Contour-based corner detection via angle difference of principal directions of anisotropic Gaussian directional derivatives
Introduction
Corners, as essential features of images, carry abundant information on image structure and are invariant features under many geometric transforms to images. Corner detection plays an important role in many image processing tasks, for example, image registration, stereo matching, motion tracking, objection recognition [1], [2], [3], [4], [5]. There have existed many corner detectors and these detectors are broadly classified into three groups: intensity-based methods [6], [7], [8], [9], model-based methods [10], [11], and contour-based methods [12], [13], [14].
Intensity-based detectors find corners from all the pixels of an image and the underlying corner measure needs to tell corners from non-edge pixels and smooth edge pixels. Moravec found that the intensity variations around a corner are significant at no less than two directions and introduced the original idea of intensity-based detection [6]. Starting from this idea, Harris developed the famous Harris detector [7]. The local autocorrelation matrix of intensity variations reflects the difference between corners and non-corner pixels. The corner measure is constructed from the two eigenvalues of the local autocorrelation matrix. The Harris detector was shown to be optimal only for L-junctions [8]. Recently, the Log-Gabor wavelets [17] were employed to extract multiscale intensity variations and from which the local autocorrelation matrix is constructed for corner detection in the Harris framework [9]. Model-based detectors find corners by matching a small patch of an image against a predefined model. Smith and Brady proposed the SUSAN detector using a circular mask [10]. In substance, the SUSAN detector uses the number of the pixels similar to the center pixel in the circular template as the corner measure, which is ineffective for some composite corners such as X-junctions. The SUSAN detector can be improved by replacing the circular mask by a pair of oriented cross operators [11]. The model -based detectors are of low computational complexity but noise-sensitive and exhibit unsatisfactory performance for images with abundant texture.
Relative to intensity-based and model-based detectors, contour-based detectors are more popular for the low occurrence probability of false corners. Contour-based detectors use edge detection as the pre-process before corner detection. Corners are found from contours of an image rather than the whole image. The corner measures are defined on contours and are used to tell corners from smooth edge pixels on contours. Mokhtarian et al. developed the curvature-scale-space (CSS) corner detector [12], where the local curvature at a high scale is used for corner detection and corner tracking from lower scale to the lowest scale to improve localization accuracy. The CSS corner detectors suffer from several defects. First, the curvature computation uses the second derivatives highly sensitive to the local variation and noise on contours. Second, it is difficult to select an appropriate scale of Gaussian kernel to smooth contours. Third, the threshold choice in corner decision is difficult from image to image. At last, the local curvature of the discrete contour on image grid has low resolution to direction variation of the contour, because adjacent pixels on contour have only eight directions. Mohammad and Lu proposed the corner detector using chord-to-point distance accumulation (CPDA) [13], which basically avoids the first two defects. He and Yung [14] use adaptive curvature threshold to improve the CSS corner detector, which partly overcomes the third defect.
It was proved that the anisotropic Gaussian directional derivatives (ANDDs) are noise-robust and provide finer directional intensity variation around a pixel [15]. In this paper, we embed the ANDDs into the contour-based corner detection framework to develop a new corner detector. Here, the angular difference of the principal directions of the ANDDs at the two pixels at the two-sides of the pixel under test is used as a new corner measure to find corner from a contour. Owing to the noise-robustness of the ANDDs, the principal directions of the ANDDs on contour are robust to small variation and noise on contours. Moreover, the fine directional intensity variation description of the ANDDs makes that the new corner measure attains high angular resolution. More importantly, different from the existing contour-based detectors where the corner measures are based upon the geometric features of contours, in the new corner detector the local directional intensity variations participate in corner decision to improve corner detection performance. The proposed corner detector is compared with the three state-of-the-art corner detectors, the Harris detector [7], the CPDA detector [13], and the He and Yung detector [14] by using two common-used test images with ground truths to evaluate detection and localization performance and using twenty-four images with different scenes and without ground truths to assess the repeatability under affine transforms, JPEG compression, and noise degradation of images. The experimental results show that the proposed corner detector attains better overall performance.
This paper is organized as follows. Section 2 reviews the anisotropic Gaussian directional derivative (ANDD) and its properties. Section 3 presents the new corner measure on contours and gives the detailed flowchart of the proposed new corner detector. Section 4 includes the comparison of the proposed corner detector with the three state-of-the-art detectors in detection capability, localization accuracy, and repeatability under affine transforms, JEPG compression, and noise degradation.
Section snippets
Anisotropic Gaussian directional derivatives
Edges and corners are anisotropic features in images. Traditional edge and corner detection often uses the gradients to capture anisotropic intensity variation around an edge pixel or a corner. Gradients are generally derived from an isotropic Gaussian smoothing filter followed by the two first-order partial derivative operator. It is pointed out that using the isotropic Gaussian smoothing and gradient operator is in a dilemma: small-scale Gaussian filters have good edge localization and
Corner measure on Contours and new corner detector
Contour-based method is popular in corner detection and the state-of-the-art detectors include the CSS detector [12], the CPDA detector [13], and He and Yung detector [14]. These detectors share a three-step flowchart: edge detection, contour extraction, and corner decision. First, the edge map of an image is extracted by an edge detector (for instance, the Canny detector [16]). Next, contours are extracted from the edge map and each contour is a loop or open discrete planar curve in the image
Experimental results and performance comparison
The full performance evaluation of the proposed corner detector is reported in this subsection. It is compared with the three state-of-the-art corner detectors, Harris detector [7], CPDA detector [13], and He and Yung detector [14] by using the two commonly-used test images with ground truths for detection and localization performance and twenty-four test images with different scenes but without ground truths for the repeatability under affine transforms, JPEG compression, and noise degradation
Conclusion
Corner decision in the existing contour-based corner detection mainly depends upon the geometric information of extracted contours. The local intensity variations of images only react on the contour extraction. The principal directions of the ANDDs on contours are used to construct the new corner measure on contours. The ANDD-based corner measure inherits the noise-robustness and high angular resolution of the ANDDs. Compared with the corner measures based upon the geometric property of
Conflict of interest
None declared.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant no. 61271295). The authors would like to thank the reviewers for their constructive suggestions. One of the reviewers suggested us to use the D-P algorithm to improve the quality of extracted contours, which brings an improvement in corner detection performance of the three contour-based corner detectors.
Wei-Chuan Zhang was born in Zhejiang, China, in 1980. He received the M.S degree in signal and information processing from the Southwest Jiaotong University in 2005. He is currently working toward the Ph.D degree in signal and information processing in National Lab of Radar Signal Processing, Xidian University, China. His research interests include image edge and corner detection and their applications.
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Wei-Chuan Zhang was born in Zhejiang, China, in 1980. He received the M.S degree in signal and information processing from the Southwest Jiaotong University in 2005. He is currently working toward the Ph.D degree in signal and information processing in National Lab of Radar Signal Processing, Xidian University, China. His research interests include image edge and corner detection and their applications.
Peng-lang Shui received the M.S degree in mathematics from Nanjing University, Nanjing, China and the Ph.D in signal and information processing from Xidian University, Xi'an, China, in 1992 and 1999, respectively. He is currently a professor of National Lab of Radar Signal Processing, Xidian University. His research interests includes filter bank design and their applications, image processing, and radar target detection. Up to now, he has published over 50 journal papers in these fields.
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