On the foundations of vision modeling II. Mining of mirror symmetry of 2-D shapes

Vision can be considered as a feature mining problem. Visually meaningful features are often geometrical, e.g., boundaries (or edges), corners, T-junctions, and symmetries. Mirror symmetry or near mirror symmetry is one of the most common and useful symmetry types in image and vision analysis. The current paper proposes several different approaches for studying 2-dimensional (2-D) mirror symmetric shapes. Proper mirror symmetry metrics are introduced based upon the Lebesgue measure, Hausdorff distance, as well as lower-dimensional feature sets. Theory and computation of these approaches and measures are developed, and numerical results are demonstrated.