![Page 1: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/1.jpg)
Image Registration – Introduction
Jan Kybic
December 5, 2007
![Page 2: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/2.jpg)
Outline
What is image registration
The purpose of image registration
Warping and interpolation
Classification of registration methods
Manual landmark registration
Automatic elastic B-spline registration
Automatic elastic dense PDE based registration
ITK Registration Toolkit
![Page 3: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/3.jpg)
Find corresponding points
American Tux Tux bordelais
![Page 4: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/4.jpg)
Find corresponding points
American Tux Tux bordelais
![Page 5: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/5.jpg)
Find corresponding points
American Tux Tux bordelais
![Page 6: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/6.jpg)
Registration example 2
Michael Unser Philippe Thevenaz
![Page 7: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/7.jpg)
Registration example 3
James Bond Lupe
![Page 8: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/8.jpg)
Registration example 4
EPI MRI anatomical MRI
![Page 9: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/9.jpg)
Correspondence function
source
destination
Reference image Test image
![Page 10: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/10.jpg)
Correspondence function
(x , y)(x ′, y ′)
Reference image Test image
g(
[x y ]T)
= [x ′ y ′]T
![Page 11: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/11.jpg)
Deformation field
0 % deformation
![Page 12: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/12.jpg)
Deformation field
25 % deformation
![Page 13: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/13.jpg)
Deformation field
50 % deformation
![Page 14: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/14.jpg)
Deformation field
75 % deformation
![Page 15: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/15.jpg)
Deformation field
100 % deformation
![Page 16: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/16.jpg)
Image warping
0 % deformation
![Page 17: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/17.jpg)
Image warping
25 % deformation
![Page 18: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/18.jpg)
Image warping
50 % deformation
![Page 19: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/19.jpg)
Image warping
75 % deformation
![Page 20: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/20.jpg)
Image warping
100 % deformation
![Page 21: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/21.jpg)
Image warping = geometric transformation
Rozepıseme vektorovou transformaci T do dvou slozek
x′ = T (x) → x ′ = Tx(x , y) , y ′ = Ty (x , y) .
![Page 22: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/22.jpg)
Transformace souradnic + interpolace
Transformace souradnic bodu pocıta se nova poloha kazdehobodu ve spojitych souradnicıch (realna cısla). x′ = T (x)
Aproximace jasove funkce z necelocıselnych pozic x ′, y ′ hledahodnotu jasu v celocıselnych pozicıch
Problemy:
Nekdy x′ mimo obraz.
Interpolace z neusporadanych (scattered) dat je tezka uloha.
![Page 23: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/23.jpg)
Dualnı transformace
Souradnice bodu (x , y) ve vstupnım obraze lze vypocıtatinvertovanım vztahu (x ′, y ′) = T (x , y), tj.
(x, y) = T−1 (x′, y′) .
Aproximuje se jas ve vstupnım obraze, ktery odpovıda jasuhledaneho bodu x ′, y ′ ve vystupnı mrızce.Interpolace z usporadanych dat (pravouhla sıt) je ‘lehka’ uloha.
![Page 24: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/24.jpg)
Transformace souradnic bodu
Obvykle se x ′ = Tx(x , y), y ′ = Ty (x , y) aproximuje polynomemm-teho stupne.
x ′ =
m∑
r=0
m−r∑
k=0
ark x r yk , y ′ =
m∑
r=0
m−r∑
k=0
brk x r yk .
Vztah je linearnı vzhledem ke koeficientum ark , brk ⇒ odhadmetodou nejmensıch ctvercu.Potrebne dvojice sobe odpovıdajıcıch (vlıcovacıch/klıcovych) bodux , y a x ′, y ′.
![Page 25: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/25.jpg)
Bilinearnı, afinnı transformace souradnic
Kdyz se geometricka transformace v zavislosti na pozici v obrazeprılis nahle nemenı, postacujı aproximacnı polynomy nızkehostupne m = 2 nebo m = 3.Bilinearnı transformace
x ′ = a0 + a1x + a2y + a3xy ,
y ′ = b0 + b1x + b2y + b3xy .
Jeste specialnejsı je afinnı transformace ktera zahrnuje v praxipotrebnou rotaci, translaci a zkosenı.
x ′ = a0 + a1x + a2y ,
y ′ = b0 + b1x + b2y .
![Page 26: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/26.jpg)
Homogennı souradnice
Homogennı souradnice jsou obvykle v teoreticke mechanice,projektivnı geometrii, pocıtacove grafice a robotice.
