Multiresolution graph fourier transform for compression of piecewise smooth images

IEEE Transactions on Image Processing

Volumn 24, Issue 1, 2015, Pages 419-433

  Hu, Wei ^a   Cheung, Gene ^b   Ortega, Antonio ^c   Au, Oscar C ^a  

^a HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

^b GRADUATE UNIVERSITY FOR ADVANCED STUDIES   (Japan)

^c University of Southern California   (United States)

Author keywords

Graph Fourier Transform; Image Compression; Piecewise Smooth Images

Indexed keywords

ANIMATION; CLUSTERING ALGORITHMS; COMPUTER GRAPHICS; COSINE TRANSFORMS; DECODING; DISCRETE COSINE TRANSFORMS; GRAPHIC METHODS; IMAGE CODING; IMAGE COMPRESSION; IMAGE QUALITY; IMAGE SEGMENTATION; LOW PASS FILTERS; PIXELS; SIGNAL PROCESSING; SIGNAL TO NOISE RATIO; TABLE LOOKUP;

COMPUTATION COMPLEXITY; ENCODING AND DECODING; GRAPH FOURIER TRANSFORMS; PEAK SIGNAL TO NOISE RATIO; PIECEWISE SMOOTH; SIGNAL CHARACTERISTIC; SIGNAL REPRESENTATIONS; TRANSFORM COEFFICIENTS;

FOURIER TRANSFORMS;

EID: 84920157216     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2014.2378055     Document Type: Article

References (41)

