## 1 Introduction  
Dense stereo matching is a significant research topic in the field of photogrammetry and computer vision, greatly benefiting applications like 3D reconstruction, DSM (Digital Surface Model) production, visual reality and autonomous vehicles [1; 2; 3; 4]. A large number of efficient stereo matching algorithms have been developed in recent years, but it is still a challenging task to handle the stereo matching problem in occluded, textureless and discontinuous regions. According to the classical taxonomy method proposed by [PERSON] and [PERSON] [5], these existing stereo algorithms can be mainly classified into global and local approaches. Global algorithms explicitly incorporate smoothness assumption into an energy function that combines data and smoothness terms and estimate disparity by minimizing the global energy function. Belief propagation [6; 7], graph cuts [8], and dynamic programming [9] are among the most commonly used global stereo matching optimization algorithms. They usually produce a more accurate disparity map than local methods but with higher computational complexity. On the other hand, local stereo matching algorithms only use the local information within a finite support window to compute disparity. These algorithms have lower complexity and can be implemented much easier and faster. Thus, they are widely used in real-time applications. Local methods generally consist of four steps: (1) matching cost computation; (2) cost aggregation; (3) disparity computation/optimization; and (4) disparity refinement. In terms of matching cost computation, [PERSON] and [PERSON] [10; 11] evaluated the performances of numerous different matching costs including parametric and nonparametric matching costs. The common parametric costs include pixel-based costs: absolute differences (AD), squared differences (SD), sampling-insensitive absolute differences, along with window-based matching costs: the sum of absolute or squared differences (SAD/SSD) and normalized cross correlation (NCC). Since most of these individual cost functions have its own strengths and weaknesses, combinations of multiple matching costs are exploited to obtain better performance. The works in [6; 12; 13] adopted a mixed cost computation method by combining the sum of absolute difference with gradient. [PERSON] et al. [14] combined the absolute differences and Census transform to achieve an impressive performance. In [15; 16; 17], a combination of absolute difference, gradient and census transform or the variant versions were used for initial cost computation. The combination of multiple matching costs provides an alternative way to improve the performance of stereo matching algorithms. Cost aggregation plays a decisive role in improving the matching efficiency and accuracy in local stereo matching algorithms. The initial matching cost is aggregated by summing or averaging over a support window to reduce image ambiguity. The naivest aggregation approach is to apply a simple low-pass filter with a fixed-size window, such as box filter or Gaussian filter, to the initial per-pixel cost. Nevertheless, the matching accuracy is determined on the fixed-size window, which easily leads to incorrect matching in textureless and discontinuous regions with fattening edges. To address this problem, a large number of cost aggregation strategies were proposed to achieve a more accurate disparity map while preserving edges. These improved aggregation methods can be categorized into two types: variable support window (VSW) and adaptive support weight (ASW). Methods based on variable support window try to find an appropriate regular or irregular support window to eliminate more outliers. [PERSON] [18] selected multiple windows from a number of candidates to produce smaller matching costs. [PERSON] et al. [19] proposed a cross-based local support window and dynamically constructed an adaptive shape region for cost aggregation. Then [PERSON] et al.