Volumetric Calibration Refinement using masked back projection and image correlation superposition

This paper deals with a new, reconstruction based, approach of refining a volumetric calibration. The technique is based on a 2D cross-correlation between particle images on the sensor plane with a planar back projection from a tomographic reconstruction in the same sensor plane to determine potential disparities between the initial camera calibration and the measurement. Additive superposition of the correlation maps from different sets or particle images allows reducing the influence of noise and ghost particles such that the systematic errors in the calibration can be corrected. The different sections describe the theory, the principle processing steps and the convergence of the procedure. Furthermore, the concept is proven by simulating the entire process of the measurement chain, with the help of a synthetic comparison. The results show that disparities of over 9 pixels could be corrected to an average of below 0.1 pixels during the refinement steps. Finally, the technique demonstrates it´s potential to measured data, where the numbers of outliers in the raw results are reduced after the volumetric calibration refinement

Extrinisic Calibration of a Camera-Arm System Through Rotation Identification

Determining extrinsic calibration parameters is a necessity in any robotic system composed of actuators and cameras. Once a system is outside the lab environment, parameters must be determined without relying on outside artifacts such as calibration targets. We propose a method that relies on structured motion of an observed arm to recover extrinsic calibration parameters. Our method combines known arm kinematics with observations of conics in the image plane to calculate maximum-likelihood estimates for calibration extrinsics. This method is validated in simulation and tested against a real-world model, yielding results consistent with ruler-based estimates. Our method shows promise for estimating the pose of a camera relative to an articulated arm's end effector without requiring tedious measurements or external artifacts. Index Terms: robotics, hand-eye problem, self-calibration, structure from motio

Accurate Feature Extraction and Control Point Correction for Camera Calibration with a Mono-Plane Target

The paper addresses two problems related to 3D camera calibration using a single mono-plane calibration target with circular control marks. The first problem is how to compute accurately the locations of the features (ellipses) in images of the target. Since the structure of the control marks is known beforehand, we propose to use a shape-specific searching technique to find the optimal locations of the features. Our experiments have shown this technique generates more accurate feature locations than the state-of-the-art ellipse extraction methods. The second problem is how to refine the control mark locations with unknown manufacturing errors. We demonstrate in a case study, where the control marks are laser printed on a A4 paper, that the manufacturing errors of the control marks can be compensated to a good extent so that the remaining calibration errors are reduced significantly. 1

3D Particle Tracking Velocimetry Method: Advances and Error Analysis

A full three-dimensional particle tracking system was developed and tested. By using three separate CCDs placed at the vertices of an equilateral triangle, the threedimensional location of particles can be determined. Particle locations measured at two different times can then be used to create a three-component, three-dimensional velocity field. Key developments are: the ability to accurately process overlapping particle images, offset CCDs to significantly improve effective resolution, allowance for dim particle images, and a hybrid particle tracking technique ideal for three-dimensional flows when only two sets of images exist. An in-depth theoretical error analysis was performed which gives the important sources of error and their effect on the overall system. This error analysis was verified through a series of experiments, which utilized a test target with 100 small dots per square inch. For displacements of 2.54mm the mean errors were less than 2% and the 90% confidence limits were less than 5.2 μm in the plane perpendicular to the camera axis, and 66 μm in the direction of the camera axis. The system was used for flow measurements around a delta wing at an angle of attack. These measurements show the successful implementation of the system for three-dimensional flow velocimetry

Extrinsic calibration of camera networks using a sphere

In this paper, we propose a novel extrinsic calibration method for camera networks using a sphere as the calibration object. First of all, we propose an easy and accurate method to estimate the 3D positions of the sphere center w.r.t. the local camera coordinate system. Then, we propose to use orthogonal procrustes analysis to pairwise estimate the initial camera relative extrinsic parameters based on the aforementioned estimation of 3D positions. Finally, an optimization routine is applied to jointly refine the extrinsic parameters for all cameras. Compared to existing sphere-based 3D position estimators which need to trace and analyse the outline of the sphere projection in the image, the proposed method requires only very simple image processing: estimating the area and the center of mass of the sphere projection. Our results demonstrate that we can get a more accurate estimate of the extrinsic parameters compared to other sphere-based methods. While existing state-of-the-art calibration methods use point like features and epipolar geometry, the proposed method uses the sphere-based 3D position estimate. This results in simpler computations and a more flexible and accurate calibration method. Experimental results show that the proposed approach is accurate, robust, flexible and easy to use

A camera model for cameras with hypercentric lenses and some example applications

We propose a camera model for cameras with hypercentric lenses. Because of their geometry, hypercentric lenses allow to image the top and the sides of an object simultaneously. This makes them useful for certain inspections tasks, for which otherwise multiple images would have to be acquired and stitched together. After describing the projection geometry of hypercentric lenses, we derive a camera model for hypercentric lenses that is intuitive for the user. Furthermore, we describe how to determine the parameter values of the model by calibrating the camera with a planar calibration object. We also apply our camera model to two example applications: in the first application, we show how two cameras with hypercentric lenses can be used for dense 3D reconstruction. For an efficient reconstruction, the images are rectified such that corresponding points occur in the same image row. Standard rectification methods would result in perspective distortions in the images that would prevent stereo matching algorithms from robustly establishing correspondences. Therefore, we propose a new rectification method for objects that are approximately cylindrical in shape, which enables a robust and efficient reconstruction. In the second application, we show how to unwrap cylindrical objects to simplify further inspection tasks. For the unwrapping, the pose of the cylinder must be known. We show how to determine the pose of the cylinder based on a single camera image and based on two images of a stereo camera setup