Absolute Orientation Problem Research Articles

Algorithms to solve absolute orientation problem for GL(3), O(3), and SO(3) groups

Algorithms to solve absolute orientation problem for GL(3), O(3), and SO(3) groups

An Efficient Closed Form Solution to the Absolute Orientation Problem for Camera with Unknown Focal Length.

In this paper we propose an efficient closed form solution to the absolute orientation problem for cameras with an unknown focal length, from two 2D–3D point correspondences and the camera position. The problem can be decomposed into two simple sub-problems and can be solved with angle constraints. A polynomial equation of one variable is solved to determine the focal length, and then a geometric approach is used to determine the absolute orientation. The geometric derivations are easy to understand and significantly improve performance. Rewriting the camera model with the known camera position leads to a simpler and more efficient closed form solution, and this gives a single solution, without the multi-solution phenomena of perspective-three-point (P3P) solvers. Experimental results demonstrated that our proposed method has a better performance in terms of numerical stability, noise sensitivity, and computational speed, with synthetic data and real images.

Assessment of surface topography modifications through feature-based registration of areal topography data

Surface topography modifications due to wear or other factors are usually investigated by visual and microscopic inspection, and—when quantitative assessment is required—through the computation of surface texture parameters. However, the current state-of-the-art areal topography measuring instruments produce detailed, areal reconstructions of surface topography which, in principle, may allow accurate comparison of the individual topographic formations before and after the modification event. The main obstacle to such an approach is registration, i.e. being able to accurately relocate the two topography datasets (measured before and after modification) in the same coordinate system. The challenge is related to the measurements being performed in independent coordinate systems, and on a surface which, having undergone modifications, may not feature easily-identifiable landmarks suitable for alignment. In this work, an algorithmic registration solution is proposed, based on the automated identification and alignment of matching topographic features. A shape descriptor (adapted from the scale invariant feature transform) is used to identify landmarks. Pairs of matching landmarks are identified by similarity of shape descriptor values. Registration is implemented by resolving the absolute orientation problem to align matched landmarks. The registration method is validated and discussed through application to simulated and real topographies selected as test cases.

A solution to the hand-eye calibration in the manner of the absolute orientation problem

PurposeThis paper aims to introduce a simple hand-eye calibration method that can be easily applied with different objective functions.Design/methodology/approachThe hand-eye calibration is solved by using the closed form absolute orientation equations. Instead of processing all samples together, the proposed method goes through all minimal solution sets. Final result is chosen after evaluating the solution set for arbitrary objectives. In this stage, outliers can be excluded optionally if more accuracy is desired.FindingsThe proposed method is very flexible and gives more accurate and convenient results than the existing solutions. The mathematical error expression defined by the calibration equations may not be valid in practice, where especially systematic distortions are present. It is shown in the simulations that the solution which results the least mathematical error in systems may have incorrect, incompatible results in the presence of practical demands.Research limitations/implicationsThe performance of the calibration performed with the proposed method is compared with the reference methods in the literature. When the back-projection error is benchmarked, which corresponds to the point repeatability, the proposed approach is considered as the most successful method among all others. Due to its robustness, it is decided to make tooling-sensor calibrations by the recommended method, in the robotic non-destructive testing station in Ford-OTOSAN Kocaeli Plant Body Shop Department.Originality/valueArranging the well-known AX = XB calibration equation in quaternion representation as Q_A = Q_x × Q_B × Q_x reveals another common spatial rotation equation. In this way, absolute orientation solution satisfies the hand-eye calibration equations. The proposed solution is not presented in the literature as a standalone hand-eye calibration method, although some researchers drop a hint to the relative formulations.

Automatic detection of a one dimensional ranging pole for robust external camera calibration in mobile mapping

A mobile mapping system (MMS) is the answer of the geoinformation community to the exponentially growing demand for various geospatial data with increasingly higher accuracies, captured by multiple sensors. As the mobile mapping technology is pushed to explore its use for various applications on water, rail, or road, the need emerges to have an external sensor calibration procedure that is portable, fast and easy to perform. This way, sensors can be mounted and demounted depending on the application requirements without the need for time consuming calibration procedures. A new methodology is presented to provide a high quality external calibration of cameras which is automatic, robust and fool proof. The method uses a portable, standard ranging pole which needs to be positioned on a known ground control point. While the literature focuses on solving the absolute orientation problem of the calibration, an automatic method to detect the calibration object is missing. Here, we present a mutual information based image registration technique for automatic sub-pixel localization of the ranging pole under realistic outdoor conditions. We include several robust error detection rules to allow the calibration to run without human intervention, giving as little outliers as possible, to ensure a correct calibration. Several tests are performed under various lighting and noise conditions which prove the methodology’s robustness.

Achieving a common view point: yaw, pitch, and roll

Objects move and tracking them is an essential ingredient in applications such as navigation and robot motion. Surprisingly, the same mathematical tools used in tracking are also used in the absolute orientation problem of comparing two objects (such as proteins or machine parts) to see if they have the same structure. In this paper, we develop the mathematical and computational tools to solve such problems.