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M. Wu: ENEE631 Digital Image Processing (Fall'01)
Image Compression (3)Image Compression (3)Wavelet Coding & Vector QuantizationWavelet Coding & Vector Quantization
Min Wu
Electrical & Computer Engineering University of Maryland, College Park
http://www.ece.umd.edu/class/enee631/
[email protected]
ENEE631 Fall 2001ENEE631 Fall 2001LectureLecture-
-9^9
M. Wu: ENEE631 Digital Image Processing (Fall'01)
Lec9 – Wavelet Coding & VQ 10/2/01 [2]
Review of Last Time Review of Last Time "
Predictive coding
"
Transform coding
"
JPEG compression standard^ –
Baseline block-DCT based algorithm #^
lossy part: quantization with different step size for each coeff. Band #^
lossless part: differential coding, run-length coding, Huffman
"
Binary image coding
"
Today^ –
Wavelet coding
Brief introduction to Wavelet-based JPEG 2000
Brief introduction to Vector Quantization (VQ)
M. Wu: ENEE631 Digital Image Processing (Fall'01)
Lec9 – Wavelet Coding & VQ 10/2/01 [3]
RecallRecall Haar
Haar Transform
Transform
"
Two major sub-operations
Scaling captures info. at different frequencies
Translation captures info. at different locations
"
Can be represented by filtering and downsampling
"
Poor energy compaction of Haar transform
1
x
M. Wu: ENEE631 Digital Image Processing (Fall'01)
Lec9 – Wavelet Coding & VQ 10/2/01 [4]
Wavelet Transform for Image Compression Wavelet Transform for Image Compression "^
ENEE631 emphasis
–^
Conceptual aspects related to image compression
-^
Wavelet is also useful for denoising, enhancement, and image analysis
-^
For more info. on wavelet: ENEE624, wavelet math course, & other ref.
"
K-level 1-D wavelet decomposition
–^
Successive lowpass/highpass filtering and downsampling #^
on different level: capture transitions of different frequency bands #^
on the same level: capture transitions at different locations
From MatlabWavelet ToolboxDocumentation
M. Wu: ENEE631 Digital Image Processing (Fall'01)
Lec9 – Wavelet Coding & VQ 10/2/01 [5]
Examples of 1-^ Examples of 1
-D Wavelet TransformD Wavelet Transform
From MatlabWavelet ToolboxDocumentation
M. Wu: ENEE631 Digital Image Processing (Fall'01)
Lec9 – Wavelet Coding & VQ 10/2/01 [6]
(^2) 2-
-D Wavelet Transform via Separable FiltersD Wavelet Transform via Separable Filters
From MatlabWavelet ToolboxDocumentation
M. Wu: ENEE631 Digital Image Processing (Fall'01)
Lec9 – Wavelet Coding & VQ 10/2/01 [7]
OrthonormalOrthonormal Filters
Filters
"
Equiv. to projecting input signal to orthonormal basis
"
Energy preservation property
Convenient for quantizer design
MSE by transform domain quantizer is same as reconstruction MSE
"
Shortcomings: “coefficient expansion”
N-element input & M-element filter $
(N+M-1)-element output
(N+M)/2 after downsample
Length of output per stage grows ~ undesirable for compression
M. Wu: ENEE631 Digital Image Processing (Fall'01)
Lec9 – Wavelet Coding & VQ 10/2/01 [8]
Solutions to Coefficient Expansion Solutions to Coefficient Expansion "
Circular convolution
Periodic extension of input signal
Problem: artifacts by large discontinuity at borders
"
Symmetric extension of input
Reduce border artifacts
Problem: output at each stage may not be symmetric
From Usevitch (IEEESig.Proc. Mag. 9/01)
M. Wu: ENEE631 Digital Image Processing (Fall'01)
Lec9 – Wavelet Coding & VQ 10/2/01 [13]
Two Key Concepts of EZWTwo Key Concepts of EZW "^
Significance map coding via zero-Tree^ –
Encode only high energy coefficients^ #
