barcode generator vb.net download Nonlinear Method for Camera Calibration in Software

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Nonlinear Method for Camera Calibration
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Given a set of calibration points, determine the projections of the calibration points in the image plane, calculate the errors in the projected positions, and use these errors to solve for the camera calibration parameters Since it is necessary to know where the calibration points should project to in the image plane, the exterior orientation problem is solved simultaneously The method presented in this section is different from the procedure explained in Section 12102, where the interior and exterior orientation problems were combined into a single affine transformation, in that the actual camera calibration parameters are obtained and can be used regardless of where the camera is later located in scene The principle behind the solution to the camera calibration problem is to measure the locations (x~, y:) of the projections of the calibration points onto the image plane, calculate the deviations (bXi, bYi) of the points from the correct positions, and plug these measurements into the equations that model the camera parameters Each calibration point yields two equations The solution requires at least enough equations to cover the unknowns, but for increased accuracy more equations than unknowns are used and the overdetermined set of equations is solved using nonlinear regression Assume that the approximate position and orientation of the camera in absolute coordinates is known Since we have initial estimates for the rotation angles, we can formulate the exterior orientation problem in terms of
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CHAPTER 12 CALIBRATION
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the Euler angles in the rotation matrix The parameters of the regression problem are the rotation angles w, <jJ, and ""; the position of the camera in absolute coordinates Px, PY' and Pz; the camera constant f; the corrections to the location of the principal point (xp, Yp); and the polynomial coefficients for radial lens distortion ""1, ""2, and ""3 The equations for the exterior orientation problem are
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+ rxyYa + rxzZa + Px rzxXa + rzyYa + rzzZa + pz ryxXa + ryyYa + ryzZa + py rzxXa + rzyYa + rzzZa + pz
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(12181) (12182)
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Replace x' and Y' with the corrected positions from the camera model,
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(:1: -xp) (1 + ""1 r2 + ""2r4 + ""3r6)
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+ ""lr2 + ""2r4+ ""3 r6 ) f
+ rxyYa + rxzZa + Px rzxXa + rzyYa + rzzZa + pz ryxXa + ryyYa + ryzZa + py , rzxXa + rzyYa + rzzZa + pz
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and replace the elements of the rotation matrix with the formulas for the rotation matrix entries in terms of the Euler angles, provided in Equation 1213 Solve for the camera parameters and exterior orientation using nonlinear regression The regression algorithm will require good initial conditions If the target is a plane, the camera axis is normal to the plane, and the image is roughly centered on the target, then the initial conditions are easy to obtain Assume that the absolute coordinate system is set up so that the x and Y axes are parallel to the camera axes The initial conditions are:
<jJ=",,=O
translation in x from the origin translation in Y from the origin distance of the camera from the calibration plane focal length of the lens
1211 BINOCULAR STEREO CALIBRATION
It is easy to build a target of dots using a laser printer The uncorrected positions of the dots in the image can be found by computing the first moments of the connected components The disadvantage to nonlinear regression is that good initial values for the parameters are needed, but the advantage is that there is a body of literature on nonlinear regression with advice on solving nonlinear problems and methods for estimating errors in the parameter estimates
Binocular Stereo Calibration
In this section we will discuss how the techniques presented in this chapter can be combined in a practical system for calibrating stereo cameras and using the stereo measurements This provides a forum for reviewing the relationships between the various calibration problems There are several tasks in developing a practical system for binocular stereo: 1 Calibrate the intrinsic parameters for each camera 2 Solve the relative orientation problem 3 Resample the images so that the epipolar lines correspond to image rows 4 Compute conjugate pairs by feature matching or correlation 5 Solve the stereo intersection problem for each conjugate pair 6 Determine baseline distance 7 Solve the absolute orientation problem to transform point measurements from the coordinate system of the stereo cameras to an absolute coordinate system for the scene There are several ways to calibrate a binocular stereo system, corresponding to various paths through the diagram in Figure 126 To start, each camera must be calibrated to determine the camera constant, location of the
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