1. V. K. Goyal, "Theoretical foundations of transform coding," IEEE Signal Process. Mag., vol. 18, no. 5, pp. 9-21, Sep. 2001.
2. T. Wiegand, G. J. Sullivan, G. Bjontegaard, and A. Luthra, "Overview of the H.264/AVC video coding standard," IEEE Trans. Circuits Syst. Video Technol., vol. 13, no. 7, pp. 560-576, Jul. 2003.
3. J. Huang and P. M. Schultheiss, "Block quantization of correlated Gaussian random variables," IEEE Trans. Commun. Syst., vol. 11, no. 3, pp. 289-296, Sep. 1963.
4. V. K. Goyal, J. Zhuang, and M. Vetterli, "Transform coding with backward adaptive updates," IEEE Trans. Inf. Theory, vol. 46, no. 4, pp. 1623-1633, Jul. 2000.
5. S. Jana and P. Moulin, "Optimality of KLT for high-rate transform coding of Gaussian vector-scale mixtures: Application to reconstruction, estimation, and classification," IEEE Trans. Inf. Theory, vol. 52, no. 9, pp. 4049-4067, Sep. 2006.
6. M. Effros, H. Feng, and K. Zeger, "Suboptimality of the Karhunen-Loeve transform for transform coding," IEEE Trans. Inf. Theory, vol. 50, no. 8, pp. 1605-1619, Aug. 2004.
7. A. K. Jain, Fundamentals of Digital Image Processing. Upper Saddle River, NJ, USA: Prentice-Hall, 1989.
8. H. S. Malvar, A. Hallapuro, M. Karczewicz, and L. Kerofsky, "Low-complexity transform and quantization in H.264/AVC," IEEE Trans. Circuits Syst. Video Technol., vol. 13, no. 7, pp. 598-603, Jul. 2003.
9. D. K. Hammond, P. Vandergheynst, and R. Gribonval, "Wavelets on graphs via spectral graph theory," Appl. Comput. Harmon. Anal., vol. 30, no. 2, pp. 129-150, Mar. 2010.
10. P. Wan, Y. Feng, G. Cheung, I. V. Bajic, O. C. Au, and Y. Ji, "3D motion in visual saliency modeling," in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP), Vancouver, BC, Canada, May 2013, pp. 1831-1835.
11. D. Tian, P.-L. Lai, P. Lopez, and C. Gomila, "View synthesis techniques for 3D video," Proc. SPIE, vol. 7443, p. 74430T, Feb. 2009.
12. S.-C. Han and C. I. Podilchuk, "Video compression with dense motion fields," IEEE Trans. Image Process., vol. 10, no. 11, pp. 1605-1612, Nov. 2001.
13. D. S. Hochbaum, "An efficient and effective tool for image segmentation, total variations and regularization," in Proc. 3rd Int. Conf. Scale Space Variational Methods Comput. Vis., vol. 6667, 2011, pp. 338-349.
14. J. Shi and J. Malik, "Normalized cuts and image segmentation," IEEE Trans. Pattern Anal. Mach. Intell., vol. 22, no. 8, pp. 888-905, Aug. 2000.
15. R. Shukla, P. L. Dragotti, M. N. Do, and M. Vetterli, "Rate-distortion optimized tree-structured compression algorithms for piecewise polynomial images," IEEE Trans. Image Process., vol. 14, no. 3, pp. 343-359, Mar. 2005.
16. Y. Morvan, P. H. N. de With, and D. Farin, "Platelet-based coding of depth maps for the transmission of multiview images," Proc. SPIE, vol. 6055, Jan. 2006, p. 60550K.
17. P. Merkle et al., "The effects of multiview depth video compression on multiview rendering," Signal Process., Image Commun., vol. 24, nos. 1-2, pp. 73-88, Jan. 2009.
18. I. Daribo, G. Cheung, and D. Florencio, "Arithmetic edge coding for arbitrarily shaped sub-block motion prediction in depth video compression," in Proc. 19th IEEE Int. Conf. Image Process., Orlando, FL, USA, Sep. 2012, pp. 1541-1544.
19. I. Daribo, D. Florencio, and G. Cheung, "Arbitrarily shaped motion prediction for depth video compression using arithmetic edge coding," IEEE Trans. Image Process., vol. 23, no. 11, pp. 4696-4708, Nov. 2014.
20. M. B. Wakin, J. K. Romberg, H. Choi, and R. G. Baraniuk, "Wavelet-domain approximation and compression of piecewise smooth images," IEEE Trans. Image Process., vol. 15, no. 5, pp. 1071-1087, May 2006.
21. M. Maitre and M. N. Do, "Depth and depth-color coding using shapeadaptive wavelets," J. Vis. Commun. Image Represent., vol. 21, nos. 5-6, pp. 513-522, Jul./Aug. 2010.
22. 2 singularities," Commun. Pure Appl. Math., vol. 57, no. 2, pp. 219-266, Feb. 2002.
23. M. N. Do and M. Vetterli, "The contourlet transform: An efficient directional multiresolution image representation," IEEE Trans. Image Process., vol. 14, no. 12, pp. 2091-2106, Dec. 2005.
24. G. Shen, W.-S. Kim, S. Narang, A. Ortega, J. Lee, and H. Wey, "Edge-adaptive transforms for efficient depth map coding," in Proc. IEEE Picture Coding Symp., Nagoya, Japan, Dec. 2010, pp. 566-569.
25. W. Hu, X. Li, G. Cheung, and O. Au, "Depth map denoising using graph-based transform and group sparsity," in Proc. IEEE 15th Int. Workshop Multimedia Signal Process. (MMSP), Pula, Italy, Sep./Oct. 2013, pp. 001-006.
26. C. Zhang and D. Florencio, "Analyzing the optimality of predictive transform coding using graph-based models," IEEE Signal Process. Lett., vol. 20, no. 1, pp. 106-109, Jan. 2013.
27. W.-S. Kim, A. Ortega, P. Lai, D. Tian, and C. Gomila, "Depth map coding with distortion estimation of rendered view," Proc. SPIE, vol. 7543, p. 75430B, Jan. 2010.
28. N.-M. Cheung, D. Tian, A. Vetro, and H. Sun, "On modeling the rendering error in 3D video," in Proc. 19th IEEE Int. Conf. Image Process., Orlando, FL, USA, Sep./Oct. 2012, pp. 3021-3024.
29. G. Cheung, A. Kubota, and A. Ortega, "Sparse representation of depth maps for efficient transform coding," in Proc. IEEE Picture Coding Symp., Nagoya, Japan, Dec. 2010, pp. 298-301.
30. G. Cheung, J. Ishida, A. Kubota, and A. Ortega, "Transform domain sparsification of depth maps using iterative quadratic programming," in Proc. 18th IEEE Int. Conf. Image Process., Brussels, Belgium, Sep. 2011, pp. 129-132.
31. S. Yea and A. Vetro, "View synthesis prediction for multiview video coding," Signal Process. Image Commun., vol. 24, nos. 1-2, pp. 89-100, Jan. 2009.
32. D. B. Graziosi, N. M. M. Rodrigues, S. M. M. de Faria, D. Tian, and A. Vetro, "Analysis of depth map resampling filters for depth-based 3d video coding," in Proc. Int. Conf. Telecommun., Castelo Branco, Portugal, May 2013.
33. G. Shen, W.-S. Kim, A. Ortega, J. Lee, and H. Wey, "Edge-aware intra prediction for depth-map coding," in Proc. 17th IEEE Int. Conf. Image Process. (ICIP), Hong Kong, Sep. 2010, pp. 3393-3396.
34. W. Hu, G. Cheung, X. Li, and O. Au, "Depth map compression using multi-resolution graph-based transform for depth-image-based rendering," in Proc. 19th IEEE Int. Conf. Image Process., Orlando, FL, USA, Sep./Oct. 2012, pp. 1297-1300.
35. U. Von Luxburg, "A tutorial on spectral clustering," Statist. Comput., vol. 17, no. 4, pp. 395-416, Dec. 2007.
36. R. M. Gray and D. L. Neuhoff, "Quantization," IEEE Trans. Inf. Theory, vol. 44, no. 6, pp. 2325-2383, Oct. 1998.
37. D. Geman and C. Yang, "Nonlinear image recovery with half-quadratic regularization," IEEE Trans. Image Process., vol. 4, no. 7, pp. 932-946, Jul. 1995.
38. W.-S. Kim, S. K. Narang, and A. Ortega, "Graph based transforms for depth video coding," in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP), Kyoto, Japan, Mar. 2012, pp. 813-816.
39. K. S. C. Papadimitriou, Combinatorial Optimization: Algorithm and Complexity. New York, NY, USA: Dover, 1998, p. 165.
40. D. A. Huffman, "A method for the construction of minimum-redundancy codes," Proc. IRE, vol. 40, no. 9, pp. 1098-1101, Sep. 1952.
41. W.-S. Kim, A. Ortega, P. Lai, D. Tian, and C. Gomila, "Depth map distortion analysis for view rendering and depth coding," in Proc. 16th IEEE Int. Conf. Image Process. (ICIP), Cairo, Egypt, Nov. 2009, pp. 721-724.