sampling and checking to maximize the object function. For 2D correspondence selection, the desired parametric model is usually a plane homography matrix or a fundamental matrix. Taking the homography matrix as an example, it first randomly samples several correspondences (at least 4) from $\mathcal{C}$ and generates the model hypothesis ${\mathbf{H}}_i$ for those samples at the $i$th iteration. Then, the hypothesis ${\mathbf{H}}_i$ is verified via the following object function $$\label{eq:LRF2}
{O_i=\sum\limits_{ {c} \in \cal C }{h_i({c})}},$$ where $h(\cdot)$ is a binary function defined as $$\label{eq:LRF3}
h_i({c})=\left\{ \begin{array}{*{35}{l}}1,\text{ if }{{{\| {\mathbf{x}^{'}}-{\rho} \left({\mathbf{H}_i}\left[ {\begin{array}{*{20}{c}}{\bf x}\\1\end{array}} \right]\right)\|_2}}}\le {{t}_{ransac}} \\
0,\text{ otherwise} \\
\end{array}\right.,$$ with $\rho([a_1\;a_2\;a_3]^{T})=[a_1/a_3\;a_2/a_3]^{T}$ and $t_{ransac}$ being a threshold that determines the accuracy of a judged inlier. Above steps are repeated $n_{ransac}$ times and the model with the maximum object function is selected as the final model ${\mathbf{H}}^{\star}$. Correspondences agreeing with ${\mathbf{H}}^{\star}$ (producing 1 values using Eq. \[eq:LRF3\]) are identified as inliers.

**Spectral Technique [@Leordeanu2005A].** ST locates the most reliable element by matrix decomposition. It assumes that the connection among correct matches is much tighter than the one among mismatches. Based on this assumption, ST first builds an adjacency matrix $\mathbf{A}$ as $$\label{eq:LRF5}
{{{a}_{ij}}=\min \left( \frac{{{\| {\mathbf{x}_{i}}-{\mathbf{x}_{j}} \|}_{2}}}{{{\| \mathbf{x}_{i}^{'}-\mathbf{x}_{j}^{'} \|}_{2}}},\text{ }\frac{{{\| \mathbf{x}_{i}^{'}-\mathbf{x}_{j}^{'} \|}_{2}}}{{{\| 