SSII2012 2D&3Dレジストレーション　～画像と3次元点群の合わせ方～　第1部

SSII2012 2012/6/6 13:45 15:45 (120 )

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@ttttamaki @payashim

tamaki@hiroshima-u.ac.jp mhayashi@aoki-medialab.org

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SSII2012 2D&3D © 2012 Toru Tamaki

SSII2012 2012/6/6 13:45 15:45 (120 )

13:45 15:45

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SSII2012 2D&3D ©*2012*Toru*Tamaki

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当然と言えば
当然。

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2D / 3D volume / 3D points
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AAM ICP, Softassign, EM-ICP

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2D

↓

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AutoStitch: SIFT

http://itunes.apple.com/WebObjects/MZStore.woa/wa/
viewSoftware?id=318944927&mt=8

Matthew Brown, Autostitch™ :: a new dimension in automatic image stitching, http://cs.bath.ac.uk/brown/autostitch/autostitch.html
M. Brown and D. Lowe. Automatic Panoramic Image Stitching using Invariant Features. IJCV, 74(1), 59-73, 2007
M. Brown and D. G. Lowe. Recognising Panoramas. ICCV2003.
24

MATLAB Toolbox

© 1994-2012 The MathWorks, Inc.
http://www.mathworks.co.jp/products/computer-vision/description3.html

© 1994-2012 The MathWorks, Inc.
http://www.mathworks.co.jp/products/image/description6.html 25

Mathematica ImageAlign[]

© 2012 Wolfram Research, Inc.
http://reference.wolfram.com/mathematica/ref/ImageAlign.html

26

Windows

Microsoft, – Windows Live on MSN, http://windowslive.jp.msn.com/photo.htm 27

ICIA

Research Project, Super-Resolution( ), http://www.ok.ctrl.titech.ac.jp/res/CSR/CSR-ja.html
, , , ,
D, Vol.J92-D, No.11, pp.2033-2043, November, 2009.
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MRI CT

MRI CT

Derek L G Hill, Philipp G Batchelor, Mark Holden and David J Hawkes,
Medical image registration, TOPICAL REVIEW, Physics in Medicine and Biology, Vol. 46, No. 3, pp.R1–R45 (2001).
http://ee.sharif.edu/~miap/Files/Medical%20Image%20Registration.pdf 30
http://iopscience.iop.org/0031-9155/46/3/201 SSII2012 2D&3D © 2012 Toru Tamaki

Toru Higaki, Toru Tamaki, Kazufumi Kaneda, Nobutada Date, Shogo Azemoto: "Non-rigid Image Registration for
Medical Diagnosis using Free-form Deformation with Multiple Grids", The Journal of the IIEEJ, Vol.37, No.3, pp. 31
286-292, 2008. SSII2012 2D&3D © 2012 Toru Tamaki

3D Slier, http://www.slicer.org/ 32

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3

, , , , , 34
, Vol. 10, No. 3, pp.429-436, 2005.10. SSII2012 2D&3D © 2012 Toru Tamaki

PCL 3

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The PCL Registration API, http://pointclouds.org/documentation/tutorials/registration_api.php SSII2012 2D&3D © 2012 Toru Tamaki

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2D 3D

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2D-2D

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3D-3D

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2D-2D
3D-3D
3D-3D

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, , —SIFT
—, , Vol. 77, No. 12, pp.1109-1116,
2012.

, ,
SSII2012 , 2012 6 .
, —
GPU , PRMU2011-131, 2011
, , ,
2, , , 2010.
, ,
CVIM 165, pp. 221-236, November, 2008
, Gradient - SIFT HOG –,
CVIM 160, pp. 211-224, 2007.

2012 12 J-STAGE 39

2D-2D
3D-3D
3D-3D

2D-2D
3D-3D

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2D-2D
3D-3D
3D-3D

2D-2D
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2D-2D
3D-3D
3D-3D

2D-2D
3D-3D

2D-2D
3D-3D
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では具体的に。

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The Robotics Institute, Mellon University, AAM Fitting Algorithms, http://www.ri.cmu.edu/research_project_detail.html?project_id=448&menu_id=261 45

46

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Richard Szeliski, Computer Vision: Algorithms and Applications, Springer, 2010.

49

Richard Szeliski, Computer Vision: Algorithms and Applications, Springer, 2010.

