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Filtering and enhancement of color images in the block DCT domain

This paper explores techniques for filtering and enhancing color images in the block discrete cosine transform (DCT) domain. It discusses the motivations for processing in the compressed domain, DCT domain processing, image resizing using DCT, and color image resizing. The paper also presents algorithms for downsampling, upsampling, and arbitrary resizing, as well as a hybrid resizing approach.

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Filtering and enhancement of color images in the block DCT domain

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  1. Filtering and enhancement of color images in theblock DCT domain Jayanta Mukhopadhyay Dept. of Computer Science and Engg.

  2. Processing with compressed image: Compresed domain approach J. Mukhopadhyay, “Image and video processing in the compressed domain”, CRC Press, 2011.

  3. Motivations • Computation with reduced storage. • Avoid overhead of forward and reverse transform. • Exploit spectral factorization for improving the quality of result and speed of computation. • DCT domain processing under consideration. • Image Resizing

  4. 2D DCT • Type-II Even: • Type-II DCT of x(m,n):

  5. Useful properties of DCT blocks

  6. 2D DCT: Sub-band relation Sub-band approximation: 2D DCT of xLL(m,n) Low-pass truncated approximation: S.-H. Jung, S.K. Mitra, and D. Mukherjee, Subband DCT: Definition, analysis and applications. IEEE Trans. on Circuits and systems for VideoTechnology, 6(3):273–286, June 1996.

  7. Image downsampling Sub-band approximation 4x4 4x4 8x8 8x8 4x4 4x4 8x8 8x8 4x4 4x4 4x4 4x4 J. Mukherjee and S.K. Mitra. Image resizing in the compressed domain using subband DCT. IEEE Transactions on Circuits and systems for Video Technology, 12(7):620–627, July 2002.

  8. Image upsampling Sub-band approximation 0 0 0 0 0 0 4x4 4x4 0 0 0 0 0 0 4x4 4x4 8x8 8x8 4x4 4x4 4x4 4x4 8x8 8x8

  9. 2D DCT: Block composition and decomposition J. Jiang and G. Feng. The spatial relationships of DCT coefficients between a block and its sub-blocks. IEEE Trans. on Signal Processing, 50(5):1160–1169, May 2002.

  10. Block composition and decomposition 8x8 4x4 4x4 4x4 4x4

  11. Image Resizing

  12. Image Halving • Use of linear and distributive properties.

  13. Not so sparse matrix multiplication! No gain! DCT(p0): Not so sparse. DCT(p1)

  14. Typical result: Original Bi-linear Linear and distributive method

  15. 2D DCT: Sub-band relation Low-pass truncated approximation:

  16. Block composition and decomposition • To convert M adjacent N-point DCT blocks to a single MxN-point DCT block. NxN zero matrix

  17. 2D DCT: Block composition and decomposition

  18. Useful conversion for halving or doubling 8-point DCT blocks. Composition Decomposition

  19. Image Halving: Approximation followed by Composition (IHAC)

  20. Image Halving: Composition followed by Approximation (IHAC)

  21. Image Doubling: Decomposition followed by Approximation (IDDA) x2

  22. Image Doubling: Approximation followed by Decomposition (IDAD) x2

  23. IDDA

  24. IDAD

  25. Resizing with integral factors To convert NxN block to LNxMN block. LN x MN block NxN DCT block LxM D/S (LMDS) 1. Merge LxM adjacent DCT blocks. 2. Sub-band approximation to a NxN DCT block.

  26. LMDS

  27. LxM U/S (LMUS) 1. Convert NxN to LNxMN block Efficiently compute exploiting large blocks of zeroes. 2. Decompose into LxM NxN blocks.

  28. LMUS

  29. An example: 3x2 D/S and U/S

  30. Arbitrary Resizing (P/Q x R/S) • U/S-D/S Resizing Algorithm (UDRA) • U/S by PxR • D/S by QxS • D/S-U/S Resizing Algorithm (DURA) • D/S by QxS • U/S PxR

  31. HDTV (1080x920) to NTSC (480x640) DURA UDRA

  32. Hybrid Resizing (HRA) More general sub-band relation Truncated DCT block of X or padded with zeroes, if required. X: DCT block of QNxSN Y: DCT block of PNxRN

  33. HRAS

  34. HRAC

  35. Original image (Watch)

  36. HRAC: A few examples

  37. HRAC UDRA HRAS

  38. Color Image Resizing

  39. Color encoding in JPEG • Y-Cb-Cr color space: Cb Y Cr

  40. Baseline JPEG Compression: Usually  the chromatic components Cb and Cr are at lower resolution than the Y component. •  Cascaded stages of down-sampling and up-sampling(the DURA algorithm) faces a problem of dimensionality mismatch.

  41. DURA

  42. HRAS HRAC

  43. Thank you!

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