L(\mathcal{W},\lambda_{lpm} )=\sum\limits_{i=1}^{N}{{{w}_{i}}\left( {{l}_{i}}-\lambda_{lpm}  \right)}+\lambda_{lpm} N,$$ where $$\label{eq:LRF27}
l_i=\sum\limits_{j|{\mathbf{x}_{j}}\in {\mathcal{K}_{{\mathbf{x}_{i}}}}}{d\left( \mathbf{x}_{i}^{'},\mathbf{x}_{j}^{'} \right)}+\sum\limits_{j|\mathbf{x}_{j}^{'}\in {\mathcal{K}^{'}_{\mathbf{x}_{i}^{'}}}}{d\left( {\mathbf{x}_{i}},{\mathbf{x}_{j}} \right)}$$ is a constraint item measuring the local geometric structure changes. With the objective of minimizing the cost function, a correspondence with the cost, i.e., ${l_i}>\lambda_{lpm}$, is negative. For this purpose, the correct correspondence set is determined by $$\label{eq:LRF28}
{{w}_{i}}=\left\{ \begin{array}{*{35}{l}}
1,\text{ if }{{l}_{i}}\le \lambda_{lpm}   \\
0,\text{ otherwise}  \\
\end{array}\right.,i=1,\text{ }...\text{ },N.$$

Experimental setup {#sec:exper}
==================

The experimental setup is introduced detailedly in this section. First, we list implementations and parameter settings of the evaluated methods. Second, characteristics of four datasets, the experimental criteria and the deployment are formulated.

Implementations
---------------

In our experiments, Hessian-affine detector [@Mikolajczyk2004Hessian] and SIFT descriptor [@lowe2004distinctive] (a popular detector-descriptor combination [@moreels2007evaluation]) are employed in default for image keypoint detection and description. Notice that another reason for using the Hessian-affine detector is that the evaluated GTM method requires local affine information, while we also consider different detector-descriptor combinations in Sect. \[sub:sub3\]. The initial correspondence set $\mathcal{C}$ is generated by brute-force matching, i.e., greedy comparison of two feature sets. Parameters and implementations for each algorithm are listed in Table \[tab:para\].

[lccccc]{} No. & Algorithm & Implementation & Parameters & Setting\
1 & NNSR [@lowe2004distinctive] 