This document proposes a system to improve image registration performance using N-fold blur removal. It discusses existing registration systems that have drawbacks like inaccurate PSF symmetry assumptions. The proposed system uses a global, blur-invariant phase correlation approach to register blurred images by first estimating the PSF and performing N-fold (e.g. 3-fold, 6-fold) blur removal. Key steps include converting images to grayscale, estimating the PSF, performing N-fold deblurring, and registering images while accounting for rotational and reflectional symmetries. The system achieves better registration accuracy, lowering mis-registration from 31% to 20% for 3-fold images and from 22.5% to 12% for 6-

1. IMAGE REGISTRATION USING
N-FOLD BLUR REMOVAL

2. CONTENTS
• Introduction
• Objective
• Existing system
• Proposed system
• Block diagram
• Formulae
• Output
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3. INTRODUCTION
• The original method works for unknown blurs,
assuming the blurring point-spread function(PSF)
exhibits an N-fold rotational symmetry.
• This makes registration algorithm well-suited in
applications where blurred image registration must be
used as a preprocess step.
• This leads to an improvement of the image registration
performance.
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4. OBJECTIVE
• To improve the performance of image registration and
reduce the error occurrence, we implement the N-fold
blur removal.
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5. EXISTING SYSTEM
S.no Title Algorithm Drawback Performance
1. Automatic image
registration for
applications in
remote sensing
Edge-based
Selection of
the control
points
Feature
inconsistance
Accuracy is
76.5%
2. Blur invariant
translational image
registration for N-
fold symmetric blurs
Global based
blur invariant
PSF has no
symmetry
Computational
speed is 170
seconds
3. Combined invariants
to similarity
transformation and to
blur using orthogonal
zernike moments
Orthogonal
zernike
moments
Not adaptive
for order
invariance(on
ly even order
invariance)
Accuracy 92%
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6. Cond…
S.no Title Algorithm Drawback Performance
4. Moment forms
invariant to rotation
and blur in arbitrary
number of
dimensions
Moment forms
invariant
Degraded
performance
of boundary
effect
Accuracy 83%
5. Blur Invariant Phase
Correlation in X-Ray
Digital
Subtraction
Angiography
spline
image warping
Not support
for motion
artifacts
Registration
error is 0.9
6. Multichannel blind
deconvolution of
spatially misaligned
images
Maximum a
posteriori
probability
(MAP)
Inaccurate
registration
of channels
Better
performance and
high SNR
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7. Cond…
S.no Title Algorithm Drawback Performance
7. Wavelet-domain blur
invariants for image
analysis
Spatial-
Domain Blur
Invariants(SD
BI)
Failed in
asymmetric
blur
registration
task
Accuracy is 75%
8. Degraded image
analysis: An invariant
approach
Combined
invariants
Focused only
on combined
invariants not
on image
rotation and
affine
transform.
SNR value is
lower than 10 db
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8. PROPOSED SYSTEM
• Registration method designed specifically for registering
blurred images.
• Registration of blurred images requires special methods
because general registration methods usually do not perform
well on blurred images.
• Global based blur invariant approach of phase correlation.
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9. BLOCK DIAGRAM
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Image Blurred image PSF estimation
N-fold blur removal
(3-fold and 6-fold)
Deblurred image

10. Image taken with camera having shutter with four blades and shape of the PSF can
be clearly viewed in the out-of-focus background. PSF has 4-fold
rotational symmetry
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11. Reference image Blurred sensed image
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12. 9-fold 6-fold 4-fold
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13. Registration of two images
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14. formulae
Recalling the original method
g⟹ blurred sensed image
f⟹ reference image
h⟹ point spread function
Δ⟹ shift
x⟹ number of pixels
h⟹ h(r,θ) = h(r, θ+2πj/N)
N⟹ number of folds
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g(x) = (f * h)(x - Δ)

15. Cond…
Projection operators
⟹Used to eliminate the blur
𝐾𝑗
(𝑓)
(𝐮) = F(u) / F(𝑅𝑗u) ; j=1,………,N
F(u) ≝ F{f}(u) is the Fourier transform of f(x)
Rju⟹ Rotation of frequency coordinates by the angle 2πj/N
Rju= 2*pi*j/N
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16. Cond…
Blur Invariant Operators
⟹ To calculate reflection operator
S(x) =
cos 2𝛼 sin 2𝛼
sin 2𝛼 − cos 2𝛼
𝑥
𝑦
S(x)⟹ Reflection operator
𝛼 ⟹ Angle b/w reflection line and horizontal axis
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17. Cond…
⟹ To calculate the Fourier Transform for original image and
dihedral blurred image
f ⟹Original image
Df ⟹Dihedral blurred image
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F{f} / F{Df}

18. Cond…
⟹ To calculate the invariants to dihedral blur
𝐾𝑗 = F{f} / F{𝑅𝑗 𝑓} ; j=1,………,N
F{f} ⟹ Fourier transform of original image
F{𝑅𝑗 𝑓} ⟹ Rotational symmetry(Cyclic groups,Cf)
L𝑗 = F{f} / F{𝑅𝑗S𝑓} ; j=1,………,N
F{𝑅𝑗S𝑓} ⟹ Rotational and Reflectional symmetry (Dihedral
groups, Df)
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19. Cond…
Image registration algorithm
⟹used to design a robust blur-invariant registration method
To calculate the normalized cross-power spectra
Cj = 𝑘𝑗
(𝑓)
𝑘𝑗
g ∗
; j=1,…N (Rotation)
│ 𝑘𝑗
(𝑓)
𝑘𝑗
g
│
Bj = 𝐿𝑗
(𝑓)
𝐿𝑗
g ∗
│ 𝐿𝑗
(𝑓)
𝐿𝑗
g
│ ; j=1,…N (Rot+Ref)
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20. Cond…
Inverse Fourier Transform of Cj
f −1
{Cj }(x) = 𝛿(x +Δ - 𝑅 𝑁−𝑗 Δ)
Inverse Fourier Transform of Bj
f −1
{Bj }(x) = 𝛿(x +Δ - S𝑅 𝑁−𝑗 Δ)
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21. Two images acquired by a hand-held camera with different
focus settings and shift
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22. Two frames from a video sequence taken with different focus settings
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23. Original image
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24. Blurred image
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25. Rgb to gray converted image
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26. Psf for Dihedral blurred image
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27. dihedral blurred image
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28. Psf for blurred image
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29. Registration of 3-fold and 6-fold
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30. Performance
N-Folds
Mis-Registration (%) MSE PSNR
(dB)
Only fold Fold+ dihedral
3-Folds 31% 20% 0.005 33 dB
6-Folds 22.5% 12% 0.0019 38.5 dB
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31. Thank you
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