pay-offs.

Given a pair of correspondences $(c_i,c_j)$, the payoff function is defined as $$\label{eq:LRF7}
{{\Pi }_{ij}}={{e}^{-{{\lambda }_{gtm}}\max (\left| {{T}_{i}}({\mathbf{x}_{i}})-{{T}_{j}}({\mathbf{x}_{i}}) \right|,\left| {{T}_{i}}({\mathbf{x}_{j}})-{{T}_{j}}({\mathbf{x}_{j}}) \right|)}},$$ where ${\lambda }_{gtm}$ is a selectivity parameter, $\left|{\cdot}\right|$ represents the $L_1$ norm and $T_{i}(\mathbf{x})$ is the similarity transformation estimated by (similarly for $T_{j}(\mathbf{x})$) $$\label{eq:LRFt}
{{T}_{i}}(\mathbf{x})=\rho \left( {\mathbf{H}_{c_i}}\left[ \begin{matrix}
\mathbf{x}  \\
1  \\
\end{matrix} \right] \right),$$ where $\mathbf{H}_{c_i}$ is the homographic transformation of $c_i$. Note that this algorithm particularly requires the local affine transformation cue to compute the pay-off function. Next, the payoff matrix $\mathbf{P}_{gtm}$ with the element in the $i$th row and $j$th column that is defined as $$\label{eq:LRF8}
{{{p}_{ij}}=\left\{ \begin{array}{*{35}{l}}{{\Pi}_{ij}},\text{ if }i\ne j  \\
0,\text{ otherwise}  \\
\end{array}\right.},$$ can be generated. The population vector $\mathbf{q}$ is updated by the evolutionary stable states algorithm (ESS’s) [@weibull1997evolutionary] as $$\label{eq:LRF9}
{{{q}_{i}}(k+1)={{q}_{i}}(k)\frac{{{(\mathbf{P}_{gtm}\mathbf{q}(k)})_{i}}}{\mathbf{q}{{(k)^{T}}}\mathbf{P}_{gtm}\mathbf{q}(k)}},$$ where $q_{i}$ represents the element in the $i$th row of $\mathbf{q}$ and $k$ is the iteration number. After $n_{gtm}$ iterations, a correspondence $c_i$ is identified as inlier if its corresponding $q_{i}$ is higher than a threshold $t_{gtm}$.

**Universal RANSAC [@Raguram2013USAC].** USAC integrates a universal framework for RANSAC, where each original step is optimized by referring to the advantages of previous parametric approaches such as PROSAC [@Chum2005Matching], SPRT test [@matas2005randomized] 