Zakladnı myslenkou je reprezentovat bod ve vektorovemprostoru o jednu dimenzi vetsım.
Bod [x , y ]T se v homogennıch souradnicıch vyjadrı ve 3Dvektorovem prostoru jako [λx , λy , λ]T , kde λ 6= 0.
Pro jednoduchost se obvykle pouzıva jedno z nekonecnemnoha vyjadrenı [x , y , 1]T .
![Page 27: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/27.jpg)
Afinnı transformace
Affinnı zobrazenı se po zavedenı homogennıch souradnic vyjadrı
x ′
y ′
1
=
a1 a2 a0
b1 b2 b0
0 0 1
x
y
1
.
Po castech afinnı transformace.
![Page 28: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/28.jpg)
(Uniform) splines
![Page 29: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/29.jpg)
(Uniform) splines
Piecewise polynomial of degree n
Continuous (n − 1)th derivative
(Uniform) knots
![Page 30: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/30.jpg)
Non-uniform splines (1D)
Polynomial in each interval
Continuous derivatives
Boundary conditions (natural)
−→ band system of linear equations
Example: cubic splines
![Page 31: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/31.jpg)
Uniform B-splines
Haar β0
−2 −1.5 −1 −0.5 0 0.5 1 1.5 20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
linear β1
quadratic β2
cubic β3
![Page 32: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/32.jpg)
Uniform B-splines
Haar β0
−2 −1.5 −1 −0.5 0 0.5 1 1.5 20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
linear β1
quadratic β2
cubic β3
Generation: βn+1 = βn ∗ β0
Basis for splines: s(x) =∑
i ci β(x − i)
![Page 33: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/33.jpg)
Practical B-splines
Separability speed
B-spline transform (finding coefficients) fast through IIRfiltering
Interpolation fast (small support)
Extension to n-D by Cartesian product. Separability.
Software
Spliny Matlab, Numerical Recipes, . . .
rmnı B-spliny Unser, Thevenaz, bigwww.epfl.ch
![Page 34: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/34.jpg)
Interpolace = Aproximace jasove funkce
Transformovane souradnice x ′, y ′ lezı mimo rastr. Mame jeninformaci o vstupnım obraze f (x , y) v celocıselnych vzorcıch.
Take geometricky transformovany obraz se ma reprezentovatmaticı. Proto i zde mame predepsanou pravouhlou vzorkovacımrızku.
Prıklad: topograficka predstava.
Principialne spravnou odpoved poskytuje teorie aproximace.Ze vzorku odhadneme spojitou funkci.
Obvykle se aproximuje polynomem.
![Page 35: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/35.jpg)
Interpolace jako 2D konvoluce
Vzorkovana verze gs(l ∆ x , k ∆ y) spojite funkce f (x , y).Interpolace −→ spojita fn(x , y) aproximujıcı f .Linearita + nezavislost na posunutı (LTI) −→ konvoluce.
fn(x , y) =
∞∑
l=−∞
∞∑
k=−∞
gs(l ∆ x , k ∆ y) hn(x − l ∆ x , y − k ∆ y) .
hn je interpolacnı jadro, obvykle male pokrytı (support).
![Page 36: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/36.jpg)
Nejblizsı soused
Priradı bodu (x , y) hodnotu jasu nejblizsıho bodu gs v diskretnımrızce.
f1(x , y) = gs(round (x), round (y)) .
h
0 0.5-0.5x
1
P0 - po castech konstantnı.
![Page 37: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/37.jpg)
Linearnı interpolace
4 body v okolı (x , y), linearnı kombinace. Vliv kazdeho ze ctyrbodu klesa se vzdalenostı.
f2(x , y) = (1− a)(1− b) gs(l , k) + a(1− b) gs(l + 1, k)+b(1− a) gs(l , k + 1) + ab gs(l + 1, k + 1) ,
kde l = round (x) , a = x − l ,k = round (y) , b = y − k .
h2
-1 0 1x
P1 - po castech linearnı.
![Page 38: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/38.jpg)
Bikubicka interpolace
Lokalne interpolovan obrazovou funkci bikubickym polynomemz 16 bodu v okolı. 1D interpolacnı jadro (pro prehledne zobrazenı)
h3 =
1− 2|x |2 + |x |3 pro 0 ≤ |x | < 1 ,4− 8|x | + 5|x |2 − |x |3 pro 1 ≤ |x | < 2 ,0 jinde.
