# Robust and Efficient Corner Detector Using Non-Corners Exclusion
## 4 Experimental Results and Analysis
### Consistency of Corner Numbers  
Consistency means corner numbers should not vary with various transforms [4]. The formula of CCN has been described in Section 2. Here, the block image is used as test image to evaluate the consistency. According to the definition of CCN, its computation does not need the ground truths of test images. The number and the position of corners in the block image are shown in Figure 5. To evaluate the consistency of the five corner detectors, the rotation transformation, the shearing transformation, the brightness transformation, the uniform scaling and the Joint Photographic Experts Group (JPEG) compression are performed. The original image is first transformed with these transformations. Then, we use the five corner detectors to extract the number and the position of corners in all transformed images. Finally, the values for the CCN criterion are computed. The transformation factors are as follows:  
* Rotation: 19 different angles in [\(-90^{\circ}\), \(90^{\circ}\)] at \(10^{\circ}\) apart. * Shearing: the shearing factor of y direction in [\(-1\), \(1\)] at 0.2 apart. * Uniform scaling: 11 scaling factors in [0.5, 1.5] at 0.1 apart. * Brightness variation: 9 brightness factors in [0.2, 1.8] at 0.2 apart. * JPEG compression: the quality loss factors in [0.1, 1] at 0.1 apart. The Figure 7 shows the average consistency of corner numbers (CCN) under each transformation for five corner detectors. Figure 8 shows the CCN values of the five corner detectors under different shearing factors in vertical direction. It can be seen that the proposed RECD achieves the best performance when shearing factor is in [\(-0.2\), \(0.4\)]. The Harris performs better than the RECD in the range from \(-1\) to \(-0.4\). Although the  
Figure 8: Consistency of corner numbers (CCN) of each method under shearing transformation. Figure 7: The average CCN under each transformation for five corner detectors. FAST-9 has better CCN at the shearing factor \(-0.6\) and \(0.6\), it has large fluctuation and achieves low value at other shearing factors. As the basis of FAST-9, the SUSAU detector achieves similar results. The consistency of Moravec detector is the worst. It can be seen from Figure 7 that the average CCN value of RECD is highest which is followed slightly by Harris. The consistency performance under uniform scaling is shown in Figure 9. It is obvious that RECD detector is the most stable one for the variation of scaling factor. Moreover, it performs best when the scaling factor is in [1, 1.3] and [0.6, 0.7]. As the basis of RECD, Harris has similar CCN to it. However, RECD has better consistency owing to the strong corner validation in Section 3.1. When the image is shrunk, FAST-9 achieves the best performance followed by RECD. By contrast, it performs worst when the image is enlarged. In Figure 7, the RECD has the best average CCN. It demonstrates that RECD has better detection capability under scaling transformation than the other four detectors. Figure 10 shows the relation between CCN and image brightness. When the brightness factor is 1, the image is not changed. It becomes darker when brightness factor is less than 1 and brighter when brightness factor is more than 1. RECD and Harris both have a more stable curve and achieve better performance than other three detectors in Figure 10. FAST-9 performs worst under brightness variation. Seen from Figure 7, the RECD has highest average CCN under different brightness variations. Figure 11 shows the consistency performance of the five detectors under different JPEG compression factors. The quality loss factor determines the percent of lost image information. As the increase of quality loss factor, the lost information increases. Obviously, the Moravec detector achieves the highest CCN. This is because the Moravec detector is more sensitive to edges of different directions. FAST-9  
Figure 10: CCN of each method under brightness variation. Figure 9: CCN of each method under uniform scaling transformation.