Common image compression formats

Overview of Common Image Compression Formats

Clyde A. Lettsome, PhD, P.E.

Georgia Institute of Technology Center for Signal and Image Processing

Outline

Introduction Block Transform Method Subband Transform Method Performance References

Introduction


Figure 2.1 Basic Compression Encoder Decoder Block Diagram.

Block Transform Method

Pack high energy data at the beginning

Baseline JPEG Algorithm– Joint Photographic Experts Group or JPEG – Discrete Cosine Transform (DCT) – Based on DCT II



– JPEG Transform and Quantization Procedure

1. Divide image into 8x8 blocks

2. Apply the cosine transform

3. Round to the nearest integer

4. Maintain the dominant coefficients, a quantization weighting matrix Q[k1,k2]. smaller coefficients are placeded in the upper left corner while larger coefficients are placed in the lower right corner.

5. Coefficients are then rounded to the nearest integers

6. Unwrapping the remaining non-zero coefficients as shown in the next figure

7. DC components of each block is then extracted and encoded using the first order backward difference

8. AC non-zero components of each block are then collected and encoded using runlength coding. The general idea behind runlength coding is to encode repetitive sequences of values using a symbol





JPEG Entropy Coder Huffman coding is performed by:

1. Ordering the symbols in descending order

2. Merging the symbols with the lowest probabilities and reordering the resulting symbols in decreasing order of probability to form a tree

3. With the tree from step 2 in place, bit values (ones or zeros) are assigned to each branch of the tree starting from the right side and progressing to the left.


Subband Transform Method


Figure 2.2 Two-band analysis-synthesis filter bank

X=½X(-z) [H0(-z)G0(z) + H1(-z)G1(z)] + ½X(z) [H0(z)G0(z) + H1(z)G1(z)],

[H0(-z)G0(z) + H1(-z)G1(z)]

[H0(z)G0(z) + H1(z)G1(z)].


Important Developments in subband coding– subband transform is based on multi-rate

equation first mentioned by Schafer and Rabiner to improve coding efficiency

– Perfect reconstruction (PR) which was first introduced by Croiser, Estaban and Galand when they introduced Quadrature Mirror Filters (QMF)

– Exact reconstruction (ER) discovered by Smith and Barnwell and verified by Mintzer.



EZW– Developed by JM Shapiro in 1993


Figure 2.3 Octave-band decomposition


The quantization coding technique for the EZW is based on three principals (8).1. partial ordering of the wavelet transformed

elements based on magnitude, with the order of transmission based on subset partitioning algorithm,

2. ordering the bit transmission of refined bits,

3. exploitation of the coefficient similarities across different levels of decomposition



The SPIHT Method– Developed by Said Pearlman– Transform based on EZW with additional

discoveries symmetric extension developed by Smith and Eddins Daubechies 9/7 filters Haar filters Filter switching independent threshold is set for each subband thresholds in the highpass subbands are much more

restrictive than they are in the lowpass subbands



SPIHT’s Entropy CoderArithmetic coder - tends to perform better than

the Huffman coder in terms of reaching entropy1. The approach is based on a partitioning rule that

maps the input dynamically to a sub-interval of the line segment by sub-dividing the unit interval successively.

2. With each input symbol, the sub-interval is computed by finding the low end-point, the high-endpoint, and then the range.

3. sub-intervals are then mapped to binary codewords before being transmitted



JPEG2000– Similar to SPIHT– Constructed by the Joint Photographic Experts

Group1. images are first tiled

2. dc level shifted by subtracting the same quantity 2P-1, from the coefficient

3. JPEG group added the LeGall 5/3 biorthogonal CQF filters

Entropy coder– the arithmetic coder is the coder of choice




Figure 2.6 Transform block diagram in the JPEG2000 compression coder.

Performance


References

AFD10, Pavement Management Systems. "Delivery of Pavement Distress Data from Automated Systems." Transportation Research Board, 2007.

2. Huffman, D. A. A Method for the Construction of Minimum-Redundancy Codes. Proceedings of the IRE 'Vol.' 40, No. 9 1952, pp. 1098-101.

3. Jones, C. An Efficient Coding System for Long Source Sequences. Information Theory, IEEE Transactions on 'Vol.' 27, No. 3 1981, pp. 280-91.

4. Pennebaker, William B., and Joan L. Mitchell. Jpeg Still Image Data Compression Standard. New York: Van Nostrad Reinhold, 1993.

5. Woods, J., and S. O'Neil. Subband Coding of Images. Acoustics, Speech and Signal Processing, IEEE Transactions on 'Vol.' 34, No. 5 1986, pp. 1278-88.

6. Schafer, R. W., and L. R. Rabiner. A Digital Signal Processing Approach to Interpolation. Proceedings of the IEEE 'Vol.' 61, No. 6 1973, pp. 692-702.

7. Smith, M., and T. Barnwell. A Procedure for Designing Exact Reconstruction Filter Banks for Tree-Structured Subband Coders. Acoustics, Speech, and Signal Processing, IEEE International Conference on ICASSP '84., 1984.

8. Shapiro, J. M. Embedded Image Coding Using Zerotrees of Wavelet Coefficients. Signal Processing, IEEE Transactions on 'Vol.' 41, No. 12 1993, pp. 3445-62.

9. Said, A., and W. A. Pearlman. A New, Fast, and Efficient Image Codec Based on Set Partitioning in Hierarchical Trees. Circuits and Systems for Video Technology, IEEE Transactions on 'Vol.' 6, No. 3 1996, pp. 243-50.

10. Smith, M. J. T., and S. L. Eddins. Analysis/Synthesis Techniques for Subband Image Coding. Acoustics, Speech and Signal Processing, IEEE Transactions on 'Vol.' 38, No. 8 1990, pp. 1446-56.

11. Daubechies, Ingrid. Orthonormal Bases of Compactly Supported Wavelets Ii: Variations on a Theme. SIAM J. Math. Anal. 'Vol.' 24, No. 2 1993, pp. 499-519.

12. Skodras, A., C. Christopoulos, and T. Ebrahimi. The Jpeg 2000 Still Image Compression Standard. Signal Processing Magazine, IEEE 'Vol.' 18, No. 5 2001, pp. 36-58.

13. Kaul, V., J. Tsai, and R. Mersereau. A Quantitative Performance Evaluation of Pavement Distress Segmentation Methods. ASCE Journal of Transportation Engineering (submitted) 2008.


Common image compression formats

Technology

image processing figure

pearlman transform

transform block diagram

method ezw

spiht method

subband thresholds

method jpeg2000 similar

method important developments