image coordinate refinement & camera calibrationbethel/icr.pdf · image coordinate refinement...
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CE 503 – Photogrammetry I – Fall 2002 – Purdue University
Image Coordinate Refinement & Camera Calibration
Measurement system (row,column) defined with respect to digital image
Image (2D) and sensor (3D) coordinate system defined with respect to focal plane, optical axis and reference direction
x
y
z
Perspective center
Principal point Focal plane
Optical axis
CE 503 – Photogrammetry I – Fall 2002 – Purdue University
Coordinate Transformations to
relate measurement (r,c) and image (x,y)
coordinate systems
1
1
nonlinear parameter,-8
linear affine, parameter,-6
00
101
cossinsincos
nonlinear affine, parameter,-6
linear parameter,-4cossinsincos
nonlinear parameter,-4
00
222
00
111
2
1
2
1
++++
=
++++
=
⎥⎦
⎤⎢⎣
⎡+⎥
⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡
⎥⎦
⎤⎢⎣
⎡+⎥
⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡−
=⎥⎦
⎤⎢⎣
⎡
⎥⎦
⎤⎢⎣
⎡+⎥
⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡−
=⎥⎦
⎤⎢⎣
⎡
⎥⎦
⎤⎢⎣
⎡+⎥
⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡−
=⎥⎦
⎤⎢⎣
⎡
ybxacybxac
ybxacybxar
fe
xx
dcba
cr
tt
yx
SS
cr
dc
yx
abba
cr
tt
yx
cr
y
x
αθθθθ
θθθθ
λ
Write equations at fiducialmarks or reseau marks or any other fixed points which are known or observed in bothsystems. Solve for parameters with those equations – then apply at all other measured points.
CE 503 – Photogrammetry I – Fall 2002 – Purdue University
Fiducialmarks – given in camera calibration report
CE 503 – Photogrammetry I – Fall 2002 – Purdue University
Lens Distortion (radial)
73
52
310 rkrkrkrkr +++=∆
CE 503 – Photogrammetry I – Fall 2002 – Purdue University
Exaggerated effects of radial lens distortion
CE 503 – Photogrammetry I – Fall 2002 – Purdue University
Laboratory calibration instrument to project targets at fixed angles into the camera (multi-collimator, USGS laboratory)
CE 503 – Photogrammetry I – Fall 2002 – Purdue University
CE 503 – Photogrammetry I – Fall 2002 – Purdue University
Image resulting from multi-collimator calibration
CE 503 – Photogrammetry I – Fall 2002 – Purdue University
Atmospheric Refraction
⎟⎠⎞
⎜⎝⎛
+−−
+−=
=∆
Hh
hhh
HHHk
kd
25062410
25062410
tan
22
α
CE 503 – Photogrammetry I – Fall 2002 – Purdue University
CE 503 – Photogrammetry I – Fall 2002 – Purdue University
CE 503 – Photogrammetry I – Fall 2002 – Purdue University
CE 503 – Photogrammetry I – Fall 2002 – Purdue University
CE 503 – Photogrammetry I – Fall 2002 – Purdue University
CE 503 – Photogrammetry I – Fall 2002 – Purdue University