by $$\label{eq:LRF15}
{{\sigma ^2} = \frac{{{{(\mathcal{V} - \mathcal{F}_{vfc})}^T}\mathbf{P}(\mathcal{V} - \mathcal{F}_{vfc})}}{{D \cdot \text{tr}(\mathbf{P})}}},$$ and $$\label{eq:LRF16}
{\gamma  = \text{tr}(\mathbf{P})/N},$$ where $\mathcal{F}_{vfc}={({\mathbf{f}_{vfc}(\mathbf{u}_{1})}^T,...{\mathbf{f}_{vfc}(\mathbf{u}_{N})}^T)}^T$. The E-step and M-step are repeated until parameters are converged. Finally, the inlier set is generated as $$\label{eq:LRF17}
{\mathcal{C}_{inlier}=\left\{{c}_i:p_i>t_{vfc}\right\}},$$ where $t_{vfc}$ is a predefined threshold.

**Grid-based Motion Statistics [@bian2017gms].** GMS proves that besides feature descriptiveness, feature number also contributes to the quality of correspondences. It supposes that the quantity of correspondences in a small neighborhood around a true match is larger than that around a false match under the smooth motion. In over-large neighborhoods, regions are divided into multiple small region pairs where distributions of correspondence number are approximated by Binomial distributions. Given a correspondence $c_i$, the joint statistical distribution is modeled as $$\label{eq:LRF18}
{{{S}_{i}}\sim{\ }\left\{ \begin{array}{*{35}{l}}
    B(Kn,{{p}_{t}}),\text{ if }{{{c}}_{i}}\text{ is inlier}  \\
    B(Kn,{{p}_{f}}),\text{ otherwise}  \\
    \end{array} \right.},$$ where $S_{i}$ is the total number of correspondences in a region pair ($a$, $b$) around ${c}_i$, $K$ is the quantity of small region pairs, $p_t$ is the probability that the nearest neighbor of each keypoint in $a$ is located in $b$ under the condition that $a$ and $b$ view the same location, and $p_f$ is the probability provided that $a$ and $b$ view 