# Robust and Efficient Corner Detector Using Non-Corners Exclusion
## 1 Introduction  
Feature point detection is used as the fundamental step of image analysis and computer vision. As an important element, corner detection is still widely used today in applications including object detection, motion tracking, simultaneous localization and mapping, object recognition and stereo matching [1; 2; 3]. A corner detector can be successfully used for these tasks if it has good consistency and accuracy [4]. For this reason, a large amount of pioneering work has been performed on corner detection in recent years. These techniques can be broadly classified into two categories: intensity-based corner detectors [5; 6; 7; 8; 9; 10] and contour-based corner detectors [11; 12; 13; 14]. Both types of corner detectors have their respective merits and demerits. The contour-based corner detectors are mainly based on the curvature scale space (CSS). An edge detector is used in these detectors, for example the Canny edge detector [15], to obtain planar curves parameterized by arc-length. They are smoothed by a set of multi-scale Gaussian functions. Then the curvature is calculated on each point of the curves smoothed by the Gaussian functions. Finally, the candidate corners will be comprised of the absolute maximum curvature points from which weak and false corners will be excluded by thresholds. In order to improve localization, some CSS-based corner detectors additionally use a corner tracking step [13]. These detectors perform well in corner detection,but they suffer from two main problems. First, the curvature estimation technique is sensitive to the local variation and noise on contours because it uses second order derivatives of curve-point locations. Second, the large-scale Gaussian functions fail to detect true corners while small-scale ones detect a number of false corners. In other words, scale selection is a difficult task. In order to overcome the aforementioned problems, the multi-scale detector based on the chord-to-point distance accumulation (CPDA) technique is developed [14]. However, the complexity of the CPDA corner detector is high and it is difficult to improve from the algorithm architecture, so it cannot be applied to many computer vision systems. Other novel techniques are also proposed to improve performance, including angle difference of principal directions [16], Laplacian scale-space [17] and so on. However, all the methods in this category do not detect every corner region in an image. In particular, they fail to detect corner regions formed by a texture [18]. The intensity-based detectors indicate the presence of a corner by using the first-order or second-order derivatives of images and calculating the corner response function (CRF) of each pixel. [PERSON] computes the local sum of squared differences (SSD) between an image patch and its shifted version in four different directions [5]. The point with the largest SSD in a certain range is determined as a corner. But this technique is dramatically sensitive to noise and strong edges. [PERSON] and [PERSON] developed the smallest univalue segment assimilation nucleus (SUSAN) method for corner and edge detection [7]. This method is mainly based on a circular mask applied to the interest region. The pixels which have similar brightness to the nucleus construct the univalue segment assimilating nucleus (USAN) area. However, the accuracy of this algorithm is heavily dependent on the threshold. If the threshold is too big or too small, corner detection errors will result. [PERSON] and [PERSON] proposed the feature from accelerated segment test (FAST) algorithm based on the SUSAN corner detector [9; 10]. As with SUSAN, FAST also uses a Bresenham circle of radius 3 pixels as test mask. The difference is that FAST just uses the 16 pixels in the circle to decide whether a point is actually a corner. The FAST algorithm requires very short computation time, but it is very sensitive to noise and needs to be combined with other algorithms to improve its robustness.