Robust and accurate online pose estimation algorithm via efficient three‐dimensional collinearity model

In this study, the authors propose a robust and high accurate pose estimation algorithm to solve the perspective‐N‐point problem in real time. This algorithm does away with the distinction between coplanar and non‐coplanar point configurations, and provides a unified formulation for the configurations. Based on the inverse projection ray, an efficient collinearity model in object–space is proposed as the cost function. The principle depth and the relative depth of reference points are introduced to remove the residual error of the cost function and to improve the robustness and the accuracy of the authors pose estimation method. The authors solve the pose information and the depth of the points iteratively by minimising the cost function, and then reconstruct their coordinates in camera coordinate system. In the following, the optimal absolute orientation solution gives the relative pose information between the estimated three‐dimensional (3D) point set and the 3D mode point set. This procedure with the above two steps is repeated until the result converges. The experimental results on simulated and real data show that the superior performance of the proposed algorithm: its accuracy is higher than the state‐of‐the‐art algorithms, and has best anti‐noise property and least deviation by the influence of outlier among the tested algorithms

Line Primitives and Their Applications in Geometric Computer Vision

Line primitives are widely found in structured scenes which provide a higher level of structure information about the scenes than point primitives. Furthermore, line primitives in space are closely related to Euclidean transformations, because the dual vector (also known as Pluecker coordinates) representation of 3D lines is the counterpart of the dual quaternion which depicts an Euclidean transformation. These geometric properties of line primitives motivate the work in this thesis with the following contributions: Firstly, by combining local appearances of lines and geometric constraints between line pairs in images, a line segment matching algorithm is developed which constructs a novel line band descriptor to depict the local appearance of a line and builds a relational graph to measure the pair-wise consistency between line correspondences. Experiments show that the matching algorithm is robust to various image transformations and more efficient than conventional graph based line matching algorithms. Secondly, by investigating the symmetric property of line directions in space, this thesis presents a complete analysis about the solutions of the Perspective-3-Line (P3L) problem which estimates the camera pose from three reference lines in space and their 2D projections. For three spatial lines in general configurations, a P3L polynomial is derived which is employed to develop a solution of the Perspective-n-Line problem. The proposed robust PnL algorithm can efficiently and accurately estimate the camera pose for both small numbers and large numbers of line correspondences. For three spatial lines in special configurations (e.g., in a Manhattan world which consists of three mutually orthogonal dominant directions), the solution of the P3L problem is employed to solve the vanishing point estimation and line classification problem. The proposed vanishing point estimation algorithm achieves high accuracy and efficiency by thoroughly utilizing the Manhattan world characteristic. Another advantage of the proposed framework is that it can be easily generalized to images taken by central catadioptric cameras or uncalibrated cameras. The third major contribution of this thesis is about structure-from-motion using line primitives. To circumvent the Pluecker constraints on the Pluecker coordinates of lines, the Cayley representation of lines is developed which is inspired by the geometric property of the Pluecker coordinates of lines. To build the line observation model, two derivations of line projection functions are presented: one is based on the dual relationship between points and lines; and the other is based on the relationship between Pluecker coordinates and the Pluecker matrix. Then the motion and structure parameters are initialized by an incremental approach and optimized by sparse bundle adjustment. Quantitative validations show the increase in performance when compared to conventional line reconstruction algorithms

MLPnP - A Real-Time Maximum Likelihood Solution to the Perspective-n-Point Problem

In this paper, a statistically optimal solution to the Perspective-n-Point (PnP) problem is presented. Many solutions to the PnP problem are geometrically optimal, but do not consider the uncertainties of the observations. In addition, it would be desirable to have an internal estimation of the accuracy of the estimated rotation and translation parameters of the camera pose. Thus, we propose a novel maximum likelihood solution to the PnP problem, that incorporates image observation uncertainties and remains real-time capable at the same time. Further, the presented method is general, as is works with 3D direction vectors instead of 2D image points and is thus able to cope with arbitrary central camera models. This is achieved by projecting (and thus reducing) the covariance matrices of the observations to the corresponding vector tangent space.Comment: Submitted to the ISPRS congress (2016) in Prague. Oral Presentation. Published in ISPRS Ann. Photogramm. Remote Sens. Spatial Inf. Sci., III-3, 131-13

A Novel Method for the Absolute Pose Problem with Pairwise Constraints

Absolute pose estimation is a fundamental problem in computer vision, and it is a typical parameter estimation problem, meaning that efforts to solve it will always suffer from outlier-contaminated data. Conventionally, for a fixed dimensionality d and the number of measurements N, a robust estimation problem cannot be solved faster than O(N^d). Furthermore, it is almost impossible to remove d from the exponent of the runtime of a globally optimal algorithm. However, absolute pose estimation is a geometric parameter estimation problem, and thus has special constraints. In this paper, we consider pairwise constraints and propose a globally optimal algorithm for solving the absolute pose estimation problem. The proposed algorithm has a linear complexity in the number of correspondences at a given outlier ratio. Concretely, we first decouple the rotation and the translation subproblems by utilizing the pairwise constraints, and then we solve the rotation subproblem using the branch-and-bound algorithm. Lastly, we estimate the translation based on the known rotation by using another branch-and-bound algorithm. The advantages of our method are demonstrated via thorough testing on both synthetic and real-world dataComment: 10 pages, 7figure

Accurate and linear time pose estimation from points and lines

The final publication is available at link.springer.comThe Perspective-n-Point (PnP) problem seeks to estimate the pose of a calibrated camera from n 3Dto-2D point correspondences. There are situations, though, where PnP solutions are prone to fail because feature point correspondences cannot be reliably estimated (e.g. scenes with repetitive patterns or with low texture). In such scenarios, one can still exploit alternative geometric entities, such as lines, yielding the so-called Perspective-n-Line (PnL) algorithms. Unfortunately, existing PnL solutions are not as accurate and efficient as their point-based counterparts. In this paper we propose a novel approach to introduce 3D-to-2D line correspondences into a PnP formulation, allowing to simultaneously process points and lines. For this purpose we introduce an algebraic line error that can be formulated as linear constraints on the line endpoints, even when these are not directly observable. These constraints can then be naturally integrated within the linear formulations of two state-of-the-art point-based algorithms, the OPnP and the EPnP, allowing them to indistinctly handle points, lines, or a combination of them. Exhaustive experiments show that the proposed formulation brings remarkable boost in performance compared to only point or only line based solutions, with a negligible computational overhead compared to the original OPnP and EPnP.Peer ReviewedPostprint (author's final draft

Large Scale SfM with the Distributed Camera Model

We introduce the distributed camera model, a novel model for Structure-from-Motion (SfM). This model describes image observations in terms of light rays with ray origins and directions rather than pixels. As such, the proposed model is capable of describing a single camera or multiple cameras simultaneously as the collection of all light rays observed. We show how the distributed camera model is a generalization of the standard camera model and describe a general formulation and solution to the absolute camera pose problem that works for standard or distributed cameras. The proposed method computes a solution that is up to 8 times more efficient and robust to rotation singularities in comparison with gDLS. Finally, this method is used in an novel large-scale incremental SfM pipeline where distributed cameras are accurately and robustly merged together. This pipeline is a direct generalization of traditional incremental SfM; however, instead of incrementally adding one camera at a time to grow the reconstruction the reconstruction is grown by adding a distributed camera. Our pipeline produces highly accurate reconstructions efficiently by avoiding the need for many bundle adjustment iterations and is capable of computing a 3D model of Rome from over 15,000 images in just 22 minutes.Comment: Published at 2016 3DV Conferenc