-0.1
0.2
0.4
0.6
0.8
2.0-2.0
Interpolace P3.
![Page 39: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/39.jpg)
Interpolace obrazu B-spliny
f (x , y) =∑
i ,j
cijβn(x − i)βn(x − j)
Interpolace spliny je globalnı, zatımco P0,P1,P2,P3. . . jsoulokalnı v obou osach
Pixely na pravidelne mrızce lze predpocıtat B-splinecoeficienty (FIR filtr)
Vyhodnocenı β3 je stejne rychle jako u P3, kvalita lepsı.
Okrajove podmınky (nulove, periodicke, zrcadlo na bodu,mezi body)
Vyssı rady vedou ke vzniku Gibbsovych artefaktu na hranach(ringing).
![Page 40: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/40.jpg)
Interpolace sinc
Bandlimited (frekvencne omezeny) signal f ,supp f ⊆ [−Fs/2,Fs/2], f ∈ L2
Jednoznacne urceny svymi vzorky f (i/Fs):
f (x) =∑
i
f (i/Fs) sinc(Fsx − n)
sinc(τ) =sin(πτ)
πτ
Interpolacnı jadro sinc nenı kompaktnı −→ vypocetne narocne.Nekdy lze pocıtat pomocı FFT (zero-padding).
![Page 41: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/41.jpg)
Image registration
reference image test image
deformation
registration
![Page 42: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/42.jpg)
Image registration
reference image test image
deformation
warping
registration
warped image
![Page 43: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/43.jpg)
(Biomedical) applications
. . . of image registration
Comparing images Different times Different methods Different subjects
Analyzing sequences Motion estimation Segmentation
Qualitative and quantitative information.
![Page 44: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/44.jpg)
Other applications of image registration
video stabilization
video compression
image mosaicking
stereo matching
structure from motion
![Page 45: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/45.jpg)
video ultrazvuk srdce (2C,4C)
![Page 46: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/46.jpg)
Image alignment
reference test
before
![Page 47: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/47.jpg)
Image alignment
reference test
before warped
![Page 48: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/48.jpg)
Classification of registration methods
Feature space — intermediate data extracted from image
Search space — representation of the deformation
Similarity metric — measuring the dissimilarity
Search strategy — how to find the minimum
User interaction level
![Page 49: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/49.jpg)
Registration methods – Feature space
pixels
Fourier wavelet
transforms
intrinsic extrinsic
landmarks curves surfaces templates
features
Feature space
![Page 50: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/50.jpg)
Registration methods – Search space
Local Variational PDE
Semi-local (Quad)tree B-splines Wavelets
Global linear polynomial harmonic
RBF, krigging
Image dependent models (e.g. adaptive quadtrees)
![Page 51: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/51.jpg)
Similarity metrics
Data term for pixel based criteria l2 norm (SSD) l1 norm correlation, normalized correlation mutual information, normalized mutual information
Other data terms image interpolation — important feature-based methods — distance template-based methods — windowed pixel-based criteria transform-based methods — norm in the transform domain preprocessing — filtering, histogram equalization,. . .
Regularization Norm (lp) of the derivatives Implicit regularization (constrained model) Smoothing
![Page 52: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/52.jpg)
Search strategy
Direct solution
Exhaustive search
Dynamic programming
PDE evolution
Multidimensional optimisation gradient descent Newton-like methods, exact/estimated Hessian,
Marquardt-Levenberg, conjugated gradients, BFGS, . . .
Multiresolution
![Page 53: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/53.jpg)
User interaction level
Manual
Automatic
Semi-automatic
![Page 54: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/54.jpg)
Manual registration
Landmark identification
![Page 55: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/55.jpg)
Manual registration
?
