1. CEDOFT interpolation
Science & Engineering department
Thomas Martinuzzo
Univalor
Project Manager, Sciences and Engineering
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thomas.martinuzzo@univalor.ca
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2. Introduction
CEDOFT interpolation algorithm
CEDOFT (Continuous Extension of the Discrete O bit Function Transform)
(C ti E t i f th Di t Orbit F ti T f )
is based on Lie groups (1D, 2D, 3D or multidimensional cases)
For standard image interpolation. CEDCT (C for Cosine) is applied on a
g p ( ) pp
rectangular lattice of dimension n=2. The group used is SU(2)xSU(2) (we can
also used O(5), a triangular decomposition).
For standard 3D data interpolation CEDCT is applied on a cubic lattice of
interpolation.
dimension n=3. The group used is SU(2)xSU(2)xSU(2) or O(5)xSU(2).
Some advantages of the CEDCT interpolation
Fast computation : faster than cubic and spline interpolation from known
image processing software (Adobe photoshop, Paint Shop pro, Gi
i i f (Ad b h h P i Sh Gimp, etc.)
)
The possibility of using a filtering in the frequency domain (like-Fourier
transform) adapted to reduce artefacts
) p
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Overlapping blocks enable with different sizes.
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3. Introduction
CPU Time Benchmark
2D case (
(zoom 2 2) – CPU ti
2x2) time on pentium M760 2.0Ghz, in seconds
ti 2 0Gh i d
Image size Block size CEDCT Bicubic Spline Bilinear
512x512 16x16 0.90 1.80 4.44 1.06
1024x1024 16x16 3.76 7.06 16.9 4.1
256x256 32x32 0.28 0.47 0.62 0.24
512x512 32x32 0.89 1.81 1.79 0.95
1024x1024 32x32 3.73 8.00 7.03 3.60
3D case (zoom 2x2x2) – CPU time on pentium M760 2.0Ghz, in seconds
3D size
i Block i
Bl k size CEDCT Bi bi S li
Bicubic Spline Bili
Bilinear
256x256x16 16x16 15.15 73.17 263.26 13.92
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4. Introduction
CEDCT : a frequency-level adaptative algorithm
All non-adaptive interpolation algorithm always face a trade-off between
non adaptive trade off
artefacts : aliasing, blurring and edge halos.
Edge halos
1 : Nearest Neighbor
2 : Bilinear
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3 : Bicubic
2 1
Blurring Aliasing
Ali i
CEDCT can reduce the different artefacts by using an adaptative
filtering.
filtering
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5. Example 1 : frequency image
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6. Example 1 : frequency image
Interpolation
I t l ti
X2 with
edge detection
Bilinear Bicubic CEDCT
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7. Example 1 : frequency Image
Redimension: pixel comparaison
Bicubic CEDCT
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8. Example 2 : fine details Image
Interpolation
x4
With edge detection
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9. Example 2 : fine details Image
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Bicubic
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10. Example 2 : fine details Image
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CEDCT

11. Example 2 : fine details Image
Interpolation
x8
Halos effect reduction Bicubic
CEDCT
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12. Example 3 : noise suppression
FLIR Original Image
g g
C C
CEDCT + Filter
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13. MRI Data Interpolation (example)
1 2
4fframes
extracted from
an original
MRI data
3 4
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14. MRI Data Interpolation (example)
Frame 2
Frame 1
F
Frame 2
Interpolated
I l d
Frame 1<->2
Frame 1
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15. 1 MRI Data Interpolation (example)
CEDCT Trilinear Tricubic
Frame 1 :
CEDCT, t ili
CEDCT trilinear
and tricubic
interpolation comparison.
Remark :
- Texture preservation
p
for CEDCT and tricubic
interpolations
- Fast computation for
p
3D CEDCT interpolation
(see benchmark slide 3)
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16. 1 2
1<->2 MRI Data Interpolation (example)
CEDCT Trilinear Tricubic
Interpolated frame 1<->2 :
CEDCT, t ili
CEDCT trilinear
and tricubic
interpolation comparison.
Remark :
- Low contrast for the basic
trilinear interpolation between 2
original frames.
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17. 2 MRI Data Interpolation (example)
CEDCT Trilinear Tricubic
Frame 2 :
CEDCT, t ili
CEDCT trilinear
and tricubic
interpolation comparison.
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18. 2 3
2<->3 MRI Data Interpolation (example)
CEDCT Trilinear Tricubic
Interpolated frame 2<->3 :
CEDCT, t ili
CEDCT trilinear
and tricubic
interpolation comparison.
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19. 3 MRI Data Interpolation (example)
CEDCT Trilinear Tricubic
Frame 3 :
CEDCT, t ili
CEDCT trilinear
and tricubic
interpolation comparison.
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20. 3 4
3<->4 MRI Data Interpolation (example)
CEDCT Trilinear Tricubic
Interpolated frame 3<->4 :
CEDCT, t ili
CEDCT trilinear
and tricubic
interpolation comparison.
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21. 4 MRI Data Interpolation (example)
CEDCT Trilinear Tricubic
Frame 4 :
CEDCT, t ili
CEDCT trilinear
and tricubic
interpolation comparison.
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22. Contact
Thomas Martinuzzo
thomas.martinuzzo@univalor.ca
(
(514) 340-3243 ext 4243
)
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