An algorithm to recover generalized cylinders from a single intensity view

A general method is presented for recovering straight homogeneous generalized cylinders from monocular intensity images. In this method, it is assumed that the generalized cylinder being recovered has purely diffuse reflectance and that the diffuse reflectance coefficient is constant. It is demonstrated that contour information alone is insufficient to recover a straight homogeneous generalized cylinder uniquely. It is shown that the sign and magnitude of the Gaussian curvature at a point vary among members of a contour-equivalent class. The contour image fails to constrain two parameters of the underlying generalized cylinder, the 3D axis tilt and translation. A method for ruling straight homogeneous generalized cylinder images is described. Once the rulings of the image have been recovered, all parameters derivable from contour alone can be recovered, all parameters derivable from contour alone can be recovered. To recover the two remaining parameters (modulo scale) not constrained by image contour, additional information must be incorporated into the recovery process, e.g. intensity information. A method for recovering the tilt of the object using the ruled contour image and intensity values along extremal cross-section curves is derived, along with a method for recovering the location of the object´s 3D axis from intensity values along meridians of the surface. The methods outlined constitute an algorithm for recovering all the shape parameters (modulo scale)