Globally Optimal and Efficient Manhattan Frame Estimation by Delimiting Rotation Search Space

A typical man-made structure can be abstracted as the Manhattan world assumption, in which notion is further represented as a Manhattan Frame (MF) defined by three orthogonal axes. The problem of MF estimation can be formulated as the solution of the rotation between the MF and the camera frame (called the "MF rotation"). However, the whole rotation space is quite redundant for solving the MF rotation, which is one of the main factors that disturb the computational efficiency of those methods associated with a rotation space search. This paper proves that the volume of the space that just contains all MF rotations (called the "MFR space") is only 1 / 24 of that of the whole rotation space, and then an exact MFR space is delimited from the rotation space. Searching in the delimited MFR space, the MF estimation solved by a branch-and-bound (BnB) framework guarantees stability and efficiency simultaneously. Furthermore, the general rotation problems associated with a rotation space search are solved more efficiently. Experiments on synthetic and real datasets have successfully confirmed the validity of our approach.