Refining Image Edge Detection via Linear Canonical Riesz Transforms

Abstract. By combining the linear canonical transform and the Riesz transform, we introduce the linear canonical Riesz transform (LCRT), which is further proved to be a linear canonical multiplier. Using this LCRT multiplier, we conduct numerical simulations on images. Notably, due to the fact that the linear canonical transform itself admits a fast algorithm, the LCRT can achieve a computational speed comparable to that of the linear canonical transform. Based on this, we introduce the new concept of the sharpness [Formula: see text] of the edge strength and continuity of images associated with the LCRT and, using it, we propose a new LCRT image edge detection method (LCRT-IED method) and provide its mathematical foundation. Our experiments indicate that this sharpness [Formula: see text] characterizes the macroscopic trend of edge variations of the image under consideration, while this new LCRT-IED method not only controls the overall edge strength and continuity of the image, but also excels in feature extraction in some local regions. These highlight the fundamental differences between the LCRT and the Riesz transform, which are precisely due to the multiparameter of the former. This new LCRT-IED method might be of significant importance for image feature extraction, image matching, and image refinement.