Need to send location info.^ $
large overhead
Encode “insignificance map” using zero-trees
"
Successive approximationquantization^ –
Send most-significant-bits first and graduallyrefine coeff. value
“Embedded” nature of coded bit-stream^ #
get higher fidelity image by adding extrarefining bits
From Usevitch (IEEESig.Proc. Mag. 9/01)
M. Wu: ENEE631 Digital Image Processing (Fall'01)
Lec9 – Wavelet Coding & VQ 10/2/01 [14]
EZW Algorithm and Example^ EZW Algorithm and Example "^
Initial threshold
~
2 ^ floor(log
2 xmax
)
-^
Put all coeff. in dominant list
"
Dominant Pass
(“zig-zag” across bands)
-^
Assign symbol to each coeff. & entropyencode symbols^ #
ps – positive significance #^
ns – negative significance #^
iz – isolated zero #^
ztr – zero-tree root
-^
Significant coeff.^ #
move. to subordinate list #^
put zero in dominant list
"
Subordinate Pass^ –
Output one bit for subordinate list^ #
According to position in up/low ofquantization interval
"
Repeat with half threshold^ –
Until bit budget achieved
From Usevitch (IEEESig.Proc. Mag. 9/01)
M. Wu: ENEE631 Digital Image Processing (Fall'01)
Lec9 – Wavelet Coding & VQ 10/2/01 [15]
After 1 After 1
stst
PassPass
From Usevitch (IEEESig.Proc. Mag. 9/01)
M. Wu: ENEE631 Digital Image Processing (Fall'01)
Lec9 – Wavelet Coding & VQ 10/2/01 [16]
After 2After 2
ndnd
PassPass
From Usevitch (IEEESig.Proc. Mag. 9/01)
M. Wu: ENEE631 Digital Image Processing (Fall'01)
Lec9 – Wavelet Coding & VQ 10/2/01 [17]
Beyond EZW^ Beyond EZW "^
Cons of EZW
Poor error resilience
Difficult for selective spatial decoding
"
Set Partitioning in Hierarchal Trees (SPIHT)
Further improvement over EZW
"
EBCOT
Used in JPEG 2000
Address the shortcomings of EZW
M. Wu: ENEE631 Digital Image Processing (Fall'01)
Lec9 – Wavelet Coding & VQ 10/2/01 [18]
JPEG 2000: A Wavelet- JPEG 2000: A Wavelet
-Based New StandardBased New Standard
Targets and features^ – Excellent low bit rate performance without sacrifice at higher
bit rate
- Progressive decoding to allow from lossy to lossless– Region-of-interest (ROI) coding– Error resilience
"
For details^ – Tutorial @ IEEE Trans. on consumer electronics 11/00– Links and tutorials @ http://www.jpeg.org/JPEG2000.htm
M. Wu: ENEE631 Digital Image Processing (Fall'01)
Lec9 – Wavelet Coding & VQ 10/2/01 [19]
From Christopoulos(IEEE Trans. on CE11/00)
M. Wu: ENEE631 Digital Image Processing (Fall'01)
Lec9 – Wavelet Coding & VQ 10/2/01 [20]
ExamplesExamplesJPEG2KJPEG2Kvs.vs.JPEGJPEG^ From Christopoulos(IEEE Trans. on CE11/00)
M. Wu: ENEE631 Digital Image Processing (Fall'01)
Lec9 – Wavelet Coding & VQ 10/2/01 [25]
Summary^ Summary "
Wavelet coding
- Filters for wavelet transf.– EZW
"
Brief introduction
- JPEG 2000– Vector quantization
"
Next time
- Review of image processing basics and image compression
M. Wu: ENEE631 Digital Image Processing (Fall'01)
Lec9 – Wavelet Coding & VQ 10/2/01 [26]
AssignmentAssignment "^
Required readings^ –
[Wavelet coding] #^
Usevitch’s tutorial in IEEE Sig. Proc. Magazine 9/ #^
Xiong’s paper on DCT vs. Wavelet on IEEE Trans. CSVT
(Univ. Library’s E-journal)
#^
MATLAB 2-D Wavelet Demos
[JPEG2000] Christopoluos’ tutorial in IEEE Trans. CE 11/ #^
http://etro.vub.ac.be/~chchrist/paper_ieee_ce_jpeg2000_Nov2000.pdf
[VQ] Bovik’s Handbook Sec.5.
"
Recommended readings^ –
www.jpeg.org
Gray’s tutorial paper on VQ
Bovik’s Handbook Sec.5.
"
Reminder^ –
Project BB1 Due Thursday before class
1 st^
in-class exam ~ Next Thursday 10/11/
