1 Image Transcoding in the block DCT Space Jayanta Mukhopadhyay Department of Computer Science & Engineering Indian Institute of Technology, Kharagpur,

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Image Transcoding

in the block DCT Space

Jayanta MukhopadhyayDepartment of Computer Science & Engineering

Indian Institute of Technology, Kharagpur, 721302, India

[email protected]

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Transcoding DWT to DCT

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h'

g'g

h 2

2

2

2

)(0 nx )(~0 nx)(1 na

)(1 nd

Analysis Synthesis

Forward DWT and Inverse DWT

Discrete Wavelet Transform

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2-D DWT

1D DWT applied to vertical and horizontal direction. For Multilevel DWT:-

The LL band is recursively decomposed, vertically and horizontally.

Filtering is performed in time domain.

Image in spatial domain

LH

HL

HH

2LL 2HL

2LH 2HHLL

LH

HL

HH

Decomposition 1st Level 2nd Level

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DCT domain Upsampling with Zero Insertion

Type-II DCT of upsampled signal as obtained throughzero insertion of signal x(n) is computed by:

Note:- DCT obtained is referred as upsampled DCT.

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A typical conversion matrix4x4 block to 8x8 upsampled type-II DCT

For even sample xoxoxoxo…

For odd sampleoxoxoxox…

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Computation of upsampled DCT

W aveletcoe fficient

Block

DCT domainupsamplingEntire band

UpsampledType-II

DCT blockof

wavelet band

1. Upsampling entire wavelet bandM ethod

W aveletcoefficient

Block

UpsampledType-II

DCT blocks8 x 8

DCT domainupsampling4 x 4 blocks

UpsampledType-II

DCT blockof

wavelet band

CompositionDCT

blocks

2. Upsampling using composition of smaller DCT blocksM ethod

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Wavelet synthesis in the DCT domain

Result is transcoded type-II DCT coefficients.Operation is equivalent to IDWT + DCT.

Type-IIupsampled

DCT block ofwavlet

coefficientband

Type-IDCT block

ofSynthesis Filter

ImpulseResponse DCT

domainFiltering

Type-IIDCT block

ofFiltered

Signal/image

),({2 nmxC uee )},({)},({ 12 nmhCnmxC euee)},( nmh

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Transcoding in the DCT domain

2

2

D C T

)(1 na

)(1 nd

)(ny)(kY

)(' ng

)(' nh

W a ve le ts ubba nds

D C TB lo c k s

D W T to D C T T ra ns c o ding

S ynthe s isfilte ring

U ps a m pling

U ps am ple dType - II

D C T blo c k

T yp e-ID C T o f

F ilter

)(1 na

P o intw is e

m ultip ly

)(' nh

T ra ns c o de dD C TB lo c k

Appr o xi m at i o n s ubbands ynthe s i s i n D C T do m ai n

W a ve le ts ubba nd

S ynthe s isfilte r

Composite Operation

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Wavelet to DCT Transcoding (WDT)

LL Filteredbloc k

H L Filteredbloc k

HH Filteredbloc k

LH Filteredbloc k

Point wiseAddition

TranscodedDCT Block

LL HL

LH HH

Ups am plingand Filtering

Ups am plingand Filtering

Upsamplingand Filtering

Upsamplingand filter ing

W avelet bands

WWfT

B 22

Viswanath, Mukherejee and Biswas (2009), Springer Journal on SIVP,

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WDT computes DCT blocks of larger size. By decomposing, 8x8 blocks are obtained. Cost of transcoding increases. To reduce the cost, smaller blocks are to be considered.

WBDT:

* Three blocks of NxN size are used in a

wavelet subband of size WxW.

* Blocks are Upsampled, composed, filtered and

decomposed.

* The transcoded blocks of size 2Nx2N.

Note:- N=4 for JPEG based applications.

Wavelet to Block DCT Transcoding (WBDT)

This work is published in Springer Journal on SIVP, Jan 2009

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TL ,TH are pre-computed

Let

and

Wavelet to Block DCT Transcoding (WBDT)

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WBDT computes DCT blocks of size 8x8, Uses composing and decomposing of DCT blocks. Requires Type-I DCT of filter and Type-II DCT of data.

Linear Filtering in the DCT domain: Requires only Type-II DCT.

Blocks are processed separately and added together.

The WBDTL,

* Three adjacent NxN size subband blocks are used.

* Upsampled blocks filtered separately and the results are added.

* Computes the transcoded blocks of size 2Nx2N.

Note:- For JPEG based applications, N=4.

Wavelet to Block DCT Transcoding by Linear Filtering (WBDTL)

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Where

and

are the even upsampled DCT blocks of wavelet approximation subband blocks and DCT matrices of the lowpass synthesis filter.

are the odd upsampled DCT blocks of wavelet detail subband blocks and DCT matrices of the highpass synthesis filter.

Where

and

Wavelet to Block DCT Transcoding by Linear Filtering (WBDTL)

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Wavelet to Block DCT Transcoding by Linear Filtering (WBDTL)

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Transcoding with Multilevel DWT

LH

HL

HHLH

HL

HH

2LL 2HL

2LH 2HHLL

2LL 2HL

2LH 2HH

2nd level Transcoding

LH

HL

HH

LL

1st level Transcoding Reconstructed image DCT Blocks

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For a tile size of 64 x64In JPEG2000

For blocks of size 8x8

Cost of Multilevel Transcoding

Hybrid Approach

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JPEG2000 9/7 wavelet filters

Analysis Filter Coefficients

Synthesis Filter Coefficients

i Lowpass H(i)

Highpass G(i)

Lowpass H’(i)

Highpass G’(i)

0 0.6029 -1.1151 1.1151 -0.6029

0.2669 0.5913 0.5913 0.2669

-0.0782 0.0575 -0.0575 0.0782

-0.0169 -0.0913 -0.0913 -0.0169

0.0267 -0.0267

1234

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Analysis Filters

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Synthesis Filters

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Wavelet filters and responses

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Wavelet filters and responses

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Other wavelet filters

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Results

PSNR close to

~300 dB

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Results: Quantization of wavelet subbands

For Lena image

Large number of coefficients

are zeros

No. of zero coefficients

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Observations

The proposed new algorithms for transcoding the DCT coefficients from wavelet coefficients are computationally efficient.

