Image Interpolation
- 1. CEDOFT interpolation Science & Engineering department Thomas Martinuzzo Univalor Project Manager, Sciences and Engineering 1 thomas.martinuzzo@univalor.ca © Gestion Univalor, limited partnership
- 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 2 Overlapping blocks enable with different sizes. © Gestion Univalor, limited partnership
- 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 3 © Gestion Univalor, limited partnership
- 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 3 3 : Bicubic 2 1 Blurring Aliasing Ali i CEDCT can reduce the different artefacts by using an adaptative filtering. filtering 4 © Gestion Univalor, limited partnership
- 5. Example 1 : frequency image 5 © Gestion Univalor, limited partnership
- 6. Example 1 : frequency image Interpolation I t l ti X2 with edge detection Bilinear Bicubic CEDCT 6 © Gestion Univalor, limited partnership
- 7. Example 1 : frequency Image Redimension: pixel comparaison Bicubic CEDCT 7 © Gestion Univalor, limited partnership
- 8. Example 2 : fine details Image Interpolation x4 With edge detection 8 © Gestion Univalor, limited partnership
- 9. Example 2 : fine details Image 9 Bicubic © Gestion Univalor, limited partnership
- 10. Example 2 : fine details Image 10 © Gestion Univalor, limited partnership CEDCT
- 11. Example 2 : fine details Image Interpolation x8 Halos effect reduction Bicubic CEDCT 11 © Gestion Univalor, limited partnership
- 12. Example 3 : noise suppression FLIR Original Image g g C C CEDCT + Filter 12 © Gestion Univalor, limited partnership
- 13. MRI Data Interpolation (example) 1 2 4fframes extracted from an original MRI data 3 4 13 © Gestion Univalor, limited partnership
- 14. MRI Data Interpolation (example) Frame 2 Frame 1 F Frame 2 Interpolated I l d Frame 1<->2 Frame 1 14 © Gestion Univalor, limited partnership
- 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) 15 © Gestion Univalor, limited partnership
- 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. 16 © Gestion Univalor, limited partnership
- 17. 2 MRI Data Interpolation (example) CEDCT Trilinear Tricubic Frame 2 : CEDCT, t ili CEDCT trilinear and tricubic interpolation comparison. 17 © Gestion Univalor, limited partnership
- 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. 18 © Gestion Univalor, limited partnership
- 19. 3 MRI Data Interpolation (example) CEDCT Trilinear Tricubic Frame 3 : CEDCT, t ili CEDCT trilinear and tricubic interpolation comparison. 19 © Gestion Univalor, limited partnership
- 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. 20 © Gestion Univalor, limited partnership
- 21. 4 MRI Data Interpolation (example) CEDCT Trilinear Tricubic Frame 4 : CEDCT, t ili CEDCT trilinear and tricubic interpolation comparison. 21 © Gestion Univalor, limited partnership
- 22. Contact Thomas Martinuzzo thomas.martinuzzo@univalor.ca ( (514) 340-3243 ext 4243 ) 22 © Gestion Univalor, limited partnership