Landmark identification
Landmark interpolation
![Page 56: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/56.jpg)
Landmark interpolation (2)
Constraints
Hard constraints
g(xi ) =
[
gx(xi )gy (xi)
]
= zi for all i ∈ 1, . . . , N
Soft constraintsN
∑
i=1
‖g(xi )− zi‖2≤ ε
Properties invariance to scale, shifts, rotations representability of linear transforms
![Page 57: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/57.jpg)
Thin-plate splines
Minimize an energy
J(g) =
∫(
∂2g
∂x2
)2
+ 2
(
∂2g
∂x∂y
)2
+
(
∂2g
∂y2
)2
dxdy
J(g) = J(gx ) + J(gy )
under constraints
g(xi , yi ) = zi
![Page 58: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/58.jpg)
Thin-plate splines
Minimize an energy
J(g) =
∫(
∂2g
∂x2
)2
+ 2
(
∂2g
∂x∂y
)2
+
(
∂2g
∂y2
)2
dxdy
J(g) = J(gx ) + J(gy )
under constraints
g(xi , yi ) = zi
Solution
g(x , y) =N
∑
i=1
λi(‖x− xi‖) + a0x + a1y + a2
with ‖x− xi‖ =√
(x − xi)2 + (y − yi)2 = r
where (r) is a radial basis function and(r) = r2 log r
![Page 59: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/59.jpg)
Automatic rigid registration
Look for rigid (euclidean or affine) transformation
To compensate different position, scale
. . . or to simplify a more complicated problem
![Page 60: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/60.jpg)
Registration as minimization
deformation
optimization
test image
reference image
deformed image
difference
criterion E
deformation function g(x)
![Page 61: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/61.jpg)
ITK (Insight Registration and segmentation toolbox)
![Page 62: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/62.jpg)
Automatic elastic B-spline registration
Look for elastic (non-linear) transformation
Smooth deformation wanted
Semi-local model with many parameters
![Page 63: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/63.jpg)
Spline based warping
Approximationproperties precision
Short support speed
Scalability
Representability oflinear transforms
g(x) = x +∑
i∈Z2
c(i)β(x/h + d− i)
![Page 64: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/64.jpg)
Evaluating the difference
![Page 65: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/65.jpg)
Evaluating the difference
![Page 66: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/66.jpg)
Evaluating the difference
E = (1/N)∑
i
(
f ct (g(i))− fr (i)
)2
![Page 67: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/67.jpg)
Multiresolution
32× 32
![Page 68: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/68.jpg)
Multiresolution
64× 64
![Page 69: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/69.jpg)
Multiresolution
128× 128
![Page 70: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/70.jpg)
Multiresolution
256× 256
![Page 71: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/71.jpg)
video of the registration
![Page 72: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/72.jpg)
Applications
EPI distortion
Before (with Arto Nirkko)
![Page 73: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/73.jpg)
Applications
EPI distortion
After
![Page 74: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/74.jpg)
Applications
EPI distortion
MRI atlas
Atlas
![Page 75: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/75.jpg)
Applications
EPI distortion
MRI atlas
Aligned
![Page 76: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/76.jpg)
Applications
EPI distortion
MRI atlas
CT alignment
Before
![Page 77: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/77.jpg)
Applications
EPI distortion
MRI atlas
CT alignment
After
![Page 78: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/78.jpg)
Applications
EPI distortion
MRI atlas
CT alignment
SPECT atlas
(with University Hospital in Geneva)
![Page 79: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/79.jpg)
Applications
EPI distortion
MRI atlas
CT alignment
SPECT atlas
Ultrasound
velocity (with Marıa J. Ledesma-Carbayo)
![Page 80: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/80.jpg)
Applications
EPI distortion
MRI atlas
CT alignment
SPECT atlas
Ultrasound
MRI heartsequence
![Page 81: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/81.jpg)
Applications
EPI distortion
MRI atlas
CT alignment
SPECT atlas
Ultrasound
MRI heartsequence
MRI perfusion
origin
al
unco
rrec
ted
corr
ecte
d
![Page 82: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/82.jpg)
Automatic dense PDE-based registration
Look for elastic (non-linear) transformation
General motion (vector) field is sought
Criteria formulated in the continuous domain
Regularization to impose smoothness
![Page 83: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/83.jpg)
Some facts about cervical cancer
Cervical cancer is the second most common cancer amongwomen worldwide
Nearly 380,000 new cases are diagonosed yearly
When detected early, cervical neoplasia is nearly 100% curable
Papanicolau test (Pap Smear) and Colposcopy are the mostwidespread tests for cancer screening
Female Anatomy
![Page 84: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/84.jpg)
Diagnosis: Colposcopy
Colposcopy visually inspects inspects the cervix area at lowmagnification
The application of acetic-acid will temporally alter theappearence of cancerous tissue
Colposcopists must subjectively asses appearence changes insmall areas over prolonged periods of time
60 seconds 300 seconds
![Page 85: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/85.jpg)
Deformation as a Vector Field
We represent correspondence function H as a dense vector field
H([x , y ]) = [x ′, y ′]
Original Image Deformation Field Deformed Image
![Page 86: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/86.jpg)
Deformation as a Vector Field
We represent correspondence function H as a dense vector field
H([x , y ]) = [x ′, y ′]
Original Image Deformation Field Deformed Image
![Page 87: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/87.jpg)
Deformation as a Vector Field
We represent correspondence function H as a dense vector field
H([x , y ]) = [x ′, y ′]
Original Image1 Deformation Field Deformed Image
![Page 88: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/88.jpg)
Deformation as a Vector Field
We represent correspondence function H as a dense vector field
H([x , y ]) = [x ′, y ′]
Original Image1 Deformation Field Deformed Image
![Page 89: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/89.jpg)
Deformation as a Vector Field
We represent correspondence function H as a dense vector field
H([x , y ]) = [x ′, y ′]
Original Image1 Deformation Field Deformed Image
![Page 90: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/90.jpg)
Registration as optimization
Correspondence function H and vector field h are related by:
H([i , j]) = [i , j] + h(i , j) (1)
The problem is then formulated as the minimization of acriterion J with respect to vector field h:
h∗ = arg minh
(J(f h,g,h )) (2)
where h∗ is the optimal solution, f and g are the images to beregistered and J is a cost function measuring the dissimilaritybetween the images and the likelyhood of the transformation.
