特征匹配--GMS: Grid-based Motion Statistics for Fast, Ultra-robust Feature Correspondence

GMS: Grid-based Motion Statistics for Fast, Ultra-robust Feature Correspondence CVPR2017 c++ code: https://github.com/JiawangBian/GMS-Feature-Matcher

主要本要针对特征匹配问题，提出了一个简单的基于统计的解决方法，可以快速区分出正确的匹配和错误的匹配，提高了匹配的稳定性。

首先来个直观的特征匹配图示

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特征匹配是计算机视觉里一个基础性问题，对于特征匹配当前主要的问题在 robust 的匹配速度慢，快的匹配经常不稳定。 there is a wide performance gap between slow (but robust) feature matchers and the much faster (but often unstable) real-time solutions.

问题的核心在于邻域一致性这个约束的怎么利用。The central problem lies in the coherence constraints (neighboring pixels share similar motion) utilized in the more powerful feature correspondence techniques.

一致性是一个很强大的约束，但是稀疏特征不能很好的定义邻域。这导致基于一致性的特征匹配的计算量比较大，很难实现。 Coherence is a powerful constraint but sparse features lack well defined neighbors。 This causes coherence based feature correspondence [16, 42] to be both expensive to compute and complex to implement.

本文提出 GMS (Grid-based Motion Statistics) 可以有效的解决这个问题。 a means of encapsulating motion smoothness as a statistical likelihood of having a certain number of feature matches between a region pair. We show GMS can rapidly and reliably differentiate true and false matches

本文的核心思想很简单：运动的平滑性导致了匹配的特征点邻域有较多匹配的点。我们可以通过计数邻域的匹配点个数来判断一个匹配正确与否。 Motion smoothness induces correspondence clusters that are highly unlikely to occur at random. Thus true and false matches can be differentiated by simply counting the number of matches in their neighborhood.

2 Our approach

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S_i is a measure of neighborhood support

Assumption 1. Motion smoothness causes a (small) neighborhood around a true match to view the same 3D location. Likewise, the neighborhood around a false match views geometrically different 3D locations. 运动的平滑性导致了正确的匹配点附近的邻域里的特征点也是一一对应的。

下面首先用数学的角度推导出 正确匹配点附近的邻域中正确匹配和错误匹配的概率分布。 最终的结论如下：

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分布图示

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我们的目标是：

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下面是将上面的理论分析变成可以实际中的运行算法 主要解决下面四个问题： a) Efficient score computation through grid-cells; b) Which neighborhoods to use; c) How many grid-cells to use; d) How to compute an effectively threshold S

3.1. Griding the problem

a) Efficient score evaluation， 这里我们主要通过将图像分为 G = 20×20 网格来实现 Scores of potential cell-pairs are computed only once. All matches between cell-pairs deemed true are accepted

b) Grouping match neighborhoods (cell-pairs) for robustness. 这里我们计算了一个网络四周的3*3=9个网格，如下图所示

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c) How many grid-cells should be used? 经验值 G = 20 × 20 cells for 10,000 features n 大约为 25

d) Thresholding S_ij to divide cell-pairs into true and false sets {T ,F}.

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整个算法流程图如下所示：

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效果对比图

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Dataset details

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F-measure, Recall and Precision vs baseline

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