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3D-2D
3 2

3

min {
}
3D-2D AR, MR

Image guided surgery

Grimson WL, Ettinger GJ, White SJ, Lozano-Perez T, Wells WM, Kikinis R., An automatic registration method for frameless
stereotaxy, image guided surgery, and enhanced reality visualization. IEEE Trans Med Imaging. 1996;15(2):129-40.
http://groups.csail.mit.edu/vision/medical-vision/surgery/surgical_navigation.html
51

3D-2D
R. Kurazume, K. Nishino, Z. Zhang and K. Ikeuchi,, Yasuyo Kita, Nobuyuki Kita, Dale L. Wilson, J. Alison Noble, "A
Simultaneous 2D Images and 3D Geometric Model Quick 3D-2D Registration Method for a Wide-Range of
Registration for Texture Mapping Utilizing Reflectance Applications," ICPR'00, vol. 1, pp.1981, 2000.
Attribute, ACCV2002, pp. 99--06, 2002.
Territory-based Territory-based
Territory-based
Model-based feature 3D-2D matching
Model-based feature
3D-2D matching
Quick 3D-2D Registratio
extraction using initial
extraction using initialextraction using initial based on linearization
projected shape projected shape
projected shape of rotation matrix
Territory-based
renewed
renewed
a) 3D model a) 3D model
a) 3D model
extraction using initial
projected shape
position
position Predicted
Predicted
andand pose
pose view
view

