1. 3-D Direction Aligned Wavelet Transform for Scalable Video Coding Yu Liu 1, King Ngi Ngan 1, and Feng Wu 2 1 Department of Electronic Engineering The Chinese University of Hong Kong 2 Internet Media Group, Microsoft Research Asia, Beijing, China ISCAS2008, Seattle, USA, May 18-21, 2008 Y. Liu, K.N. Ngan and F. Wu13-D Direction Aligned Wavelet Transform for SVC

2. Introduction 3-D Directional Threading 3-D Extension of Weighted Adaptive Lifting Experimental Results Conclusion Y. Liu, K.N. Ngan and F. Wu23-D Direction Aligned Wavelet Transform for SVC Outline Introduction 3-D Directional Threading 3-D Extension of Weighted Adaptive Lifting Experimental Results and Conclusion

3. 3-D Wavelet-based Scalable Video Coding – full spatio-temporal-quality scalability – non-redundant 3-D subband decomposition – comparable with H.264-based JSVM scheme In temporal domain – Motion Aligned Temporal Filtering (MATF) motion compensation is incorporated into temporal wavelet transform In spatial domain – Conventional 2-D lifting-based wavelet transform uses the elements in neighbor horizontal or vertical direction – However, richly directional attributes in natural image/video such as linear edges, in neither horizontal nor vertical direction Y. Liu, K.N. Ngan and F. Wu33-D Direction Aligned Wavelet Transform for SVC Introduction 3-D Wavelet–based Scalable Video Coding Directionally Spatial Wavelet Transform for Image Coding Introduction 3-D Directional Threading 3-D Extension of Weighted Adaptive Lifting Experimental Results and Conclusion

4. 2-D DWT with directionally spatial prediction for image coding – Adaptive Directional Lifting (ADL)-based DWT [Ding2007] – Direction-Adaptive (DA) DWT [Chang2007] – Weighted Adaptive Lifting (WAL)-based DWT [Liu2007a] There is no literature incorporating directionally spatial wavelet transform into the framework of video coding, not to mention scalable video coding Y. Liu, K.N. Ngan and F. Wu43-D Direction Aligned Wavelet Transform for SVC Introduction 3-D Wavelet–based Scalable Video Coding Directionally Spatial Wavelet Transform for Image Coding Introduction 3-D Directional Threading 3-D Extension of Weighted Adaptive Lifting Experimental Results and Conclusion

5. Temporal Motion Threading (MTh) [Liu2007b] – an efficient implementation of Motion Aligned Temporal Filtering (MATF) – Direction Aligned Spatial Filtering (DASF) vs. MATF by aligning the direction of the spatial wavelet filtering to the direction of the edges 2-D Spatial Directional Threading vs. Temporal Motion Threading – two separable 1-D threading: » horizontal directional threading » vertical directional threading Y. Liu, K.N. Ngan and F. Wu53-D Direction Aligned Wavelet Transform for SVC 3-D Directional Threading Temporal Motion Threading 3-D Direction Coordinate System Generalized Separable 3-D Directional Threading Introduction 3-D Directional Threading 3-D Extension of Weighted Adaptive Lifting Experimental Results and Conclusion

6. 3-D Direction Coordinate System – 3-D direction coordinate system in a unified framework where x, y, and z denote the horizontal, vertical, and temporal direction, respectively – 3-D direction vector, dv={dx,dy,dz} dz =-1, dz = 1, and dz = 0 indicate that the current block is forward, backward and not temporal direction compensated, respectively. {dx, dy} denote displacements in horizontal and vertical direction Y. Liu, K.N. Ngan and F. Wu63-D Direction Aligned Wavelet Transform for SVC 3-D Directional Threading Temporal Motion Threading 3-D Direction Coordinate System Generalized Separable 3-D Directional Threading Introduction 3-D Directional Threading 3-D Extension of Weighted Adaptive Lifting Experimental Results and Conclusion

7. Generalized separable 3-D directional threading – to unify the concepts of temporal motion threading and 2-D spatial directional threading – in each direction axis, pixels along the same directional trajectory are linked to form a directional thread according to direction vectors of blocks they belong to. Y. Liu, K.N. Ngan and F. Wu73-D Direction Aligned Wavelet Transform for SVC 3-D Directional Threading Temporal Motion Threading 3-D Direction Coordinate System Generalized Separable 3-D Directional Threading Introduction 3-D Directional Threading 3-D Extension of Weighted Adaptive Lifting Experimental Results and Conclusion

