Revealing Hidden 3-D Reflection Symmetry

Reflection symmetry is present in most of the man-made or naturally formed objects. In computer vision, real-world scenes are represented by dense 3-D models or by 2-D projections, such as images captured by cameras. Most of the existing methods either detect reflection symmetry from dense 3-D models or 2-D projections. However, generating a dense 3-D model is a computationally expensive process and reflection symmetry may not be evident in any of the 2-D views obtained through projections. In this letter, we propose an energy minimizationbased approach to detect the reflection symmetry present in the object from its multiple 2-D projections captured from different viewpoints and the sparse 3-D model obtained using these projections. The proposed approach only estimates the sparse 3-D model and utilizes content of the images in terms of local scale invariant features. The energy minimization problem reduces to the problem of finding the eigenvector corresponding to the smallest eigenvalue of a small matrix, thereby leading to reduction in computations.