A Variational Approach to 3D Cylindrical Geometry Reconstruction from Multiple Views

In this paper we present a variational technique for the reconstruction of 3D cylindrical surfaces. Roughly speaking by a cylindrical surface we mean a surface that can be parameterized using the projection on a cylinder in terms of two coordinates, (l, θ), representing the displacement and angle in a cylindrical coordinate system respectively. The starting point for our method is a set of different views of a cylindrical surface, as well as a precomputed disparity map estimation between pair of images. The proposed variational technique is based on an energy minimization where we balance on the one hand the regularity of the cylindrical function given by the distance of the surface points to cylinder axis, and on the other hand, the distance between the projection of the surface points on the images and the expected location following the precomputed disparity map estimation between pair of images. One interesting advantage of this approach is that we regularize the 3D surface by means of a bi-dimensional minimization problem. We show some experimental results for large stereo sequences.