Tadamasa Sawada, Yunfeng Li, Zygmunt PizloA 3D mirror-symmetrical shape can be recovered from a single 2D orthographic or perspective image by applying several a priori constraints: 3D mirror symmetry, 3D compactness and planarity of contours. From the computational point of view, the application of a 3D symmetry constraint is challenging because it requires establishing 3D symmetry correspondence among features of a 2D image, which itself is asymmetrical for almost all viewing directions relative to the 3D symmetrical shape. We describe new invariants of a 3D to 2D projection for the case of a pair of mirror-symmetrical planar contours and we formally state and prove the necessary and sufficient conditions for detection of this type of symmetry in a single orthographic and perspective image.
Demo 1. Two different 3D symmetric curves produced from the same 2D curve in Figure 2.
Demo 2. Two 3D symmetric curves produced from 2D curves in Figure 9a and 9b.
Demo 3. A symmetric pair of helices that project to the pair of 2D curves in Figure 11.
Demo 4. A symmetric pair of 3D curves produced from the pair of 2D curves in Figure 15.