AlignPlus 2D Hand-Eye
Calibration Concepts
5/12/2014
Version 1.0
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VisionPro
5481712, 5495537, 5548326, 5583954, 5602937, 5640200, 5751853, 5768443, 5825913, 5850466, 5872870, 5901241, 5943441, 5978080, 5978521, 5987172,
6005978, 6039254, 6064388, 6075881, 6137893, 6141033, 6167150, 6215915, 6240208, 6324299, 6381366, 6381375, 6411734, 6421458, 6459820, 6490375,
6516092, 6563324, 6658145, 6687402, 6690842, 6697535, 6718074, 6748110, 6771808, 6804416, 6836567, 6850646, 6856698, 6920241, 6959112, 6963338,
6973207, 6975764, 6985625, 6993177, 6993192, 7006712, 7016539, 7043081, 7058225, 7065262, 7088862, 7164796, 7190834, 7242801, 7251366, 7313761,
EP0713593, JP3522280, JP3927239
DataMan
5742037, 5943441, 6215915, 6236769, 6282328, 6381375, 6408109, 6457032, 6690842, 6941026, 7175090, 7181066, 7412106, 7427028, 7549582, 7604174,
7614563, 7617984, US-2005-0087601-A1, US-2006-0131418-A1, US-2006-0131419-A1, US-2006-0133757-A1, US-2007-0090193-A1, US-2007-0091332-A1,
US-2007-0152064-A1, US-2007-0170259-A1, US-2008-0004822-A1, US-2008-0011855-A1, US-2008-0142604-A1, US-2008-0143838-A1, US-2008-0158365-A1,
US-2009-0090781-A1, US-2009-0108073, US-2009-0121027-A1, US-2009-0166424-A1, US-2009-0294541-A1, WO06065619A1, EP1687752
CVL
5495537, 5548326, 5583954, 5602937, 5640200, 5717785, 5751853, 5768443, 5825483, 5825913, 5850466, 5859923, 5872870, 5901241, 5943441, 5949905,
5978080, 5987172, 5995648, 6002793, 6005978, 6064388, 6067379, 6075881, 6137893, 6141033, 6157732, 6167150, 6215915, 6240208, 6240218, 6324299,
6381366, 6381375, 6408109, 6411734, 6421458, 6457032, 6459820, 6490375, 6516092, 6563324, 6658145, 6687402, 6690842, 6718074, 6748110, 6751361,
6771808, 6798925, 6804416, 6836567, 6850646, 6856698, 6920241, 6959112, 6975764, 6985625, 6993177, 6993192, 7006712, 7016539, 7043081, 7058225,
7065262, 7088862, 7164796, 7190834, 7242801, 7251366, EP0713593, JP3522280, JP3927239
VGR
5495537, 5602937, 5640200, 5768443, 5825483, 5850466, 5859923, 5949905, 5978080, 5995648, 6002793, 6005978, 6075881, 6137893, 6141033, 6157732,
6167150, 6215915, 6324299, 6381375, 6408109, 6411734, 6421458, 6457032, 6459820, 6490375, 6516092, 6563324, 6658145, 6690842, 6748110, 6751361,
6771808, 6804416, 6836567, 6850646, 6856698, 6959112, 6975764, 6985625, 6993192, 7006712, 7016539, 7043081, 7058225, 7065262, 7088862, 7164796,
7190834, 7242801, 7251366
OMNIVIEW
AlignPlus 2D Hand-Eye Calibration Concepts
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Legal Notices
6215915, 6381375, 6408109, 6421458, 6457032, 6459820, 6594623, 6804416, 6959112, 7383536
CVL Vision Library
5495537, 5548326, 5583954, 5602937, 5640200, 5717785, 5751853, 5768443, 5825483, 5825913, 5850466, 5859923, 5872870, 5901241, 5943441, 5949905,
5978080, 5987172, 5995648, 6002793, 6005978, 6064388, 6067379, 6075881, 6137893, 6141033, 6157732, 6167150, 6215915, 6240208, 6240218, 6324299,
6381366, 6381375, 6408109, 6411734, 6421458, 6457032, 6459820, 6490375, 6516092, 6563324, 6658145, 6687402, 6690842, 6718074, 6748110, 6751361,
6771808, 6798925, 6804416, 6836567, 6850646, 6856698, 6920241, 6959112, 6975764, 6985625, 6993177, 6993192, 7006712, 7016539, 7043081, 7058225,
7065262, 7088862, 7164796, 7190834, 7242801, 7251366, EP0713593, JP3522280, JP3927239
SMD 4
5995648, 5850466, 6751361, 6690842, 6563324, 6490375, 5949905, 5978080, 6137893, 6167150, 6075881, 6748110, 5859923, 6411734, 6324299, 6516092,
7190834, 6658145, 6836567, 6850646, 6975764, 6985625, 6993192, 7006712, 7043081, 7058225, 7065262, 7088862, 7164796, 7251366, 6856698, 6002793,
6005978, 6771808, 6804416, 7016539, 6959112, 5602937, 7242801, 5640200, 5495537, 5768443, 5825483, 6421458, 6459820, 6215915, 6381375, 6457032,
6157732, 6408109, 6141033, 6026176, 6442291, 6151406, 6396942, 6614926, 5371690, 5845007, 5943441, 6963338, 5805722, 5909504, 5933523, 5964844,
5974169, 5987172, 6078700, 6252986, 6278796, 6307210, 6408429, 6424734, 6526165, 6571006, 6639624, 6681039, 6748104, 6813377, 6853751, 6898333,
6950548, 6993177, 7139421, 5757956
BGA II and BGA III
5495537, 5602937, 5640200, 5768443, 5801966, 5825483, 5850466, 5859923, 5949905, 5978080, 5995648, 6002793, 6005978, 6026176, 6055328, 6075881,
6115042, 6118893, 6130959, 6137893, 6141009, 6141033, 6151406, 6157732, 6167150, 6215915, 6289117, 6324299, 6353676, 6381375, 6396942, 6408109,
6411734, 6421458, 6442291, 6457032, 6459820, 6490375, 6516092, 6563324, 6577775, 6614926, 6658145, 6690842, 6748110, 6751361, 6771808, 6804416,
