# Hierarchical Guided-Image-Filtering for Efficient Stereo Matching
## 1 Introduction
The local methods generally perform the stereo matching in four stages [1]: (1) The calculation of the preliminary matching cost, (2) aggregation of the cost over support windows, (3) estimation of the disparity, and (4) refining the disparity. Among them, the cost aggregation step is usually transformed into an image filtering procedure of the matching cost and the disparity maps are obtained by the winner-takes-all method [1]. The local methods require less computation and are popular for fast disparity calculations. Cost aggregation is crucial for matching performance in the local algorithms. Bilateral filtering [14] is among the early approaches that led to the increase of computational complexity with the increase of support-window size. Later, tree filtering [15], domain transformation [16], recursive edge-aware filter [17], and full-image guided filtering [18] were proposed to decouple computational complexity with the support window size. However, these approaches all suffer from the weight-decay problem when there is a significant intensity difference between neighboring pixels. This behavior deteriorates information propagation and impairs the resulting matching performance. [PERSON] [19] suggested treating the generation of disparity as a labeling problem, which is implemented through the steps of constructing a cost volume, cost volume filtering, followed by winner-takes-all label selection. Along this line, the guided-image-filter (GIF) [20] substantially involves cost volume filtering because it can generate clear edge profiles free from the gradient-reversal artifacts. Later, [PERSON] [21] introduced an edge-aware weighting, denoted as the weighted guided-image-filtering (WGIF), to improve GIF. [PERSON] [22] proposed a gradient-domain guided-image-filter (GDGIF) to reduce halo artifacts by incorporating an explicit first-order edge-aware constraint. Nevertheless, due to the lack of pixel information outside the fixed window, the implementation of WGIF by [PERSON] [23] results in restricted performance. To remove the fixed-window limitation, approaches with adaptive guided filters were proposed [24]. However, information outside the support windows is still missing. In a recent paper [25], we introduced weights that take both distance and intensity differences into account to extend the scheme of GIF. We called our approach the pervasive guided-image-filtering, denoted as PGIF [25], which exploits the whole image for aggregation. Also, recent years have seen the development of coarse-to-fine (CTF) strategies to enhance the stereo matching accuracy. For instance, [PERSON] [26] proposed to reduce the search space of local stereo matching by introducing a candidate set of neighbor pixels. [PERSON] [27] introduced a multi-scale pixel feature vector to provide effective matching of radiometric differences. Advanced techniques to find improved disparity range was provided in the work of [PERSON] [28] by recursive multi-scale decomposition. These methods assume the existence of disparity consistency. In contrast to these approaches, the matching cost integration method of [PERSON] [29] resulted in superior matching, where cost aggregation is formulated to enforce the consistency of the cost volume among the neighboring scales. Inspired by the multiscale scheme of [PERSON] [29], we extend the pervasive guided-image-filtering, PGIF [25], to exploit the cross-scale features in the cost volume. In our approach, the consistency is imposed on the GIF parameters, rather than the cost volume of [PERSON] [29], in the neighboring-scale direction. We call it hierarchical guided-image-filtering, denoted as HGIF. The main contribution of this paper can be summarized as:  
1. We created an innovative aggregation approach that efficiently combines the model parameters of PGIF [25] to allow the features of the image pairs in different resolutions to be considered;
2.