the projection of 3D
a) with b) Observed image d) Highc) Extracted
b) Extracted
c) with
b) Observed image3D modelObserved image with c)ratio of Ourd)Registration of
the projection of correctfeatures
the projection of 3D 3D
Extracted
3D-2D
Our ratio
e)d) High ratio of
High
correct 3D-2D
correct 3D-2D
result
renewed 3D 3D initial state Viewat image state pairs
model at View image
features
model at initial state
model initial point
features
proposed
proposed
point pairs
point pairs
position graphics Predicted
graphics 3D-2D
3D-2D
and pose renewed system system view registarat
registaration
position more general shapes,dealiswith morePredictedistaken c) Extracted method ratio
to deal with to deal with Observed shapes, itwith into consider-
to it takenmoregeneral image itis taken into consider-
general shapes,
b) into consider-
method High 3D-2D
d)
3D 3D model the occluding contour asto use theprojection of as the feature for 3D-2D
model to use
and ation ation to the occluding contour 3D feature for 3D-2D
pose To quickly calculateation contourthequicklycalculate theascontourfeatures
the featureview contour the
use occluding Our
for 3D-2D correct
model at initial thecontour generator that
matching. To generatorcalculate
matching. Toquickly that state generator that point pairs
3D matching. the
View image is the 3D line on the object’s surface corresponding to the
proposed
is the 3D line on the object’s surface 3Dline on the object’s surface corresponding to the
is the corresponding to the
graphics occluding contour in the observed image, we take the3D3D-2D Our aa 3D
occluding contour in the observed image, we take 3D
occluding contour in a observed image, we take
system 3D graphics system like OpenGLdeal withsystemimage registaration points
View graphicsDepth OpenGL intoitour3D proposed Observed
image like image ismodel consider-
Depth like OpenGL into 3D-2D registration
method and
3D methodimageeffectivelyby shapes, ourtakensuppliedby it. image
graphics systemregistration 3D 3D-2D registration
to into our 3D-2D general
more
graphicseffectively useationdepth and effectively useit.method feature for 3D-2D
the method and supplied usethe depth image 3D-2D it.
model
into points
the depth imagesupplied by
3D model we the following sections, first on on contour generators
contour generators Obs
Into use the occluding contour as the explain our basic
system briefly explain our basic we briefly
In the following sections, first In the following sections, first we briefly explain our basic
registaration
matching. and quickly calculate the contourimprovements
strategy, To then describe the details of these generator that Magnificationpairs
strategy, and then describe the details of thesethendescribe the details of these improvements
strategy, and improvements Closest pairs Closest pairs
Closest of
3D model with lots of
with lots of experiments showing their effects. on the object’s surface effects.
with lots of experiments showing their effects. method
is the 3D line experiments showing their corresponding to the a part of Fig.1dima
occluding contour in the observed image, we take a 3D
3 Depth image graphics system like points
3D model
2. Basic strategy pose 2. Basic strategyOpenGL into our 3D-2D registration around axis axis
4. Position pose methodBasiceffectivelyof 3D vessel rotationbyaround
2. strategy
4. Position andand estimation of 3D generators rotation the the (0.7
estimation use the depth image supplied it.
3D on and contour vessel 2D images
The basic strategy is shown image strategy can in Fig. 1. The details basic
Depth the The basic strategy shown in points angle
model using multiple X-ray1.imagesismodelFig. 1. explain ourcan is clearly far from t
model using multipleFig.basic The 3D is shownwe briefly The detailsiscan
X-ray details
The images
In in following sections, first angle clearly far from the ac
be found in [1]. Fig. 1b is a be X-ray image describe1b is aa X-ray image improvements
be found in [1].of Fig. right is X-ray these of theto 20 degree. On the othe
found then
in [1]. Fig. the details of image of the right
the 1b right
strategy, and on contourside ofto 20 degree.not been extracted inpai
generatorsnot been extracted hanClosest t
On the other inth
internal carotid circulation (the right side of the cerebral(the right been extracted in the observed image. Finally, ta
not
internal carotid circulation (the right side of the cerebral
internal carotid circulation the cerebral
To vessels) in effect of withnewofin contrast medium calibrationof the high-ratio of viable 3D-2D the high-ra
examine the effectaftervessels) experimentscalibration effects. medium simultaneously pair
of lots formulae,takenafter injecting contrast views advantage of point giv
showing advantage
their
To examine the Fig. 1a takenthe vessels)new formulae,afterinjecting contrast medium views simultaneousl
the inFig. 1a taken
injecting Fig. 1a two two advantage of the high-r
tained by the previous
tained
tained by the previous processes, the by the previous p
of a 3Davessel3D
3D vessel with a
model right part. vessel acquisition using givenThe acquisition angle is given -0.44, 3D transformatio
4. Position and poseofestimationmodel with afrom the graduations of the X-ray system butisincludessome the separatingquicklycalc
into only the of 3D X-ray systemangle isusing X-ray the angle is the both images. Althou
into only system part. around
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the rotation given
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themodel is quickly ca
model is the transla
from the graduations of the2. Basic strategy of the X-raythe model includes calculated by
X-ray systemgraduations some
from the but includes system but quickly some
images werewere images projection positionmodeltheofclearlyofthe3Dand linearizingground truth data the
images conducted. the positionAs3Dresult,thepose of3D thefrom thepoints the truth out and for Altho
conducted. The of theandanglepointsthe effect out modelground value,data linearizin
model using multiple X-ray estimation of 3D vessel The errors. As aaresult, isprojectionthe 3D the the
errors. and
pose projection offar 3D model points rotation out and linearizi
actual effect matrix[2].is kn
effect which fo
4. Position model poseAsthethethe system known to 20isatshownthethe correctaroundhand, axis correct position and(-
and errors. a to skeleton ofThe 3D model fromgraduations modelother rotation aroundaxis (0.81
relative
sampled
result,
model relative tofrom system known fromthe skeleton of rotation The details poseinthe (0.78,istheinaccur
sampled from vessel degree. On the position at the of the the the axis
the basicfrom the skeleton graduations rotationthe
its 3D
the in 3D 1. vessel at the model -0.44,
sampled strategy its of the Fig. model vessel and around correct position and
can Fig. 4c, not obtain resu
inaccurate once, pairs andof inaccu
once, because lineariza
model using newisformulae, calibrationisindeviatedinfromandis about vessel 3D ofshown by matchingbecause ofmodelqu
state
include about deviated from theimages [1]. as from the observed because shown by
state
state
in shown
once,
To examine the effect of the multiple X-ray1b.observedindeviated Fig.viewsobservedtheis clearlythequickly converges to3Dproject
include aboutblack 20 degrees be foundis vessel twoFig.1b1b. and thevessel as model rightreasonablethevalue,
20 degrees black points rotation simultaneously faris
errorerrorpoints in Fig. the a X-ray projected shape is errors,actualmodel q
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about as gives the the correct
errors, the not been
the points in Fig. internalblackprojected shape1b. First,
First, carotid circulation is First, side of the cerebral
the
the the projected
of a 3D vessel model with ( X-ray system200)(mm)vessels) in Fig.to1a sinceafteronpositionto5. Visualotheradvantage for a
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a 100, 200)(mm) two intwo-dimensionally translated oninjecting tothe point unfortunately, weofFig.m
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tothe
20 hand, do h
by iterating the
two-dimensionally translatedX-rayimage the both images. Although, matching and model transforma
ontranslation, translated the iterating the position
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two-dimensionally position
the the
processes. In this medium
To examineposeposition theoptimal overlap onwhichgives the X-ray system.darkregions (possible experiments,Inthis16.9
the pose ofhead head isformulae, givesoptimalgroundonthe dark regions (possible theprocesses. In reason
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Baowei Lin, Yuji Ueno, Kouhei Sakai, Toru Tamaki, Bisser Raytchev, Kazufumi Kaneda, Koji Ichii, hood of the projected shape inhood of the the skeleton ofinrotation around the the camera coordinateo
model relative becausesystemsince the positionfromthe way(white in aa3.model-basedvessel at axis3. Generalization o
to of Imagethe known the hood of the projected shape thesystem, determined 3. Generalization
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( 100, 100, 200)(mm) in translation, this stage,offromlines).deviatedofX-rayre-observed extraction for active(0.81, because of in
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its determinedonce, -0.01, 0.5
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error in the quired. and of Visual features projected shape as is not re-
Based Detection of 3D Scene Change, submitted (2012). At not
degrees enough system. ignore isallowed, First,to the be allowed, the the calculate modelo
Yuji Ueno, Baowei Lin, Kouhei Sakai, Toru Tamaki, Bisser Raytchev, of the head is not calibrated to quired. about 1b.
and pose Kazufumi Kaneda: "Camera PositionLack of correspondingignoreLack in comparingfeatures can allowed,
the the errors to black Lack of corresponding To calculate by
comparing
features can be the can 52
errors, Based
To camera. 3D
To calculate the 3D
Estimation for Detecting 3D Scene Change", FCV2012, pp. 344-350, 2012.100, 100, geometry the relation between3D the characteristics2D&3D 3DX-rayterritory-based environment surroun
( errors in the relation betweenofsincetothe position andX-ray model feedbackpairs, wecorresponding
200)(mm) in translation,two-dimensionally translated the following to of proposed3D-2Diterating the fe
the position for correspondingp
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in to the characteristics X-ray the characteristics of on 3D-2D correspondingToru method active ca
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the following territory-based
SSII2012 model 5.following proposed the visual