6836567, 6850646, 6856698, 6959112, 6975764, 6985625, 6993192, 7006712, 7016539, 7043081, 7058225, 7065262, 7088862, 7164796, 7190834, 7242801,
7251366
Wire Bonder
5495537, 5532739, 5581632, 5602937, 5640199, 5640200, 5642158, 5676302, 5754679, 5757956, 5768443, 5825483, 5835622, 5850466, 5859923, 5861909,
5949905, 5978080, 5991436, 5995648, 6002793, 6005978, 6035066, 6061467, 6075881, 6137893, 6141033, 6157732, 6167150, 6215915, 6289492, 6324299,
6381375, 6408109, 6411734, 6421458, 6457032, 6459820, 6490375, 6516092, 6563324, 6658145, 6690842, 6748110, 6751361, 6771808, 6804416, 6836567,
6850646, 6856698, 6959112, 6975764, 6985625, 6993192, 7006712, 7016539, 7043081, 7058225, 7065262, 7088862, 7164796, 7171036, 7190834, 7242801,
7251366
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AlignPlus 2D Hand-Eye Calibration Concepts
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Contents
Introduction ..........................................................................................................................6
How Hand-Eye Calibration is Performed ............................................................................... 11
Train Time ................................................................................................................................... 11
Run Time ..................................................................................................................................... 11
Calibration Process ...................................................................................................................... 12
Train-Time Calibration Process ................................................................................................ 12
Run-Time Process Using Calibration Results ............................................................................ 16
Hand-eye Calibration Coordinate Spaces .............................................................................. 18
Raw2D ......................................................................................................................................... 18
Home2D ...................................................................................................................................... 19
Stage2D ....................................................................................................................................... 21
Plate2D ........................................................................................................................................ 23
Camera2D .................................................................................................................................... 25
Handedness of Coordinate Spaces .............................................................................................. 26
Transforms .......................................................................................................................... 27
General Transforms .................................................................................................................... 27
Home2DFromStage2D.............................................................................................................. 27
UncorrectedHome2DFromStage2D ......................................................................................... 27
Raw2DFromHome2D................................................................................................................ 27
ConvertUncorrectedHome2DFromStage2DToHome2DFromStage2D() and
ConvertHome2DFromStage2DToUncorrectedHome2DFromStage2D() Conversion Functions
.................................................................................................................................................. 27
Raw2DFromCamera2D ............................................................................................................. 27
Stationary Camera Configuration transforms ............................................................................. 27
Home2DFromStationaryCamera2D ......................................................................................... 27
Stage2DFromMovingPlate2D ................................................................................................... 28
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Contents
Moving Camera Configuration transforms ................................................................................. 28
Home2DFromStationaryPlate2D .............................................................................................. 28
