Transcript Image Transcoding in the block DCT Space Jayanta Mukhopadhyay

Image Transcoding
in the block DCT Space
Jayanta Mukhopadhyay
Department of Computer Science & Engineering
Indian Institute of Technology, Kharagpur, 721302, India
[email protected]
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Transcoding DWT to DCT
2
Discrete Wavelet Transform
x0 (n)
h
2
a1 (n)
2
h'
g
2
d1 (n)
2
g'
Analysis
~
x0 (n)
Synthesis
Forward DWT and Inverse DWT
3
2-D DWT
Decomposition
1st Level
2nd Level
2LL 2HL
Image in
spatial
domain


LL
HL
HL
2LH 2HH
LH
HH
LH
HH
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.
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DCT domain Upsampling with Zero Insertion
Type-II DCT of upsampled signal as obtained through
zero insertion of signal x(n) is computed by:
Note:- DCT obtained is referred as upsampled DCT.
5
A typical conversion matrix
4x4 block to 8x8 upsampled type-II DCT
For even sample
xoxoxoxo…
For odd sample
oxoxoxox…
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Computation of upsampled DCT
M ethod 1. Upsampling entire wavelet band
Wavelet
DCT domain
coefficient
Block
upsampling
Entire band
Upsampled
Type-II
DCT block
of
wavelet band
M ethod 2. Upsampling using composition of smaller DCT blocks
Wavelet
coefficient
Block
DCT domain
upsampling
4 x 4 blocks
Upsampled
Type-II
DCT blocks
8x8
Composition
DCT
blocks
Upsampled
Type-II
DCT block
of
wavelet band
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Wavelet synthesis in the DCT domain
C2e{xue (m, n)
h(m, n)}  C2e{xue (m, n)}C1e{h(m, n)}
Type-I
DCT block
of
Synthesis Filter
Impulse
Response
Type-II
upsampled
DCT block of
wavlet
coefficient
band
DCT
domain
Filtering
Type-II
DCT block
of
Filtered
Signal/image
 Result is transcoded type-II DCT coefficients.
 Operation is equivalent to IDWT + DCT.
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Transcoding in the DCT domain
a1 ( n)
Wavelet
subbands
d1 ( n )
h' ( n)
2
Upsampling
Synthesis
filtering
y (n)
DCT
DCT
Blocks
g ' ( n)
2
Y (k )
DWT to DCT Transcoding
a1 ( n)
Wavelet
subband
h' ( n)
Synthesis
filter
Upsampled
Type-II
DCT block
Point
wise
multiply
Type-I
DCT of
Filter
Transcoded
DCT
Block
Approximation subband
synthesis in DCT domain
Composite Operation
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Wavelet to DCT Transcoding (WDT)
Upsampling
and Filtering
LL
HL
LL Filtered
block
Upsampling
and Filtering
Upsampling
LH
HH
Wavelet bands
and Filtering
Upsampling
and filtering
H L Filtered
block
HH Filtered
block
LH Filtered
block
Point wise
Addition
Transcoded
DCT Block
B2fTW 2W
Viswanath, Mukherejee and Biswas (2009), Springer Journal on SIVP,
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Wavelet to Block DCT Transcoding (WBDT)




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.
This work is published in Springer Journal on SIVP, Jan 2009
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Wavelet to Block DCT Transcoding (WBDT)
Let
TL ,TH
are pre-computed
and
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Wavelet to Block DCT Transcoding by
Linear Filtering (WBDTL)
 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
added.
* Computes the transcoded blocks of size 2Nx2N.
Note:- For JPEG based applications, N=4.
are
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Wavelet to Block DCT Transcoding by
Linear Filtering (WBDTL)
and
Where
are the even upsampled DCT blocks of wavelet approximation
subband blocks and DCT matrices of the lowpass synthesis filter.
and
Where
are the odd upsampled DCT blocks of wavelet detail subband blocks
and DCT matrices of the highpass synthesis filter.
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Wavelet to Block DCT Transcoding by
Linear Filtering (WBDTL)
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Transcoding with Multilevel DWT
2LL 2HL
2LL 2HL
HL
LL
2LH 2HH
LH
HH
LL
HL

LH
HL
2LH 2HH
2nd
level Transcoding
LH
HH
HH
1st level Transcoding
DCT Blocks
Reconstructed image
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Cost of Multilevel Transcoding
For a tile size of 64 x64
In JPEG2000
Hybrid Approach
For blocks of
size 8x8
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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
1
0.2669
0.5913
0.5913
0.2669
2
-0.0782
0.0575
-0.0575
0.0782
3
-0.0169
-0.0913
-0.0913
-0.0169
4
0.0267
-0.0267
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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
No. of zero coefficients
Large number
of coefficients
are zeros
For Lena image
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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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Block DCT to wavelet transcoding
h(n)
X (k )
IDCT
x(n)
DCT
Blocks
Analysis
filtering
2
a1 ( n)
Downsampling Wavelet
subbands
g (n)
2
d1 ( n )
DCT to DWT Transcoding
DCT
Blocks
IDCT
Type-I
DCT of
the Filter
Filtering and
Down
sampling
a1 ( n)
Wavelet
subband
h( n)
Approximation subband
transcoding in DCT domain
Composite operation
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Downsampling from block DCT
For LL
subband
For LH
subband
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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
34
Results: DCT to Wavelet transcoding
PSNR close
to
300 dB
Ref: 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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Observations
 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.
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JPEG2000 to JPEG
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JPEG2000 Compression Standard
Source
Image
Forward
Wavelet
Transform
Quantization
Entropy
Encoding
Compressed
Image data
....01010001....
Inverse
Wavelet
Transform
Reconstructed
Image
Compression
Compressed
Image data
....01010001....
Entropy
Decoding
Dequantization
Decompression



JPEG2000 is an emerging image compression standard
Uses Discrete wavelet transform (DWT) as transform .
Transform coefficients are quantized an encoded.
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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
Source
Image
Forward
Wavelet
Transform
Quantization
Compressed
Image data
....01010001....
Entropy
Encoding
Compression
Compressed
Image data
....01010001....
Entropy
Decoding
Dequantization
Decompression
DWT to DCT
Transcoder
Reconstructed
Image
Block DCT
Transcoding
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Tanscoding…

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.
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Transform domain Transcoding
JPEG2000
Entropy
Decoding
Wavelet
bands
Quantize
JPEG
DCT
Blocks
Entropy
Encoding
Wavelet
DCT
Transcoder
compressed
Image
NxN
DCT
Blocks
JPEG
compressed
Image
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JPEG2000 Decoding
Original Image
PSNR=41.5460 at 1.044 bpp
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Transcoding Results
Spatial Domain
bpp=0.720, PSNR=35.77
Transform Domain
bpp=0.7208, PSNR=35.77
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IMAGE to JPEG
Original Image
bpp=0.712 PSNR=35.8082
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Transcoder
Performance evaluation
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We have defined three measures as follows:



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.
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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
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