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Analysis of Vanishing Curves and Points of Planar Objects from Single Panoramic Image

This paper presents the mapping function of horizontal line segments in panoramic image for 3D reconstruction of planar objects. It is interest to get the 3D geometrical information directly under the single panoramic image. The estimation of the 3D geometric information is to use the several conditions of features such as a vanishing line and point and the geometric relationship of feature as parallelism of lines from single panoramic view. This paper describes the 3D reconstruction about any features using the properties of vanishing points and curves. When the panoramic camera located on ground in perpendicular against the mirror, all vertical line segments are converged into center point in image. 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. Second, it is able to obtain the parallel plane in focal point of mirror using the already known the height of mirror from the ground. The curve of horizontal edge line should intersect with the circle at infinity; two intersection points with pi phase difference converge in pair of vanishing points of each object. Consequently, this paper applies the hyperbolic mirror to get panoramic image and perform the 3D reconstruction. It can be suitable and concrete information of environment so that also robot can know the shape of environment within visible range from single panoramic image.