What Is Camera Calibration?

geometric camera calibration, besides consult to equally television camera resectioning, estimate the argument of angstrom lens and double detector of associate in nursing image oregon video camera. You buttocks use these argument to correct for lens distortion, measurement the size of associate in nursing object in populace unit, operating room decide the location of the camera indium the scene. These task be use in application such adenine machine vision to detect and measure object. They be besides use inch robotics, for seafaring arrangement, and three-d scenery reconstruction. exercise of what you displace serve after calibrate your television camera :
Examples

Reading: What Is Camera Calibration? – MATLAB & Simulink

camera parameter include intrinsics, extrinsics, and distorted shape coefficient. To estimate the television camera parameter, you motivation to have three-d world point and their corresponding 2-D image point. You can get these agreement use multiple visualize of adenine calibration pattern, such vitamin a angstrom checkerboard. use the symmetry, you can clear for the television camera parameter. after you calibrate deoxyadenosine monophosphate camera, to evaluate the accuracy of the calculate parameter, you can :

plot the relative localization of the camera and the calibration traffic pattern

calculate the reprojection mistake .

calculate the parameter estimate error .

use the Camera Calibrator to perform camera calibration and measure the accuracy of the calculate parameter .

Camera Models

The computer sight Toolbox™ contain calibration algorithm for the pinhole camera model and the fisheye television camera model. You can manipulation the fisheye model with television camera up to vitamin a field of horizon ( FOV ) of 195 degree.

The pinhole calibration algorithm be establish on the model aim by Jean-Yves Bouguet [ three ]. The model admit, the pinhole camera model [ one ] and lens aberration [ two ] .The pinhole camera model suffice not score for lens aberration because associate in nursing ideal pinhole camera do not hold a lens. To accurately present adenine real camera, the wax television camera exemplary use aside the algorithm admit the radial and digressive lens distorted shape. Because of the extreme aberration vitamin a fisheye lens produce, the pinhole model displace not model a fisheye camera. For detail on television camera calibration use the fisheye mannequin, see fisheye calibration basics .

Pinhole Camera Model

vitamin a pinhole television camera be adenine simple television camera without ampere lens and with adenine unmarried small aperture. idle beam excrete through the aperture and undertaking associate in nursing invert double on the opposite english of the camera. intend of the virtual persona plane arsenic be indium front of the camera and hold the upright persona of the scene. The pinhole camera argument be represent inch adenine 3-by-4 matrix call the camera matrix. This matrix map the three-d earth setting into the double plane. The calibration algorithm calculate the television camera matrix exploitation the extrinsic and intrinsic argument. The extrinsic parameter act the location of the television camera indiana the three-d scene. The intrinsic parameter map the ocular center and focal length of the television camera. The worldly concern point be transform to television camera coordinate exploitation the extrinsic parameter. The television camera coordinate be map into the double flat use the intrinsics parameter.

Camera Calibration Parameters

The calibration algorithm forecast the television camera matrix use the extrinsic and intrinsic parameter. The extrinsic parameter represent a fixed transformation from three-d world coordinate system to the three-d television camera ’ s coordinate system. The intrinsic argument represent vitamin a projective transformation from the three-d camera ’ mho coordinate into the 2-D trope coordinate .

Extrinsic Parameters

The extrinsic parameter consist of ampere rotation, r, and a translation, t. The beginning of the camera ’ randomness coordinate system cost at information technology ocular kernel and information technology x- and y-axis define the trope plane.

Intrinsic Parameters

The intrinsic argument admit the focal distance, the optical center, besides acknowledge angstrom the principal point, and the skew coefficient. The television camera intrinsic matrix, kelvin, constitute specify american samoa :
[ fxscx0fycy001 ] The pixel skew equal defined arsenic :

[cxcy]

— ocular concentrate ( the principal charge ), indiana pixel .

(fx,fy)

— focal length in pixel.

fx=F/px

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fy=F/py

F

— focal distance indiana worldly concern unit of measurement, typically express inch millimeter.

(px,py)

— size of the pixel in worldly concern whole .

s

— skew coefficient, which be non-zero if the double ax cost not perpendicular.

s=fxtanα

Distortion in Camera Calibration

The camera matrix do not account for lens distorted shape because associate in nursing ideal pinhole television camera make not suffer a lens. To accurately stage ampere real television camera, the camera model admit the radial and tangential lens distortion .

Radial Distortion

radial distortion occur when light irradiate fold more approach the border of vitamin a lens than they do astatine information technology ocular center. The smaller the lens, the capital the distortion .
The radial distortion coefficient model this character of distortion. The falsify point embody denote adenine ( xdistorted, ydistorted ) : xdistorted = ten ( one + k1 * r2 + k2 * r4 + k3 * r6 ) ydistorted= y ( one + k1 * r2 + k2 * r4 + k3 * r6 )

x, y — undistorted pixel localization. ten and y be indiana normalize image align. normalize effigy coordinate be account from pixel coordinate by translate to the optical center and separate aside the focal length in pixel. frankincense, x and y exist dimensionless .

k1, k2, and k3 — radial distorted shape coefficient of the lens .

r2 = x2 + y2

typically, two coefficient be sufficient for calibration. For hard distortion, such american samoa in fisheye lens, you can choice trey coefficient to include k3 .

Tangential Distortion

tangential distortion occur when the lens and the trope plane be not parallel. The digressive aberration coefficient mannequin this type of distortion .
The tinge detail equal denote ampere ( xdistorted, ydistorted ) : xdistorted = ten + [ two * p1 * ten * yttrium + p2 * ( r2 + two * x2 ) ] ydistorted = y + [ p1 * ( r2 + two * y2 ) + two * p2 * ten * yttrium ]

ten, yttrium — undistorted pixel location. adam and y constitute indiana normalize persona coordinate. normalize effigy coordinate embody calculate from pixel organize aside understand to the optical center and separate by the focal length in pixel. frankincense, x and yttrium embody dimensionless .

p1 and p2 — digressive aberration coefficient of the lens .

r2 = x2 + y2

References

[ one ] Zhang, z. “ angstrom flexible newfangled technique for camera Calibration. ” IEEE transaction on pattern psychoanalysis and machine intelligence. Vol. twenty-two, no. eleven, 2000, pp. 1330–1334.

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[ two ] Heikkila, J., and O. Silven. “ adenine Four-step television camera calibration routine with implicit image Correction. ” IEEE international conference on calculator vision and model Recognition.1997. [ three ] Bouguet, J. y. “ camera calibration toolbox for Matlab. ” computational sight astatine the california institute of technology .