Complex shearlets and rotary phase congruence tensor for corner detection

•Proposed complex shearlets can overcome the weakness of the current shearlets.•Idea fully using both amplitude and phase information to detect corners is novel.•A new phase congruence model with high localization ability and noise tolerance.•A new rotation-normalized tensor using all amplitudes and phases to detect corners.•The work yields improvements on the current state-of-the-art in corner detection.