In theory, the pose of a calibrated camera can be uniquely determined from a minimum of four coplanar but noncollinear points. In practice, there are many applications of camera pose tracking from planar targets and there is also a number of recent pose estimation algorithms which perform this task in real-time, but all of these algorithms suffer from pose ambiguities. This paper investigates the pose ambiguity for planar targets viewed by a perspective camera. We show that pose ambiguities--two distinct local minima of the according error function--exist even for cases with wide angle lenses and close range targets. We give a comprehensive interpretation of the two minima and derive an analytical solution that locates the second minimum. Based on this solution, we develop a new algorithm for unique and robust pose estimation from a planar target. In the experimental evaluation, this algorithm outperforms four state-of-the-art pose estimation algorithms.

We present a novel and fast algorithm to solve the Perspective-n-Point problem. The PnP problem-estimating the pose of a calibrated camera based on measurements and known 3D scene, is recasted as a minimization problem of the Object Space Cost. Instead of limiting the algorithm to perspective cameras, we use a formulation for general camera models. The minimization problem, together with a quaternion based representation of the rotation, is transferred into a semi definite positive program (SDP). This transfer is done in O(n) time and leads to an SDP of constant size. The solution of the SDP is a global minimizer of the PnP problem, which can be estimated in less than 0.15 seconds for 100 points.

We propose a novel, hybrid SLAM system to construct a dense occupancy grid map based on sparse visual features and dense depth information. While previous approaches deemed the occupancy grid usable only in 2D mapping, and in combination with a probabilistic approach, we show that geometric SLAM can produce consistent, robust and dense occupancy information, and maintain it even during erroneous exploration and loop closure. We require only a single hypothesis of the occupancy map and employ a weighted inverse mapping scheme to align it to sparse geometric information. We propose a novel map-update criterion to prevent inconsistencies, and a robust measure to discriminate exploration from localization.

This paper presents a novel algorithm to solve the Structure and Motion problem. The novelty is in the use of a general camera model, which does not constrain the algorithm to a specific camera, and the use of the Object Space Error for General Camera Models as cost function. We show that, using this cost function, the structure and the translation part of the motion can be estimated from the rotation part of the motion in closed form. So only the rotation part of the motion needs to be optimized to estimate the minimum of the total cost function. This results in an iterative algorithm which has a theoretical speedup factor of 8 compared to the bundle adjustment method. We also prove the global convergence of the presented algorithm.

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