1D-1D
DP

f(t)

t

g(t)

DP 2D
t

1D-1D

(Dynamic Time Warp, DTW)
1 (Elastic matching) (DP)
1 (Relaxation matching) (HMM)
(Dynamic (time) alignment)

Seiichi Uchida and Hiroaki Sakoe, A survey of elastic matching techniques for handwritten character recognition, IEICE Transactions on
Information & Systems, vol.E88-D, no.8, pp.1781-1790, Aug. 2005. 53

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2D-2D
3D-3D
3D-3D

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3D-3D

2D-2D
3D-3D
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Have a break…

• 
• 
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• 
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2D-2D
3D-3D
3D-3D

2D-2D
3D-3D

2D-2D
3D-3D
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てん，てん．

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2D-2D

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i SSII2012 2D&3D © 2012 Toru Tamaki

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75

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76

2D-2D

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77

点はおしまい。
次は画像です。
78

2D-2D

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2D-2D

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(sum of squared differences)
all x1i

81

I1 I2
x11 x11 + t

I1 (x11 ) I2 (x11 + t)

|I1 (x11 ) I2 (x11 + t)|2 ' 0
x11

|I1 (x11 ) I2 (x11 + t)|2 ' 0
83

I1 I2
x11 x11 + t

I1 (x11 ) I2 (x11 + t)

|I1 (x11 ) I2 (x11 + t)|2 ' 0
x11

|I1 (x11 ) I2 (x11 + t)|2 ' 0
84

I1 I2
x11 x11 + t

I1 (x11 ) I2 (x11 + t)

|I1 (x11 ) I2 (x11 + t)|2 ' 0
x11

|I1 (x11 ) I2 (x11 + t)|2 ' 0
85

0
I1 I2 I2
x11 x11 t x11 + t

I1 (x11 ) I2 (x11 + t)
I2 30
I’2 I1 t=30
OK 30

x11

|I1 (x11 ) I2 (x11 + t)|2 ' 0
87

1
W 0
I1 I2 I2
xi xi 1 W (xi )
W

I1 (xi ) I2 (W (xi ))

SSD 2
X
x11 , 1 0 1i )
min dist(I1|II2 (p))
(x I2 (W (x1i , p))|2
p
t
all x1i

|I1 (x1i ) I2 (W (x1i , p))|2 ' 0
88

1
W
T I
xi xi 1 W (xi )
W

T (xi ) I(W (xi ))

SSD 2
X
0
x11 min dist(I1 , I2 (p)) I(W (xi , p))|2
min |T (xi )
p
t
all xi

X
min |T (xi ) I(W (xi , p))|2
t
all xi
89

Lucas-Kanade
1
W
T I
xi xi 1 W (xi )
W

T (xi ) I(W (xi ))

SSD 2
X
0
x11 min |I(W (x
min dist(I1 , I2 (p)) i , p)) T (xi )|2
p
t
all xi

|I(W (xi , p)) T (xi )| Bruce D. Lucas and Takeo Kanade, An Iterative Image Registration Technique
with an Application to Stereo Vision, Proceedings of the 1981 DARPA Image
Understanding Workshop, 1981, pp.121-130. IJCAI '81, pp.674-679, 1981.
90

はあ。。。
で、うまく
いくの？

91

T T I

tx=0

tx=10

tx=20

tx=30

92

T T I

tx=0

tx=10
E

2

tx=20

tx=30

93

E

p0

94

E

p0

95

E

p0

96

E

p0

97

pn = pn 1 + ↵ pn 1
E

■ 

! 
! 

p0 p1 p2 · · · pn ! 
!  Newton

99

pn = pn 1 + ↵ pn 1
E

■ 

! 
! 

p0 p1 p2 · · · pn ! 
!  Newton

100

SSII2012 2D&3Dレジストレーション　～画像と3次元点群の合わせ方～　第1部

SSII2012 2D&3Dレジストレーション　～画像と3次元点群の合わせ方～　第1部

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