3D Reconstruction of Planar Objects using the Properties of Plane and Vanishing Points from a Single Panoramic Image

This paper presents the 3D reconstruction of planar objects using the normal vector of plane and vanishing points from a single panoramic image. We get the geometric information of plane or line with feature points which use the constraints of coplanarity, perpendicularity and parallelism of planes or lines. We describe the 3D reconstruction about any features using the properties of vanishing points and several constraints like a coplanarity, perpendicularity and parallelism in planes and lines even though it may not extract the intersection point. When the panoramic camera located on ground in perpendicular, all vertical lines are converged into center point in image. However, horizontal line with ground plane projected as the curve on the basis of each vanishing point in image; the parallel lines with ground are projected as the curve in panoramic image. In order to get 3D information of line, we find out the parallel plane in focal point of mirror using the already known the height of mirror from the ground. We call the plane as the plane at infinity. Plane at infinity is projected as the circle at infinity in image which has the vanishing points on his area. Using this proposed method, we analyze the results from corridor or indoor environments; we also apply the hyperboloidal mirror to get panoramic image and perform the 3D reconstruction.