# Linear Time Non-Local Cost Aggregation on Complementary Spatial Tree Structures
## 4 Results and Discussions
### Stereo Matching
#### 4.1.2 KITTI Dataset
Due to this, there is no informative message in these areas, resulting in matching costs at different candidate disparities becoming identical. Our method performs non-local coat aggregation on two complementary spatial tree structures, and the geodesic distances in both spatial and intensity spaces are used to evaluate the similarity of pixels along these two trees. Therefore, our method propagates informative messages across the entire image to deal with challenging occasions, for example, the degradation of region-based cost function for fine-scale structures and the lack of useful information in homogeneous areas. The results of each method using different features to compute matching cost demonstrate that handcrafted features tend to generate more edge-aware disparity images while deep features produce better results in textureless regions. The reason is that deep CNNs with a large receptive field can utilize textural information from a wide range, improving the robustness of deep features for pixels in homogeneous areas. Quantitative evaluation: Table 4 presents the error rate and average end-point error of typical cost aggregation methods on the KITTI 2012 dataset. Our approach surpasses NL, ST, and FCGF in all metrics. Although the error rates of both initial and final disparity images are smaller than ours, the average end-point error of our method is close to or even smaller than that of GF. The main reason for this phenomenon is that only the disparities of pixels near the ground are provided in ground-truth disparity images. Most of those valid pixels are located in highly textured regions so that GF can utilize the structure information in the local area to generate high-quality results. Our method is superior to GF in homogeneous  
Figure 4: Comparison of disparity images using deep features from PSMNet [24] (top row) and handcrafted feature (second row) to compute matching cost on the KITTI 2012 dataset. (**a**) Guidance image and sparse ground-truth disparity image. (**b**) Guided Filter [11]. (**c**) Our method. Figure 5: Comparison of disparity images using deep features from PSMNet [24] (top row) and handcrafted feature (second row) to compute matching cost on the KITTI 2015 dataset. (**a**) Guidance image and sparse ground-truth disparity image. (**b**) Guided Filter [11]. (**c**) Our method. regions, as shown in Figures 4 and 5. HASR incorporates edge information with _CT_ to further compensate for radiometric changes and adopts a hierarchical cross-based cost aggregation scheme to fuse costs at multiple scales. These strategies make their method obtain the lowest error rate in non-occluded regions. However, the end-point errors in non-occluded and all areas are 1.9 px and 2.9 px, which are 0.3 px and 1.02 px larger than ours. The reason is that they incorporate multi-scale costs by an exponential function while we take advantage of the inter-scale regularization [10]. Table 5 lists the results of GF, NL, FCGF, ST, LRNL, and our method using deep features extracted by PSMNet [24] to compute the matching cost. Compared with the results generated by the handcrafted feature of GF, FCGF, NL, and ST, the average error rate and end-point error of these cost aggregation methods in non-occluded regions decreased from 12.54% and 2.50 px to 9.27% and 2.32 px, improved by 26.08% and 7.20%, respectively. The average error rates of final disparity images are still lower than that of the handcrafted feature. The reason is that CNNs can incorporate information in a large receptive field to improve the robustness of features in textureless areas. Our method outperforms LRNL in all metrics by a margin. It turns out that keeping the information propagated along all directions in balance is vital for improving the quality of disparity images. Figure 6 presents examples of disparity images and corresponding error maps of our method using the handcrafted feature and deep ones to compute the matching cost. Our approach correctly estimates the disparities of most pixels in the guidance image.