The disparity results of six images by CTHW and CT with a 21 × 21 window size are shown in Figure 8, and the PoBMP results are shown in Table 1. According to the results, we can see that we obtained a better PoBMP with the proposed CTHW. Especially in the case of small conversion windows, such as 3 × 3 and 5 × 5, the PoBMP was less than 10% lower than the CT. In some exceptional cases—for example, Reindeer and Cloth2 with 13 × 13 window sizes—although the PoBMP of CTHW was higher than the PoBMP of CT, the accuracy of CTHW was still higher with a small window size. In the disparity results, the black points represent unknown disparity. We can see that the disparity images of CTHW was better than that of CT because there were significantly fewer black points. The results show that CTHW obtained better disparity results.

**Figure 8.** The results, sequentially, of CTHW and CT. (**a**) Moebius, (**b**) Flowerpots, (**c**) Reindeer, (**d**) Cloth2, (**e**) Midd1, and (**f**) Baby1.


**Table 1.** The results of CTHW and CT with percentages of bad matching pixels (PoBMP) (%).

#### *4.2. Results of AWCT*

The results of Moebius by AWCT are shown in Figure 9. The edge detection result is shown in Figure 9a. The main idea of the AWCT is that the windows can be adapted. The worst option is to select the largest window size. In order to show the worst case for the size of each window, the pixels which are adapted to the largest windows size in 13 × 13, 15 × 15, 17 × 17, 19 × 19, and 21 × 21 are set as white and shown in Figure 9b–f, respectively. We can observe that when using a 13 × 13 and 15 × 15 window size, not all edge areas are applied to the largest window. At a 17 × 17 and 19 × 19 window size, the largest window was used for almost all edge points. Similar experimental results of Flowerpots, Reindeer, Cloth2, Midd1 and Baby1 are also shown in Figures 10–14, respectively. The results of six images with RMS are shown in Figures 15–20, respectively. These results show that AWCT's RMS is equivalent to the results of the largest windows (7 × 17, 19 × 19 or 21 × 21) with CT. The detailed results of AWCT and the results of CT with the largest window are listed in Table 2. According to the results, we can see that when we use the windows sizes with 13 × 13, 15 × 15, 17 × 17, or 19 × 19, the number used of the largest window is significantly less. This means that the AWCT can effectively adjust the window size and reduce the number of the largest windows. The results also show that the accuracy (PoBMP and RMS) of AWCT is similar to that of CT, but the reduction ratio of the operation number of calculation points (total pixels are calculated in Equation (3)) is about 4%–7%.

**Figure 9.** The results of Moebius by AWCT. (**a**) Edge information and schematic diagrams of the biggest window size in (**b**) 13 × 13, (**c**) 15 × 15, (**d**) 17 × 17, (**e**) 19 × 19, and (**f**) 21 × 21.

.2 .2 .**!**2 .2 .2 .2

**Figure 10.** The results of Flowerpots by AWCT. (**a**) Edge information and schematic diagrams of the biggest window size in (**b**) 13 × 13, (**c**) 15 × 15, (**d**) 17 × 17, (**e**) 19 × 19, and (**f**) 21 × 21.

**Figure 11.** The results of Reindeer by AWCT. (**a**) Edge information and schematic diagrams of the biggest window size in (**b**) 13 × 13, (**c**) 15 × 15, (**d**) 17 × 17, (**e**) 19 × 19, and (**f**) 21 × 21.

.2 .2 .**!**2 .2 .2 .2

**Figure 12.** The results of Cloth2 by AWCT. (**a**) Edge information and schematic diagrams of the biggest window size in (**b**) 13 × 13, (**c**) 15 × 15, (**d**) 17 × 17, (**e**) 19 × 19, and (**f**) 21 × 21.

**Figure 13.** The results of Midd1 by AWCT. (**a**) Edge information and schematic diagrams of the biggest window size in (**b**) 13 × 13, (**c**) 15 × 15, (**d**) 17 × 17, (**e**) 19 × 19, and (**f**) 21 × 21.

**Figure 14.** The results of Baby1 by AWCT. (**a**) Edge information and schematic diagrams of the biggest window size in (**b**) 13 × 13, (**c**) 15 × 15, (**d**) 17 × 17, (**e**) 19 × 19, and (**f**) 21 × 21.

**Figure 15.** RMS comparison results of Moebius between AWCT and CT.

**Figure 16.** RMS comparison results of Flowerpots between AWCT and CT.

**Figure 17.** RMS comparison results of Reindeer between AWCT and CT.

**Figure 18.** RMS comparison results of Cloth2 between AWCT and CT.

**Figure 19.** RMS comparison results of Midd1 between AWCT and CT.

**Figure 20.** RMS comparison results of Baby1 between AWCT and CT.


**Table 2.** Comparison of AWCT and CT.

#### *4.3. Results of AWSCT*

The results of AWSCT and the results of SCT with the largest window are listed in Table 3. The experimental results show that the accuracies (PoBMP and RMS) of the two methods are similar, but the proposed AWSCT is better within the terms of operational requirements. This means that AWSCT can use fewer computing resources to achieve the same accuracy.


**Table 3.** Comparison of AWSCT and SCT.

#### *4.4. Discussion of Results*

The results of CTHW show that using wavelet's high-frequency band with path searching to modify disparity can effectively reduce PoBMP. This is because most bad matching is replaced by other disparities, but the modified disparity may not be accurate. Since the main problem of using CT is conversion window selection, it is easy to understand that CTHW (without adjusting the window) is not better in RMS and operation reduction. Based on high-frequency technology, we propose an AWCT method that uses edges to adjust the window size. The results show that AWCT's quality (PoBMP and RMS) is acceptable with a reduction of 4%–7% operation. Applying the sparse concept to AWCT can also reduce the operation by 5%–9% compared to SCT.

#### **5. Conclusions**

One of the well-known methods for obtaining disparity is called CT. We discussed the key problem of CT, which is the size of the conversion window. The larger the conversion window, the more accurate the process; however, an oversized window may not only consume computational resources but also make too many errors in matching. In this paper, we proposed one method, CTHW, to increase the accuracy with a wavelet transform and another one, AWCT, to enable the conversion window size to be adjusted for every point. In the results of CTHW, only the bad matching is improved, which does not reduce the RMS and operation loading. We can see that the proposed CTHW can provide a better result with a small window size and be suitably applied to a system with low computational resources. AWCT further finds the number of edge points to select the suitable window size for each point. According to the results, AWCT achieves a better performance in reducing the operation times with acceptable quality. Compared with CT, its average reduction ratio of operation was found to be about 6.6%. When we applied the sparse census transform to AWCT, as AWSCT, and compared this with SCT, the average reduction ratio of operation was about 7.5%. In the future, it is worth studying the use of high-frequency information to improve the quality and reduce the operation, and further enhance the performance, of CT.

**Author Contributions:** Conceptualization, J.-J.L. and C.-P.L.; Investigation, J.-J.L., Y.-F.H. and Y.-H.L.; Methodology, J.-J.L. and S.-C.H.; Supervision, J.-J.L.; Visualization, C.-P.L. and Y.-H.L.; Writing—original draft, J.-J.L., Y.-H.L. and S.-C.H.; Writing—review and editing, C.-P.L. and Y.-F.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported in part by the Ministry of Science and Technology, Taiwan, under grant MOST 105-2221-E-324-008-MY2.

**Acknowledgments:** This research is partially sponsored by Chaoyang University of Technology (CYUT) and Higher Education Sprout Project, Ministry of Education, Taiwan, under the project name: "The R&D and the cultivation of talent for Health-Enhancement Products."

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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