# Hierarchical Guided-Image-Filtering for Efficient Stereo Matching
## 3 Experimental Results  
In the proposed scheme, there are two design parameters, \(\beta\) in Equation (20) and \(\gamma\) in Equation (9). According to Equations (19) and (20), we have that larger \(\beta\) will cause \(\overline{W}_{i,x,z}^{H}\) and \(\overline{W}_{j,y,z}^{V}\) to increase, so \(\omega_{z}\) is larger and \(\hat{D}(p)\) will be smoother. Based on Equation (9), we also have that when \(\gamma\) is larger, the constraint between the scale layers is stronger. We conducted experiments using the training dataset of the KITTI Vision Benchmark Suite [30] to determine the proper values for these two parameters. The dataset contains 200 image pairs and 200 ground truth disparity maps. The results of the performance of the proposed scheme using the dataset are summarized in Figure 2.  
Figure 2a,b display the mean values of the percentage of the erroneous pixels on the disparity maps, denoted as the average error rates, and the standard deviations. Each of the mean values along with the standard deviation was calculated using these 200 image pairs. When \(\beta=2\) and \(\gamma=1.5\) these two parameters achieved their best performance. We fixed these values for all the calculation experiments presented in this section. Figure 1: An overview of the proposed stereo matching process with two levels of down-sampling as an example. To validate the effectiveness of the proposed scheme, extensive comparative experiments were conducted. We studied six state-of-the-art stereo matching algorithms to compare with the proposed scheme:  
* The fast cost volume filtering scheme of Reference [19], denoted as FCVF;
* A combination of the cross-scale cost aggregation scheme of Reference [29] and FCVF [19], denoted as CS-FCVF;
* The pervasive guided-image-filter scheme of Reference [25], denoted as PGIF;
* A combination of the cross-scale cost aggregation scheme of Reference [29] and PGIF [25], denoted as CS-PGIF;
* The deep self-guided cost aggregation scheme of Reference [8], denoted as DSG;  
Figure 2: The effect of parameter selection on the performance of the proposed scheme using 200 stereo image pairs of the training dataset in the KITTI Vision Benchmark Suite [30]. The dataset was downloaded from the URL: www.cvlibs.net/datasets/kitti/index.php. Each figure shows the mean values of the error rates and their corresponding standard deviations. (**a**) The average error rate with respect to the parameter \(\beta\) when \(\gamma=1.5\). (**b**) The average error rate with respect to the parameter \(\gamma\) when \(\beta=2\). * The sparse representation over discriminative dictionary scheme of Reference [13], denoted as SRDD;
* The proposed scheme, which implements a hierarchical guided-image-filter, denoted as HGIF. We tested these frameworks using the Middlebury (version 3) benchmark stereo database downloaded via the URL: vision.Middlebury.edu/sterero/ [31]. The \"trainingQ\" image set, which contains 15 stereo pairs, were used for the performance evaluation, starting from \"Adiromdack\" to \"Vintage\". Of them, only five are shown in Figure 3 due to the space limitation. They are: \"Adiromdack\", \"Pipes\", \"Playroom\", \"Playtable\", and \"Shelves\". These pictures are with a typical resolution of 720 by 480. These image pairs are down-sized twice, to 360 by 240 and 180 by 120, for example, in the proposed scheme. This arrangement corresponds to \(K=2\). Besides, the Middlebury defines two measures for evaluating average error rates, including non-occluded (non-occ) and all regions. The weighted average error rate is an official metric of the benchmark in measuring the accuracy of matching by using different weights for different image pairs. These weights are employed to compensate for the variation in the matching difficulty, as remarked on the website. Specifically, the image pairs: \"PianoL\", \"Playroom\", \"Playtable\", \"Shelves\", and \"Vintage\" contribute only half of the error rates. Figure 4 shows the disparity maps obtained by these algorithms.