Stage2DFromMovingCamera2D ............................................................................................... 28
Transforms Overview .................................................................................................................. 29
Motion Stage Validation....................................................................................................... 31
What AlignPlus Hand-Eye Calibration Does ........................................................................... 32
Motion Capability Limitations ..................................................................................................... 32
Fundamental Requirements and Residuals ................................................................................ 33
Fixed Placement Pose of the Calibration Target and Cameras ................................................ 33
Precision of Motion Stage ........................................................................................................ 33
In-Plane Motion........................................................................................................................ 34
Indications of Violations to Requirements ............................................................................... 34
Residual Errors ......................................................................................................................... 34
Multi-Camera Hand-Eye Calibration...................................................................................... 36
Sample application .............................................................................................................. 37
AlignPlus 2D Hand-Eye Calibration Concepts
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Introduction
Introduction
AlignPlus hand-eye calibration allows you to calibrate images obtained with your cameras to the
platform on which the object to be inspected is and whose position relative to your cameras
moves. The images you obtain using your cameras may exhibit lens distortion and perspective
distortion, your motion system input may be offset from the actual position it moves to and it
may have systematic errors as well. AlignPlus hand-eye calibration allows you to view and
inspect features of objects in an undistorted manner (with physically correct length units) and
with placement in the native coordinate system of the motion system. That is, it shows you the
object to be inspected in its real physical appearance and it tells you where that object is (in the
native coordinate space).
The following are determined regarding your motion system during calibration:
• Origin and axis directions of native coordinate space – the native coordinate space of
the motion system is determined as a mapping from the image coordinate space for
each camera
• Systematic errors along the axes of movement – systematic motion system errors are
corrected
Note: Even a configuration with a perfect motion system (that is, one that performs the
movements as required within precision thresholds) and no image distortions requires hand-eye
calibration because the mappings between each image coordinate space and the native
coordinate space need to be determined. These mappings enable positioning image features in
the native coordinate space. In other words, by establishing these mappings, correspondence is
established between features found in images taken by the cameras to the physical coordinates
of these features in the native coordinate space.
To get basic feedback on your motion stage and identify problems before hand-eye calibration,
you perform motion stage validation before hand-eye calibration.
AlignPlus hand-eye calibration is a 2D calibration, it calibrates images in the plane of the
platform on which the object to be inspected is. This tool provides no 3D information.
There are two types of scenarios: either the platform moves with the object to be inspected and
the cameras are stationary or the cameras move and the platform with the object to be
inspected is stationary.
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The following figure illustrates this with a single camera.
Introduction
The motion system performs planar movement:
•
•
It can move in the X and Y directions,
It can perform Theta rotation based on your inputs.
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The following figures demonstrate the X and Y movements and the Theta rotation of the motion
stage.
Introduction
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