# A Benchmark for the Evaluation of Corner Detectors
## 3 Benchmark Evaluation Analysis
### Objective Evaluation
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Detector** & **Dataset 1** & **Dataset 2** & **Dataset 3** \\  & [4,38] & [38, 39, 40] & **(Urban-Corner)** \\ \hline \multirow{2}{*}{SUSAN [2]} & 0.0737/0.7164 & 0.0021/0.3807 & 0.0046/**0.9999** \\  & 0.3950/0.0758 & 0.1914/0.0042 & 0.5022/0.0091 \\ \hline \multirow{2}{*}{Harris-Laplacep [3]} & 0.0642/0.2143 & 0.1978/0.3578 & 0.2136/0.4409 \\  & 0.1393 /0.0951 & 0.2778/0.2298 & 0.3273/0.2318 \\ \hline \multirow{2}{*}{MSCP [19]} & 0.8259/0.8921 & 0.8182/0.6695 & 0.5751/0.5853 \\  & 0.8590/0.8421 & 0.7439/0.7221 & 0.5802/0.5229 \\ \hline \multirow{2}{*}{CPDA [22]} & 0.9107/0.7741 & 0.9156/0.5621 & **0.7206**/0.5405 \\  & 0.8424/0.8200 & 0.7389/0.6856 & 0.6305/0.5785 \\ \hline \multirow{2}{*}{He \& Yung [21]} & 0.8330/0.8831 & 0.7414/**0.7701** & 0.4040/0.7007 \\  & 0.8580/0.8483 & 0.7558/0.7413 & 0.5524/0.4728 \\ \hline \multirow{2}{*}{Fast-CPDA [37]} & 0.9058/0.7757 & **0.9221**/0.5692 & 0.7132/0.5509 \\  & 0.8407/0.8193 & 0.7457/0.6938 & 0.6321/0.5834 \\ \hline \multirow{2}{*}{DOG [35]} & 0.8631/0.7869 & 0.8159/0.6187 & 0.5877/0.5445 \\  & 0.8250/0.8114 & 0.7173/0.6888 & 0.5661/0.5097 \\ \hline \multirow{2}{*}{GCM [23]} & 0.8375/0.9187 & 0.8094/0.7030 & 0.5943/0.5983 \\  & 0.8781/0.8614 & 0.7562/0.7399 & 0.5963/0.5423 \\ \hline \multirow{2}{*}{ANDD [25]} & 0.7014/0.9104 & 0.6072/0.6952 & 0.3295/0.5260 \\  & 0.8059/0.7732 & 0.6512/0.6338 & 0.4278/0.3469 \\ \hline \multirow{2}{*}{WEAE [26]} & 0.8028/0.9487 & 0.6093/0.5634 & 0.5677/0.6487 \\  & 0.8758/0.8522 & 0.5864/0.5734 & 0.6082/0.5478 \\ \hline \multirow{2}{*}{ASJ [5]} & 0.5199/0.6865 & 0.3812/0.3989 & 0.6272/0.5684 \\  & 0.6032/0.5590 & 0.3901/0.3774 & 0.5978/0.5302 \\ \hline \multirow{2}{*}{SuperPoint [6]} & 0.4748/0.7561 & 0.6235/0.4959 & 0.4644/0.4176 \\  & 0.6154/0.5465 & 0.5597/0.5436 & 0.4410/0.3893 \\ \hline \multirow{2}{*}{New-Curvature [27]} & 0.7747/0.9487 & 0.8473/0.6823 & 0.6992/0.5992 \\  & 0.8631/0.8361 & 0.7650/0.7460 & 0.6492/0.6002 \\ \hline \multirow{2}{*}{SOGGDD [7]} & 0.2533/0.9602 & 0.6202/0.7384 & 0.3465/0.6491 \\  & 0.6068/0.3743 & 0.6793/0.6290 & 0.4978/0.3774 \\ \hline \multirow{2}{*}{MSRJ [28]} & 0.9085/0.8699 & 0.8496/0.6677 & 0.5877/0.5809 \\  & 0.8892/0.8805 & 0.7586/0.7331 & 0.5843/0.5324 \\ \hline \multirow{2}{*}{Zhang \& Sun [8]} & 0.2825/**0.9611** & 0.7315/0.7169 & 0.4844/0.6001 \\  & 0.6218/0.3997 & 0.7242/0.7135 & 0.5422/0.4774 \\ \hline \multirow{2}{*}{RPD [30]} & 0.6403/0.9500 & 0.7364/0.7293 & 0.3833/0.4516 \\  & 0.7952/0.7385 & 0.7429/0.7327 & 0.4175/0.3774 \\ \hline \multirow{2}{*}{DMC [33]} & **0.9213**/0.8771 & 0.7882/0.7437 & 0.7006/0.6365 \\  & **0.8992/0.8894** & **0.7659**/**0.7467** & **0.6685**/**0.6225** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Evaluation results in terms of precision/recall (first entry) and APR/F score (second entry) on transformed images. The highest performance with respect to each used metric achieved on each image dataset is highlighted in boldface. 20. In the last line, most corner detectors performed rather stably for different levels of Gaussian noise. Table 3 shows the performance of different methods when measuring the RGT and localization error. From this table, one can see that Fast-CPDA [37] achieved the best performance in terms of the RGT on Dataset 1 and Dataset 2, while DMC [33] obtained the best RGT on Dataset 3. As for the localization error, ANDD [25], Harris-Laplace [3], and RPD [30] achieved superior performance on Dataset 1, Dataset 2, and Dataset 3, respectively. This indicates that the use of a multi-scale curvature measurement [37] or a dynamic measurement [33] can help to achieve satisfactory corner detection performance, since strong corners can become more dominant than weak corners.