Both the approaches (WBDT and WBTL) are found to be equivalent.

Proposed transcoding achieves PSNR performances as same as the spatial domain technique.

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Block DCT to wavelet transcoding

The technique is based on the combined step of block filtering and downsampling directly in the DCT domain.

Filtering matrices are computed using wavelet analysis filters.

Three adjacent DCT blocks are used in transcoding.

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2

2

ID C T

)(nh

)(ng

)(nx)(kX

)(1 na

)(1 nd D C TB lo c k s

W a ve le ts ubba nds

D C T to D W T T ra ns c o ding

A na lys isfilte ring

D o w ns a m pling

F ilte r ing a ndD ow n

s a m pling

T yp e-ID C T o f

the F ilter)(1 naID C T

( )h n

D C TB lo c k s

Appr o xi m at i o n s ubbandtr ans c o di ng i n D C T do m ai n

W a ve le ts ubba nd

Block DCT to wavelet transcoding

Composite operation

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For LLsubba

nd

For LH

subband

Downsampling from block DCT

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Block DCT to Wavelet Transcoding (BWT)

HL and HH are computed from Type-I DCT of the analysis filters.

In 1-D:

In 2-D:

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Transcoding with Linear Filtering

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Block DCT to Wavelet Transcoding with Linear Convolution (BWTL)

This work is Accepted in IEEE ICIP 2009

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TL Matrices using 9/7 analysis lowpass filter

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DCT to Wavelet: Complexity

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Results: DCT to Wavelet transcoding

PSNR close to

300 dBRef: ST subbands

Almost equal

Almost equal

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Results: DCT Quantization effect on transcoding

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Results: DCT Quantization effect on transcoding

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Quantization effect on transcoded subbands

More degradation of quality in lower frequency subbands

This work is under revision in Springer Journal on SIVP

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Performance comparison with spatial transcoding

Reference: Original Image

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Spatial transcoding and the BWTL transcoding techniques perform at par.

However, the BWT technique perform the best among them.

This is due to the fact that the rounding errors are accumulating in spatial domain transcoding and the BWTL techniques.

But the BWT technique operates with three blocks simultaneously, and thereby rounding errors are reduced.

Observations

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JPEG2000 to JPEG

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JPEG2000 Compression Standard

JPEG2000 is an emerging image compression standard Uses Discrete wavelet transform (DWT) as transform . Transform coefficients are quantized an encoded.

SourceImage

ForwardWavelet

TransformQuantization

EntropyEncoding

Com pressedIm a ge da ta

....01010001....

ReconstructedImage

InverseWavelet

TransformDequantization

EntropyDecoding

Com pressed Im a ge da ta

....01010001....

Compression

Decompression

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Transcoding JPEG2000 to JPEG

Encoding of JPEG2000 usually gives 2-4 dB higher PSNR values at the same compression level.

Average decoding time for JPEG2000 is almost five times higher compared to JPEG

Current web browsers do not support JPEG 2000 natively.

Since JPEG is the most common compression standard and has very low complexity, transcoding to JPEG provides a smooth upgrade path.

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Transform Domain Transcoder

SourceImage

ForwardWavelet

TransformQuantization

EntropyEncoding

Com pressed Im a ge da ta

....01010001....

ReconstructedImage

Block DCT

DWT to DCTTranscoderDequantization

EntropyDecoding

Com pressedIm a ge da ta

....01010001....

Compression

Decompression Transcoding

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Since impulse responses of JPEG2000 wavelet filters are symmetric, DCT domain filtering can be used.

JPEG2000 encoded using 2-D wavelet transforms by incorporating 9-7 analysis filters.

The wavelet coefficients are encoded with different quantization levels to achieve different compression rate.

Tanscoding…

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Transform domain Transcoding

EntropyDecoding

Waveletbands

WaveletDCT

Transcoder

Q uantizeDCT

Blocks

JPEGEntropy

EncodingJPEG

JPEG2000

NxNDCT

Blocks

compressed Image

compressed Image

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JPEG2000 Decoding

Original Image PSNR=41.5460 at 1.044 bpp

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Transcoding Results

Spatial Domainbpp=0.720, PSNR=35.77

Transform Domainbpp=0.7208, PSNR=35.77

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IMAGE to JPEG

bpp=0.712 PSNR=35.8082Original Image

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Transcoder

Performance evaluation

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Guaranteed PSNR(Mg): The minimum PSNR value with respect to the JPEG2000 decoded image to be achieved by the transcoder. Here we used a typical value of 40 dB.

Equivalent rate (ρeq): The minimum compression rate of the transcoded JPEG image providing at least the guaranteed PSNR with respect to the JPEG2000 decoded image. The equivalent rate is obtained at 40 dB point with respect to JPEG2000 decoded image.

Equivalent PSNR (Meq): The transcoder PSNR with respect to the original image at the equivalent rate.

We have defined three measures as follows:

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JPEG2000 to JPEG Transcoder Performance

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Transcoder Performance

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Equivalent PSNR comparison

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Thanks