Symmetry is an important feature in natural and man-made objects; particularly, mirror symmetry is a relevant task in fields such as computer vision and pattern recognition. In the current work, we propose a new method to characterize mirror-symmetry in open and closed curves represented by means of the Slope Chain Code. This representation is invariant under scale, rotation, and translation, highly desirable properties for object recognition applications. The proposed method detects symmetries through simple inversion, concatenation and reflection operations on the chains, thus allowing the classification of symmetrical and asymmetrical contours. It also introduces a measure to quantify the degree of symmetry in quasi-mirror-symmetrical objects. Furthermore, it allows the identification of multiple symmetry axes and their location. Results show high performances in symmetrical/asymmetrical classification (0.9 recall, 0.9 accuracy, 0.97 precision) and axes’ detection (0.8 recall, 0.84 accuracy, 0.99 precision). Compared to other methods, the proposed algorithm provides properties such as: global, local, and multiple axes’ detection, as well as the capability to classify symmetrical objects, which makes it adequate for several practical applications, like the three exemplified in the paper.