Models camera calibration

J. Weng, P. Cohen, M. Hemiou, Camera calibration with distortion models and accuracy evaluation, IEEE Transactions on pattern analysis and machine intelligence 14 (1992) 965-980. 

This discussion on camera calibration is not meant to be comprehensive. However, it does provide the basic background for understanding how and why cameras ate calibrated. Additional terms can be added to the basic 11-parameter DLT model to correct for symmetrical and asymmetrical lens distortions. These errors can be treated, in part, during camera calibration, and may also be accounted for by using lens correction maps provided by the manufacturer. 

By applying the projection matrix P to the environment model M, the lane data is projected into the rear-view camera image. The matrix P is built up of the extrinsic (3D translation (y) and roll yaw (il/cX pitch (9c), angles), and intrinsic (center of distortion uq, vq and focal length ) camera calibration data (see Eq. 4). 

In the following sections our approach to stereoradioscopy will be described in detail. At first, the camera model and the calibration procedure are introduced, in the second part, the calculation of 3D defect positions and the volume estimation procedure are explained. 

The camera model has a high number of parameters with a high correlation between several parameters. Therefore, the calibration problem is a difficult nonlinear optimization problem with the well known problems of instable behaviour and local minima. In out work, an approach to separate the calibration of the distortion parameters and the calibration of the projection parameters is used to solve this problem. 

The most extensive test which has been made of this conduction model for thermal explosion is to be found in the work of Vanp e on the explosion of CH2O + O2 mixtures. He used a calibrated thread of 10 per cent Rh-Pt alloy of 20 m diameter (jacketed by a 50-m quartz sleeve) suspended at the center of a cylindrical vessel to measure directly his reaction temperature during the induction periods preceding explosion. By Uvsing He and Ar as additives and vessels of different diameters he was able to verify the dependence of the critical explosion limits on vessel size and on thermal conductivity of the gas mixture. In addition, he was able to check the maximum predicted temperature at the center of the vessel just prior to explosion and also the value of 8c = 2 [Eq. (XIV.3.12)], the critical explosion parameter for cylindrical vessels. Finally, with a high-speed camera, he was able to show directly that the explosions in this system do start at the center, the hottest region, " and propagate to the walls. 

Figures 6 and 8 show the pure, but calibrated measurements of the electronic camera and the accelerometer on the abutment. This data is superimposed by a noise. The noisebandwidth before the beginning of the braking is representing the variance of the observations. The problem which we have to solve is to determine the movements of the abutment in the direction of the brakepower, which is the direction of the bridge axis, by using the observations of the electronic camera and of the accelerometer. To achieve this we have to treat both data in a joint model with the performance function S t).

Machine under study has been calibrated using the procedures and models developed in this work and found that the camera has minimal geometric distortion for any magnifications in which it has been calibrated. 

Densitometric methods. In situ densitometry is an often-used technique for lipid quantitation and has been extensively reviewed by Prosek and Pukl (1996). Lipids are generally sprayed with reagent and their absorption or fluorescence can be measured under UV or visible light by means of a densitometer. The method needs to be standardized and suitable calibration curves need to be constructed to avoid errors. There are several models of densitometer available and some of them are highly automated and coupled to computer systems. Apart from these the use of CCD (charge-coupled device) cameras and colour printers have further improved the densitometric capabilities for accurate quantitations (Prosek and Pukl, 1996). A recent review by Ebel (1996) compares quantitative analysis in TLC with that in HPTLC, including factors that can effect quantitation, the need for careful calibration and errors in quantitative HPTLC analyses. Ebel is of the opinion that as both HPTLC and HPLC are based on the same absorption and fluorescence phenomena they should obtain similar results with respect to quantitation. 

Local bubble concentration i.e. the gas hold-up is in relation to the ability of bubbles to coalesce. Therefore, local gas hold-ups are required for the development of the models. Local gas hold-ups were determined at positions A-F with the PIV and capillary techniques. The position A was not accessed with the capillary due to impeller. PIV gas hold-ups were determined from the depth, width and height of PIV pictures. The width and the height of PIV pictures were determined by the optical settings of camera. The depth of illuminated plane in the dispersion was obtained from the calibration experiments with a bubble gel. Sensitivity analysis denoted that local gas hold-up determined from the PIV results is relatively insensitive to the depth of the illuminated... 

Calibration and 3D Reconstruction. To reconstruct the true 3D (X,Y,Z) displacements from two 2D (x,y) displacements as observed by the two cameras, a numerical model is necessary that describes how each of the two cameras image the flow field onto their CCD chips. Using the camera imaging models, four equations (which may be linear or nonlinear) with three unknowns are obtained. 

Instead of a theoretical model that requires careful measurements of distances, angles, and so on, an experimental calibration approach is preferred. The experimental calibration estimates the model parameters based on the images of a calibration target as recorded by each camera. A linear imaging model that works well for most cases, the pinhole camera model, is based on geometrical optics. This leads to the following direct linear transform equations, where x,y are image coordinates, and X,Y,Z are object coordinates. This physics-based model cannot describe nonlinear phenomena such as lens distortions. 

Such a camera API should provide information about the vendor, camera model, sensor type, calibration information and availability of feature control. The API also specifies methods for control the mode of operation, image format and certain other camera parameter. A camera API can be implemented at either end of the camera interface. This choice depends on available mounting space, component-cost considerations and cost of ownership. 

The Kalman Filter is applied to the problem of extracting position and motion parameters from a sequence of images of a moving object. The kinematic model of the moving object and the camera model are developed to construct the filter structure. Experiments are performed to calibrate the camera and to test the filter with actual data. 

Today, the flight model of the camera (see Cesarsky Plate 1 in color section), duly tested and calibrated, has been delivered to the European Space Agency. The expected launch date of the ISO satellite is September 1995. 

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