Jernej MrovljeDepartment of Systems and Control, Jožef Stefan Institute
DISTORTION IMPACT ON A STEREO DISTANCE
10th International PhD Workshop on Systems and Control
A Young Generation Viewpoint
Hluboka, 25/9/09
INTRODUCTION
RESULTS
PROBLEM
REALIZATION
optical aberrations (distortion)
camera calibration distortion model
stereoscopy STEDIMAT application
experiment results
CONTENT
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STEREOSCOPY Stereoscopy
1. a technique used for recording and presenting 3D images
2. the viewing or appearance of objects in or as if in three dimensions
Charles Wheatstone (1838): first scientist who described “stereopsis”
“...the mind perceives an object of three dimensions my means of the two
dissimilar pictures projected by it on the two ritinæ ” (C.Cheatstone)
First stereoscopic images and stereoscope
nowadays IMAX 3D (Image MAXimum 3D)
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RECORDING STEREOSCOPIC IMAGES1) Stereo camera2) Stereo attachment3) Camera and stereo slider*4) Stereo system (two single lens cameras joined
together)
(2)
(1)(3)
(4)
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1947
2009
VEIWING STEREOSCOPIC IMAGES
parallel viewing (a) cross viewing (b)
anaglyph images (c) polarized images (d)
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(a)
(b)
(c)
(d)
“STEDIMAT” APPLICATION STEreo DIstance MeAsuring Tool written in Matlab >> Matlab Compiler >> standalone application(*.exe)
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THE CALCULATION OF OBJECT’S POSITION - DISTANCE
)(2
tan2 0
0
RL xx
BxD
B – stereo base
x0 – horizontal image resolution
φ0 – horizontal angle of view
xL – object’s position in the left image
xR – objects’ position in the right image
00
B
12
D
LS
1B 2B
Lx
D
Rx
RS
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OPTICAL ABERRATIONS chromatic and spherical aberrations affect image quality only tangential and radial distortions affect image geometry radial distortion causes inward or outward displacement of a given image
point from its ideal location negative radial displacement >> barrel distortion positive radial displacement >> pincushion distortion
If the object in the image is displaced, the calculated distance is incorrect!
inexpensive cameras with wide-angle lenses suffer barrel distortion (Canon PowerShot A640)
tangential distortion is due to imperfect centering of the lens components
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DISTORTION MODEL distortion can be compensated mathematically:
1. applying parametric distortion model
2. estimating distortion coefficients
3. correcting the distortion polynomial approximation model of the radial distortion (Brown):
calibration procedure was done using “Camera Calibration Toolbox for Matlab”
toolbox uses Brown’s distortion model known as “Plumb Bob”
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RADIAL DISTORTION TANGENTIAL DISTORTION
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each camera was calibrated separately a sequence of 20 images of the calibration board was taken in different
orientations
CALIBRATION PROCESS
in each image a set of calibration points were automatically detected
using the coordinates of the distorted and undistorted calibration points, the distortion parameters kc were calculated
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CALIBRATION RESULTSleft camera right camera
centre of the image: displacement < 10px corners of the image: displacement > 100px
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CORRECTING THE DISTORTION #1 distortion model was used to build “distortion-correction function” (DCF)
as a part of Stedimat for each distance DCF has to be applied twice:
1. using image point of the object’s location in the left image (xL)
2. using image point of the object’s location in the right image (xD)
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“EXPERIMENT”/equipment: stereoscopic system with 2 digital cameras Canon PowerShot A640 StereoData Maker was used to synchronize cameras
CORRECTING THE DISTORTION #2“EXPERIMENT”:
7 test objects positioned at the distance D (30, 40, 50 and 60m) >>> four sets of stereoscopic images
image resolution: 3648x2736, focal distance: 35mm, stereo base: 0.56m, reference object : test object no.4
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0
D
x
y
23 4 5
61 7
distance to each test object was calculated twice: undistorted/distorted image
CORRECTING THE DISTORTION #2EXPERIMENT:
7 test objects positioned at the distance D (30, 40, 50 and 60m) >>> four sets of stereoscopic images
image resolution: 3648x2736, focal distance: 35mm, stereo base: 0.56m, reference object : test object no.4
INTRODUCTION PROBLEM REALIZATION RESULTS
0
D
x
y
23 4 5
61 7
distance to each test object was calculated twice: 1–distorted image points, 2-distortion-free image points
RESULTS #1
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RESULTS #2
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RESULTS #3
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RESULTS #4
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DISTORTED IMAGE POINTSTest
objectDref=30m Dref=40m Dref=50m Dref=60m
1 4,3 3,9 7,0 5,62 4,3 3,8 7,0 5,63 2,9 3,8 4,8 5,64 0 (reference point)5 3,1 6,4 8,1 6,46 6,4 8,7 14,2 17,67 11,7 16,2 28,9 31,5
DISTORTION-FREE IMAGE POINTSTest
objectDref=30m Dref=40m Dref=50m Dref=60m
1 1,5 0,5 1,9 0,52 3,3 1,8 4,4 1,63 2,2 2,5 3,0 3,14 0 (reference point)5 0,5 1,9 2,8 0,56 1,1 1,7 1,1 1,27 5,3 8,0 2,3 3,4
RESULTS (absolute distance error [%])
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