Reflection symmetry detection of shapes based on shape signatures

•A solid theoretical foundation of R-signature and LIP-signature about symmetric properties of a given shape is represented.•A verification process is theoretically justified to remove the false candidates based on an efficient symmetry measure.•Two novel datasets (UTLN-SRA & UTLN-MRA) with single & multiple reflections are designed for evaluating symmetry detectors.•A new evaluation protocol based on a lost measure is presented to evaluate reflectional symmetry detectors.•Comprehensive evaluations have verified that our proposed detectors perform well on binary images compared to state of the art.