目的：传统的基于边缘轮廓的角点检测算法需要计算每一个边缘像素点的曲率，对噪声和局部变化敏感，极易造成检测结果的不稳定。针对这一问题，提出一种利用点弦距离递归的角点检测算法。方法：首先利用Canny边缘检测器提取边缘轮廓线，然后用三个不同尺度的高斯核对边缘线进行平滑。对于每一个高斯尺度平滑后的边缘线，连接其首尾端点形成一条弦，计算边缘轮廓上每个边缘像素点到弦的距离，把点弦距离最长的像素点标为候选角点。该像素点把原边缘轮廓线分成两条边缘，然后分别把该像素点与首尾端点连接成两条弦，重新计算点弦距离,将所有距离大于设定阈值的点作为候选角点。最后，利用多尺度技术对候选角点进行判决并得到最终角点。结果：与现有的基于曲率计算的角点检测算法相比，本文提出的算法不需要计算一、二阶导数，有效避免了局部变化带来的计算误差。通过计算得到四个角点检测器的平均排名分别为：Harris 4.0，He &Yung 2.67，CPDA 1.83，本文算法 1.5。与其它三种经典的角点检测算法想比，本文提出的检测算法排名第一，因此表现出了更好的检测性能。结论：本文提出了一种新的利用点弦距离递归的角点检测算法。从实验结果来看，本文提出的角点检测器在图像仿射变换，JPEG质量压缩和高斯噪声条件下有着更好的平均重复性和定位误差。
Image corner detection using recursively maximum point-to-chord distance
liyunhong,heyarui,zhangweichuan,zhouxiaoji,fangqiaochu(Xi’an Polytechnic University)
Objective: Corners in images represent critical information in describing object features, which play a crucial and irreplaceable role in computer vision and image processing systems. Many computer vision tasks rely on the successful detection of corners, including 3-D reconstruction, stereo matching, image registration, motion estimation and object tracking. However, it still has not a strict mathematical definition for corner; corners are usually defined as the points with low self-similarity or location where variations of the intensity in all directions are high. Alternatively, corners may be defined as image points where the local maxima of curvature on the edge contour or the intersection of the two of more edge curves. In the past decades, a substantial number of promising corner detection methods based upon the different corner definitions have been proposed by vision researchers. However, the traditional contour-based corner detection algorithm needs to calculate the curvature of each edge pixel and is sensitive to noise and local variations, which will cause the instability of detection results. Therefore, this paper proposed a novel image corner detection approach based on a recursive point-to-chord distance. Method: This paper first analyzed the state–of–the–art corner detection algorithms and then proposed a new corner detection method. First, it extracts each edge contour from the input image using the Canny edge detector. Canny edge detector is one of the most widely used edge detectors in contour–based corner detectors and has also become a standard gauge in edge detection. An edge pixel is defined as if the gradient magnitudes at either side of it are lower than itself. However, the output contours may have small gaps and these gaps may possibly contain corners. Second, it smooths curves using three different Gaussian kernels respectively. For each smoothed curve of Gaussian scale, connecting the ends of the curve and form a chord, then calculate the distance between each edge pixel of the contour and the chord, and mark the pixel with the longest distance as the candidate corner. The original edge contour is divided into two edges by using the pixel point, then the pixel point is connected to the ends of the contour into two chords respectively, the distance from the point to the chord is recalculated and compared with the threshold value, we choose the point that greater than the threshold as the candidate corner. Finally, applying the multi-scale technique to candidate corner set and obtaining the final corners. Result: Compared with the existing corner detection algorithms based on curvature calculation, the proposed algorithm does not need to calculate the first- and second- derivatives, avoids the calculation error caused by the local variation effectively and very robust to noise. The four corner detectors achieved the highest average repeatability in JPEG quality compression and the worst localization error in shear transformation. The proposed and CPDA corner detectors performed better than other detectors in geometric transformations. In terms of JPEG quality compression and Gaussian noise, the proposed method achieves the highest average repeatability and lowest localization error than other three detectors. The experimental results show that the proposed detector attains better overall performance. Conclusion: The proposed detector neither need to accumulate each distance from a moving chord, nor need to computer the accumulation of each point in a curve, therefore achieves better speed while keeping the good average repeatability and accuracy. Compared with the three classic detection algorithms of Harris, CPDA, and He & Hung, the proposed detector attains better performance on average repeatability and localization error under affine transforms, JPEG compression and Gaussian noise. The existing corner detection methods can be broadly classified into three classes: intensity–based, model-based and contour–based methods. The key of the intensity–based corner detection is to extract local gray–variation and structural information effectively. Model-based methods extract corners by fitting the local image into a predefined model. Contour-based methods first obtain image’s planar curves by some edge detector and then smooth the curves by Gaussian function and compute their corresponding curvatures. Finally, the points of local curvature maxima, line intersects or rapid changes in the edge direction are marked as corners. The presence of two categories methods have their strengths and weak-nesses, and expose the defects with different degree in practical application, which makes the corner detection become research hotspot in the field of computer vision and image processing. It can be seen from the experiment result that the proposed corner detector performs better than other three classical detectors in term of robustness. Corner detection algorithm of this paper has good detection performance. Future tasks may continuously improve its detection performance and apply it in many of computer vision research.