Title :
Detecting 3-D Mirror Symmetry in a 2-D Camera Image for 3-D Shape Recovery
Author :
Sawada, Tsuyoshi ; Yunfeng Li ; Pizlo, Zygmunt
Author_Institution :
Coll. of Optometry, State Univ. of New York, New York, NY, USA
Abstract :
In this paper, we take up the long-standing problem of how to recover 3-D shapes represented by a 2-D image, such as the image on the retina of the eye, or in a video camera. Our approach is biologically grounded in a theory of how the human visual system solves this problem, focusing on shapes that are mirror symmetrical in 3-D. A 3-D mirror-symmetrical shape can be recovered from a single 2-D orthographic or perspective image by applying several a priori constraints: 3-D mirror symmetry, 3-D compactness, and planarity of contours. From the computational point of view, the application of a 3-D symmetry constraint is challenging because it requires establishing 3-D symmetry correspondence among features of a 2-D image, which itself is asymmetrical for almost all viewing directions relative to the 3-D symmetrical shape. We describe new invariants of a 3-D to 2-D 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.
Keywords :
eye; image sensors; retinal recognition; shape recognition; 2D camera image; 3D mirror symmetrical shape; 3D mirror symmetry detection; 3D shape recovery; computational point; eye; human visual system; perspective image; retina; single orthographic image; video camera; Cameras; Inverse problems; Retina; Symmetry; Two dimensional displays; Visual systems; Visualization; 3-D shape recovery; 3-D symmetry; 3-D symmetry correspondence; Perspective projection; skewed symmetry;
Journal_Title :
Proceedings of the IEEE
DOI :
10.1109/JPROC.2014.2344001