8. 3-D Extension of Weighted Adaptive Lifting Original Weighted Adaptive Lifting (WAL) [Liu2007a] – Weighted Function Integer Pixel precision: Sub-Pixel precision: where is the coefficient factor of a certain interpolation filter. Weighted Lifting 8Y. Liu, K.N. Ngan and F. Wu3-D Direction Aligned Wavelet Transform for SVC Original Weighted Adaptive Lifting Improved Weighted Lifting for 3-D Transforms Directional Adaptive Interpolation for 3-D Transforms 3-D WAL-based Direction Aligned Wavelet Transform Introduction 3-D Directional Threading 3-D Extension of Weighted Adaptive Lifting Experimental Results and Conclusion

9. 3-D Extension of Weighted Adaptive Lifting Original Weighted Adaptive Lifting (WAL) – Directional Interpolation – Adaptive Interpolation Filter To find the optimal filter, minimize the energy of the high subband by using the Wiener-Hopf equation 9Y. Liu, K.N. Ngan and F. Wu3-D Direction Aligned Wavelet Transform for SVC Original Weighted Adaptive Lifting Improved Weighted Lifting for 3-D Transforms Directional Adaptive Interpolation for 3-D Transforms 3-D WAL-based Direction Aligned Wavelet Transform Introduction 3-D Directional Threading 3-D Extension of Weighted Adaptive Lifting Experimental Results and Conclusion

10. Improved Weighted Lifting for 3-D Transforms – Weighted Lifting works well for single lifting stage, such as (6,6), 5/3-tap filters – not only in spatial transform [Chang2007,Liu2007a] – but also in temporal transform [Xiong2004] over/under-weighted update problems for multiple lifting stages, such as 9/7-tap – reason: update equation doesn’t fulfill the constraint condition in Eq.(1) – Solutions to over/under-weighted update problems Case 1: Case 2: Case 3: Y. Liu, K.N. Ngan and F. Wu103-D Direction Aligned Wavelet Transform for SVC 3-D Extension of Weighted Adaptive Lifting Original Weighted Adaptive Lifting Improved Weighted Lifting for 3-D Transforms Directional Adaptive Interpolation for 3-D Transforms 3-D WAL-based Direction Aligned Wavelet Transform Introduction 3-D Directional Threading 3-D Extension of Weighted Adaptive Lifting Experimental Results and Conclusion

11. Directional Adaptive Interpolation for 3-D Transforms – Directional interpolation extended to temporal domain – To simplify the explanations, the example is restricted to one spatial coordinate x. – 1-D image lines instead of 2-D images – 3-D filter is restricted to a 2-D filter to interpolate the sub-pixel s i,2,(i=0,1) in Frame 2m+1+(-1) i+1, the integer pixels include – not only {h i,-2,h i,-1,h i,0,h i,1 } in Frame 2m+1+(-1) i+1 – but also {h i,-3,h i,2 } in Frame 2m+1+3(-1) i+1 – Adaptive Interpolation Filter In order to find adaptive filter coefficients for temporal domain, the minimization problem can also be solved by Wiener-Hopf Eq. (5) Y. Liu, K.N. Ngan and F. Wu113-D Direction Aligned Wavelet Transform for SVC 3-D Extension of Weighted Adaptive Lifting Original Weighted Adaptive Lifting Improved Weighted Lifting for 3-D Transforms Directional Adaptive Interpolation for 3-D Transforms 3-D WAL-based Direction Aligned Wavelet Transform Introduction 3-D Directional Threading 3-D Extension of Weighted Adaptive Lifting Experimental Results and Conclusion

12. 3-D WAL-based Direction Aligned Wavelet Transform – Apply the 3-D directional threading technique to align a series of video frames to form a totally direction-aligned 3-D video cube – Within each GOP, apply temporal WAL with 5/3-tap filter to each temporal directional thread Perform the above operation to the low-pass temporal bands until the desired level of temporal wavelet decomposition is reached – Within each frame, apply the spatial WAL with 5/3-tap or 9/7-tap filters to the 2-D spatial directional thread Apply the WAL to each horizontal directional thread Apply the WAL to each vertical directional thread Perform the above operation to the low-low-pass spatial bands until the desired level of spatial wavelet decomposition is reached Y. Liu, K.N. Ngan and F. Wu123-D Direction Aligned Wavelet Transform for SVC 3-D Extension of Weighted Adaptive Lifting Original Weighted Adaptive Lifting Improved Weighted Lifting for 3-D Transforms Directional Adaptive Interpolation for 3-D Transforms 3-D WAL-based Direction Aligned Wavelet Transform Introduction 3-D Directional Threading 3-D Extension of Weighted Adaptive Lifting Experimental Results and Conclusion

