Filtering and enhancement of color images in the

Filtering and enhancement of color images in the

Filtering and enhancement of color images in the block DCT domain Jayanta Mukhopadhyay Dept. of Computer Science and Engg. Processing with compressed

image: Compresed domain approach J. Mukhopadhyay, Image and video processing in the compressed domain, CRC 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

5 2D DCT Type-II Even:

Type-II DCT of x(m,n): Useful properties of DCT blocks 7

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):273286, June Image downsampling 8x8 8x8

8x8 8x8 Sub-band approximatio n

4x4 4x4 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, 4x4 4x4 Image upsampling 4x4 4x4

4x4 4x4 Sub-band approximatio n 0 4x4 0 0 0 0 0

4x4 0 4x4 0 0 0 0 0 4x4 8x8 8x8

8x8 8x8 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):11601169, May 2002. Block composition and decomposition 4x4 4x4 4x4 4x4

8x8 Image Resizing 13 Image Halving

Use of linear and distributive properties. X00 X01 Xd

X10 X11 Not so sparse matrix multiplication! DCT(p0): Not so sparse.

No gain! DCT(p1) Typical result: Original

Bi-linear Linear and distributiv e method

2D DCT: Sub-band relation Low-pass truncated approximation: Block composition and decomposition

To convert M adjacent N-point DCT blocks to a single MxN-point DCT block. NxN zero matrix 2D DCT: Block composition and decomposition

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

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

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

followed by Decomposition (IDAD) x2 IDDA IDAD

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 bloc LMDS LxM U/S (LMUS)

1. Convert NxN to LNxMN block Efficiently compute exploiting large blocks of zeroes.

2. Decompose into LxM NxN blocks. LMUS example: 3x2 D/S and U/S

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 HDTV (1080x920) to NTSC (480x640) UDRA

DURA Hybrid Resizing (HRA) More general sub-band relation X: DCT block of QNxSN Y: DCT block of PNxRN

Truncated DCT block of X or padded with zeroes, if required. HRAS

HRAC Original image (Watch) HRAC: A few examples UDRA

HRAS HRAC Color Image Resizing

41 Color encoding in JPEG Y-Cb-Cr color space: Y

Cb Cr

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

DURA HRAS HRAC

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