Cost function J is divided into a data and a regularizationterm multiplied by a proportionality constant:
J(f,g,h) = JD(f h,g) + αJR(h) (3)
![Page 91: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/91.jpg)
Similarity criteria
The data term JD is the sum of squared differences (SSD)between the template image g and the moving image f
deformed by h:
JD(fh,g) =
∫
(x ,y)⊂Ω(f(h(x , y)+[x , y ])−g(x , y))2 dx dy (4)
Discretized version:
JD(f h,g) =∑
(i ,j)⊂Ω
(f(h(i , j) + [i , j]) − g(i , j))2 (5)
![Page 92: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/92.jpg)
Regularization
Regularization term penalizes un-smooth deformations andmakes the optimization of J a well-posed problem
Regularization criterion JR is chosen so its gradient coincideswith the linearized 2D elasticity operator describingequilibrium in an elastic material.
∇JR(h) = ξ∆h + (1− ξ)∇(∇ · h) (6)
JR(h) =1
2
∫
(x ,y)⊂Ω
[
ξ (∂xhx)2 + (1− ξ)
(
(∂xhx)2 + ∂xhx · ∂yhy
)]
+[
ξ (∂yhy )2 + (1− ξ)(
(∂yhy )2 + ∂xhx · ∂yhy
)]
![Page 93: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/93.jpg)
Gradient descent optimization
On every iteration:
Calculate the new deformation field
h′ = hi − λ(∇J(f,g,hi )) (8)
If the step is succesful, then the step is accepted and the stepsize is increased
λ← 2λ,hi+1 ← h′, Ji+1 ← J ′ (9)
Otherwise the step size is reduced
λ← λ/10 (10)
We iterate until convergence (given by a suitable threshold).
![Page 94: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/94.jpg)
Other implementation details
Multi-resolution was used
ROI masks were automatically generated
Images were rigidly pre-registred
Green color channel only
![Page 95: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/95.jpg)
Experiments
Algorithm tested with 45 image pairs
Images taken before and 60 seconds after acetic-acidapplication
Cross-polarization filters used to reduce the glint
Uncompressed 1125x750 pixel 16-bit images were used
![Page 96: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/96.jpg)
Results
Template Moving
![Page 97: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/97.jpg)
Results
Unregistered Checkerboard Unregistered Difference
![Page 98: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/98.jpg)
Results
Deformation Field Registered
![Page 99: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/99.jpg)
Results
Unregistered Checkerboard Registered Checkerboard
![Page 100: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/100.jpg)
Results
Unregistered Difference Registered Difference
![Page 101: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/101.jpg)
Insufficient Regularization
Deformation Field Registered
![Page 102: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/102.jpg)
Video cervix registration
![Page 103: Image Registration – Introductioncmp.felk.cvut.cz/cmp/courses/33DZOzima2007/slidy/...features Feature space Registration methods – Search space Local Variational PDE Semi-local](https://reader033.vdocuments.net/reader033/viewer/2022060902/609eaaa1d583ba05c25df3a4/html5/thumbnails/103.jpg)
Registration conclusions
Many different approaches
Many different applications
Very frequent in medical imaging
. . . but also video processing, 3D reconstruction. . .
Trade-off between robustness, speed and generality
A priori knowledge always usefull, sometimes essential