13. MSRA 3-D wavelet video coder VIDWAV 2.0 is used as the reference software – The 3-D DWT and MATF modules are replaced with the proposed 3-D WAL-based DAWT – Other modules, such as bit-plane coding, entropy coding, etc., keep unchanged. Two MPEG standard test sequences: (a) Carphone and (b) Foreman Y. Liu, K.N. Ngan and F. Wu133-D Direction Aligned Wavelet Transform for SVC Experimental Results Conclusion Introduction 3-D Directional Threading 3-D Extension of Weighted Adaptive Lifting Experimental Results and Conclusion

14. The performance comparison of 3-D WAL-based and 3-D DWT-based SVC for the Y component of decoded Carphone and Foreman at CIF 30 Hz with 5/3 and 9/7-tap spatial filter Y. Liu, K.N. Ngan and F. Wu143-D Direction Aligned Wavelet Transform for SVC Experimental Results Conclusion Introduction 3-D Directional Threading 3-D Extension of Weighted Adaptive Lifting Experimental Results and Conclusion

15. The performance comparison of 3-D WAL-based and 3-D DWT-based SVC for the Y component of decoded Carphone and Foreman at CIF 15 Hz with 5/3 and 9/7-tap spatial filter Y. Liu, K.N. Ngan and F. Wu153-D Direction Aligned Wavelet Transform for SVC Experimental Results Conclusion Introduction 3-D Directional Threading 3-D Extension of Weighted Adaptive Lifting Experimental Results and Conclusion

16. The performance comparison of 3-D WAL-based and 3-D DWT-based SVC for the Y component of decoded Carphone and Foreman at QCIF 15 Hz with 5/3 and 9/7-tap spatial filter Y. Liu, K.N. Ngan and F. Wu163-D Direction Aligned Wavelet Transform for SVC Experimental Results Conclusion Introduction 3-D Directional Threading 3-D Extension of Weighted Adaptive Lifting Experimental Results and Conclusion

17. The performance comparison of 3-D WAL-based and 3-D DWT-based SVC for the Y component of decoded Carphone and Foreman at QCIF 7.5 Hz with 5/3 and 9/7-tap spatial filter Y. Liu, K.N. Ngan and F. Wu173-D Direction Aligned Wavelet Transform for SVC Experimental Results Conclusion Introduction 3-D Directional Threading 3-D Extension of Weighted Adaptive Lifting Experimental Results and Conclusion

18. Coding Performance Comparison (3-D WAL vs. 3-D DWT) – The highest PSNR gain can be up to 1.62 dB – For 5/3-tap spatial filter average PSNR gains are 0.89 dB for Carphone and 1.12 dB for Foreman, respectively – For 9/7-tap spatial filter average PSNR gains are 0.69 dB for Carphone and 1.00 dB for Foreman, respectively. Complexity Comparison (3-D WAL vs. 3-D DWT) – on encoder side Increases considerably complexity due to 3-D direction estimation process – on decoder side has similar complexity due to asymmetric design Y. Liu, K.N. Ngan and F. Wu183-D Direction Aligned Wavelet Transform for SVC Experimental Results Conclusion Introduction 3-D Directional Threading 3-D Extension of Weighted Adaptive Lifting Experimental Results and Conclusion

19. 3-D Direction Aligned Wavelet Transform for Scalable Video Coding – 3-D generalized directional threading – 3-D extension of weighted adaptive lifting References – [Ding2007] W. Ding, F. Wu, X. Wu, S. Li, and H. Li, ”Adaptive directional lifting-based wavelet transform for image coding,” IEEE Trans. Image Process., vol.16, no.2, pp.416-427, Feb. 2007 – [Chang2007] C.-L. Chang and B. Girod, ”Direction-adaptive discrete wavelet transform for image compress,” IEEE Trans. Image Process., vol.16, no.5, pp.1289-1302, May 2007 – [Liu2007a] Y. Liu and K.N. Ngan, ”Weighted adaptive lifting-based wavelet transform,” 2007 IEEE Int. Conf. Image Process. (ICIP2007), San Antonio, USA, Sept. 2007 – [Liu2007b] Y. Liu, F. Wu, and K.N. Ngan, ”3-D object-based scalable wavelet video coding with boundary effect suppression”, IEEE Trans. Circuits Syst. Video Technol., vol.17, no. 5, pp.639-644, May 2007 – [Xiong2004] R. Xiong, F. Wu, J.Xu, S. Li and Y.-Q. Zhang, ”Barbell lifting wavelet transform for highly scalable video coding,” Picture Coding Symposium 2004, USA, Dec 2004 Y. Liu, K.N. Ngan and F. Wu193-D Direction Aligned Wavelet Transform for SVC Conclusion Experimental Results Conclusion Introduction 3-D Directional Threading 3-D Extension of Weighted Adaptive Lifting Experimental Results and Conclusion

20. Thank You ! Q&A 3-D Direction Aligned Wavelet Transform for SVC20Y. Liu, K.N. Ngan and F. Wu