Previous joint/guided filters directly transfer structural information from the reference to the target image. In this paper, we analyze the major drawback—that is, there may be completely different edges in the two images. Simply considering all patterns could introduce significant errors. To address this issue, we propose the concept of mutual-structure, which refers to the structural information that is contained in both images and thus can be safely enhanced by joint filtering. We also use an untraditional objective function that can be efficiently optimized to yield mutual structure. Our method results in important edge preserving property, which greatly benefits depth completion, optical flow estimation, image enhancement, stereo matching, to name a few.

中文翻译：

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联合过滤的互结构

以前的联合/引导过滤器直接将结构信息从参考传递到目标图像。在本文中，我们分析了主要缺点——即两幅图像中可能存在完全不同的边缘。简单地考虑所有模式可能会引入重大错误。为了解决这个问题，我们提出了互结构的概念，它指的是包含在两个图像中的结构信息，因此可以通过联合过滤安全地增强。我们还使用可以有效优化以产生相互结构的非传统目标函数。我们的方法产生了重要的边缘保留特性，这极大地有益于深度补全、光流估计、图像增强、立体匹配等。