Bayesian perspective-plane (BPP) with maximum likelihood searching for visual localization

Abstract

The proposed "Perspective-Plane" in this paper is similar to the well-known "Perspective-n-Point (PnP)" or "Perspective-n-Line (PnL)" problems in computer vision. However, it has broader applications and potentials, because planar scenes are more widely available than control points or lines in daily life. We address this problem in the Bayesian framework and propose the "Bayesian Perspective-Plane (BPP)" algorithm, which can deal with more generalized constraints rather than type-specific ones. The BPP algorithm consists of three steps: 1) plane normal computation by maximum likelihood searching from Bayesian formulation; 2) plane distance computation; and 3) visual localization. In the first step, computation of the plane normal is formulated within the Bayesian framework, and is solved by using the proposed Maximum Likelihood Searching Model (MLS-M). Two searching modes of 2D and 1D are discussed. MLS-M can incorporate generalized planar and out-of-plane deterministic constraints. With the computed normal, the plane distance is recovered from a reference length or distance. The positions of the object or the camera can be determined afterwards. Extensions of the proposed BPP algorithm to deal with un-calibrated images and for camera calibration are discussed. The BPP algorithm has been tested with both simulation and real image data. In the experiments, the algorithm was applied to recover planar structure and localize objects by using different types of constraints. The 2D and 1D searching modes were illustrated for plane normal computation. The results demonstrate that the algorithm is accurate and generalized for object localization. Extensions of the proposed model for camera calibration were also illustrated in the experiment. The potential of the proposed algorithm was further demonstrated to solve the classic Perspective-Three-Point (P3P) problem and classify the solutions in the experiment. The proposed BPP algorithm suggests a practical and effective approach for visual localization.