A Universal, Closed-form Approach for Absolute Pose Problems
Computer Vision and Image Understanding
We propose a general approach for absolute pose problems including the well known perspective-n-point (PnP) problem, its generalized variant (GPnP) with and without scale, and the pose from 2D line correspondences (PnL). These have received a tremendous attention in the computer vision community during the last decades. However, it was only recently that efficient, globally optimal, closed-form solutions have been proposed, which can handle arbitrary numbers of correspondences including minimal configurations as well as over-constrained cases with linear complexity. We follow the general scheme by eliminating the linear parameters first, which results in a least squares error function that only depends on the non-linear rotation and a small symmetric coefficient matrix of fixed size. Then, in a second step the rotation is solved with algorithms which are derived using methods from algebraic geometry such as the Gröbner basis method. We propose a unified formulation based on a representation with orthogonal complements which allows to combine different types of constraints elegantly in one single framework. We show that with our unified formulation existing polynomial solvers can be interchangeably applied to problem instances other than those they were originally proposed for. It becomes possible to compare them on various registrations problems with respect to accuracy, numerical stability, and computational speed. Our compression procedure not only preserves linear complexity, it is even faster than previous formulations. For the second step we also derive an own algebraic equation solver, which can additionally handle the registration from 3D point-to-point correspondences, where other rotation solvers fail. Finally, we also present a marker-based SLAM approach with automatic registration to a target coordinate system based on partial and distributed reference information. It represents an application example that goes beyond classical camera pose estimation from image measurements and also serves for evaluation on real data.
Mutual Information-Based Tracking for Multiple Cameras and Multiple Planes
Arabian Journal for Science and Engineering
Based onmutual information (MI), this paper proposes a systematic analysis of tracking a multi-plane object with multiple cameras. Firstly, a geometric model consisting of a piecewise planar object and multiple cameras is setup. Given an initial pose guess, the method seeks a pose update that maximizes the global MI of all the pairs of reference image and camera image. An object pose-dependent warp is proposed to ensure computation precision. Six variations of the proposed method are designed and tested. Mode 1, i.e., computing the 2nd-order Hessian of MI at each step as the object pose changes, leads to the highest convergence rates; Mode 2, i.e., computing the 1st-order Hessian of MI once at the beginning, occupies the least time (0.5-1.0 s). For objects with simple-textured planes, applying Gaussian blur first and then useMode 1 shall generate the highest convergence rate.
Multi-Camera Piecewise Planar Object Tracking with Mutual Information
Journal of Mathematical Imaging and Vision
Real-time and robust tracking of 3D objects based on a 3D model with multiple cameras is still an unsolved problem albeit relevant in many practical and industrial applications. Major problems are caused by appearance changes of the object. We present a template-based tracking algorithm for piecewise planar objects. It is robust against changes in the appearance of the object (occlusion, illumination variation, specularities). The version we propose supports multiple cameras. The method consists in minimizing the error between the observed images of the object and the warped images of the planes. We use the mutual information as registration function combined with an inverse composition approach for reducing the computational costs and get a near-real-time algorithm. We discuss different hypotheses that can be made for the optimization algorithm.
Mutual Information-Based Piecewise Planar Object Tracking
Darmstadt, TU, Master Thesis, 2014
This master thesis deals with a template based tracking algorithm for piecewise planar objects. It is robust against changes in the appearance of the object (occlusion, illumination variation, specularities). The version that we propose supports multiple cameras. The method consists in minimizing the error between the observed images of the object and the warped images of the planes. We use for that an estimation of the pose of the object, which is to say a rigid 3D transformation. The robustness is obtained by using the mutual information as registration function. The main drawback of the mutual information is that it has a high computation complexity. We use an inverse composition approach for the warp update, so that pre-computations can be done and it decreases the complexity of the algorithm. We develop a way of computing the warp update and analyse the impact of this initiative on the optimization process. We also determine the optimal parameters for running the algorithms.