On the generalized k-cosine arithmetic-mean curvature for multi-scale corner detection

In multi-scale feature extraction, image feature cues extracted over a set of scales are normally fused by computing their geometric mean (GM). In this paper, it has been theoretically shown that from a signal processing point of view, the arithmetic mean (AM) should be used instead of the GM; this is beneficial in conducting multi-scale corner detection. First, the generalized k -cosine is developed and exploited to compute the AM curvature. Compared to the GM curvature, the AM curvature can be more efficient in yielding higher saliency for corner points than that of insignificant local image structures. On the other hand, our developed generalized k-cosine curvature measurement can incorporate the contour's convexity and concavity into the corner detection process, while enjoying reduced computational complexity. To further improve corner detection performance, a curvature smoothing technique, with a two-stage curvature thresholding, is developed for removing noise from the computed AM curvatures. Extensive experimental results have demonstrated that our proposed AM-curvature-based corner detector can clearly outperform a number of state-of-the-art corner detection methods. In particular, the average F-score achieved on five benchmark datasets has been increased by 3.8% on clean images and 3.2% on quality-degraded images, respectively.