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Lecture 5.3
Camera calibration
Thomas Opsahl
Introduction
2•For finite projective cameras, the correspondence between points in the world and points in the image
can be described by the simple model 0݂ 001•This camera model is typically not good enough for accurate geometrical computations based on images
=1The image
World frame
Introduction
•Since light enters the camera through a lens instead of a pinhole, most cameras suffer from some kind of distortion •This kind of distortion can be modeled and compensated forA radial distortion model can look like this
ݔො=ݔ1+ߢ
ො=ݕ1+ߢ where ߢ and ߢ are the radial distortion parameters X Y Z x yNo radial distortion
X Y Z x yBarrel distortion
X Y Z x yPincushion distortion
3Introduction
•When we calibrate a camera we typically estimate the camera calibration matrix ܭ together with distortion parameters does not in general describe the correspondence between points in the world and points in the image •Instead it describes the correspondence between points in the world and points in a undistorted image - an image where the distortion effects have been removedDoes not satisfy ࢛=ܴܭ
Satisfies ࢛=ܴܭ
Image from a non
-projective cameraEquivalent projective
-camera imageImages: http://www.robots.ox.ac.uk/~vgg/hzbook/
4Undistortion
•So earlier when we estimated homographies between overlapping images, we should really have been
working with undistorted images! •How to undistort? -Matlab [undist_img,newOrigin] = undistortImage(img,cameraParams); undistortedPoints = undistortPoints(points,cameraParams); -OpenCV cv::undistort(img, undist_img, P, distCoeffs);•The effect of undistortion is that we get an image or a set of points that satisfy the perspective camera
model ࢛ much better than the original image or points -So we can continue working with the simple model 5Camera calibration
•Camera calibration is the process of estimating the matrix ܭ we use to describe radial/tangential distortion •We have seen how ܭ can be found directly from the camera matrix ܲ •The estimation of distortion parameters can be baked into this •One of the most common calibration algorithms was proposed by Zhegyou Zhang in the paper ''AFlexible New Technique for Camera Calibration
'' in 2000 -OpenCV: calibrateCamera -Matlab: Camera calibration app •This calibration algorithm makes use of multiple images of a asymmetric chessboard 6Zhang's method in short
•Zhang's method requires that the calibration object is planar •Then the 3D-2D relationship is described by a homography 12301111
XuXXYv KK Y HYéù
12 rrrt rrt 7Zhang's method in short
•This observation puts 2 constraints on the intrinsic parameters due to the fact that ܴ •Where ܪ and ܭ 1 121211
11 2211 22
00 TTTT TTT TT
KK KK KKþîrrh h
rr rr h h h h 8Zhang's method in short
00 22 211 12 13
2001021 22 23222 222 2
31 32 33
220000
00 00222 2 22 2
1 1 1 y uuvuv y T uvuv vuv v yy y uvuv v uv v vs ufs fffff bbbsvs ufvssBKK b b bff ff f ff fbbb svs uf vs uf vs uf vv ff ff f ff f 9Zhang's method in short
•If we denote •Thus we have 11 12 21 2231 13
32 23
33
then ij ij ij ij TT iji j ij ij ij ij ij ij hh hh hh hhBhh hh hh hh hhéù êú+êúêú+êúêúëûvh h vb