ContentBased Compression of Mammograms with JPEG2000

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Content-Based Compression of Mammograms with
JPEG2000

• Chan, Hung Yam (Surene)
• Thesis Committee
• Prof. Hamed Sari-Sarraf (Chair)
• Prof. Sunanda Mitra
• Prof. Thomas F. Krile

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Overview

• Previous Work
• Idea of Content-Based Compression
• Focus-of-Attention Regions (FAR) Generation
• The JPEG2000 Compression Standard
• Content-Based Compression Strategies
• Previous Approach EZW AAC
• JPEG2000 BZIP2
• JPEG2000 ONLY
• Results
• Conclusions and Future Work

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Previous Work

• Min-Mo Sung (2002)
• Perform clinically evaluation of JPEG2000 (lossy)
  for digital mammography (PSNR, t-Test, and
  observer studies)
• T-Test No detectable differences at CR up to
  151 with confidence level of 99
• PSNR and observers studies little visual
  differences for CR as high as 801
• J. Wang and H. Wong (1996 1995)
• Applied different techniques to segment the
  breast from the background
• Compressed the breast regions with lossless or
  near lossless coder (achieves CR lt 101).

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Content-Based Compression (CBC)

• Segmentation
• Extract clinically important regions
  (Regions-of-Interest or Focus-of-Attention
  Regions)
• Compression
• FAR are compressed losslessly, achieving high
  fidelity.
• BG regions (i.e., non-FAR) are compressed
  lossily, achieving high CR.

Content-Based Compression of Mammogram in this
Thesis Segmentation fractal-based encoding
method to extract the significant
tissues Compression modified version of JPEG2000
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Content-Based Compression Strategies
Independent Lossless/Lossy Compression Engine for
FAR/BG
Image data
Single Compression Engine to achieve Lossless
FAR/ Lossy BG
Segmentation
Compression
FAR
storage/transmission
Image data
Output code-stream (lossless ROI/lossy BG)
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Fractal-Based Segmentation
Stop until Lmax has been reached
Reduce partition size for Ri and D
Unmatched
Ri
N
Pool of Ranges R
Y
Start at quadtree partition depth Lmin
Affine Transformation wi
Matched
Original Image
Di
Pool of Domains D
Go to next Ri
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Fractal-Based Segmentation

• The input mammogram is padded and divided into
  512x512, non-overlapping sub-images.
• Each sub-image is partitioned into domain and
  range pools (using quadtree partitioning starting
  at a minimum level of Lmin), and the optimal
  parameters of an affine mapping are computed for
  each domain-range pair.
• If the RMS error between the transformed pairs is
  less than a tolerance level, T, then the pairs
  are said to be similar.
• Otherwise, the range partition is further
  partitioned and the previous two steps are
  repeated until a maximum partitioning depth of
  Lmax has been reached.
• 5. Those sub-regions that do not satisfy the
  similarity condition along with their reduced
  8-neighbors are outputted to a binary mask file
  as FAR.

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Summary of Microcalcification Coverage

• Fifty, 10-bit mammograms with microcalcifications
  marked by expert radiologists
• Over 90 of microcalcifications are covered with
  around 15 of FAR

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Summary of Mass Coverage

• 130, 12-bit mammograms with masses from the
  University of South Floridas mammography
  database are studied
• Mass boundaries are not as clearly defined as in
  the case of microcalcifications
• Mass coverage can be roughly ranked into three
  groups1) good coverage, 2) marginal coverage,
  and 3) poor coverage
• Good coverage if there are sufficient intensity
  changes inside a mass
• Marginal coverage if there is significant
  contrast between the mass boundary and its
  background and hence the boundary is covered
• Over 83 of mammograms have at least the
  boundaries covered, with roughly an average 15
  of FAR contained in the mammograms

Suggestive summary on mass coverage for T19
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Example of Good Coverage
Irregular mass
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Example of Good Coverage
Focal-asymmetric-density-shaped mass
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Example of Good Coverage
Irregularly-shaped mass
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Example of Marginal Coverage
Irregularly-shaped mass
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Example of Marginal Coverage
Oval-shaped mass
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Example of Marginal Coverage
Lobulated mass
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Example of Poor Coverage
Lobulated mass
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Example of Poor Coverage
Lobulated mass
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Example of Poor Coverage
Lobulated mass
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What is JPEG2000?

• ISO/IEC standard for still image compression
  using wavelet transform
• Replaced JPEG with emphasis on coding efficiency
• Quality, resolution scalability
• Lossless to lossy progression
• Region-Of-Interest coding
• Error resilience when transmitting over
  error-prone channel
• Rate allocation

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JPEG2000 Compression Engine
Original Image Data
Pre-processing
Discrete Wavelet Transform (DWT)
Uniform Quantizer With Deadzone
Embedded Block Coder (Tier 1 Coding)

• Tiling
• Level Shifting
• Color Transformation

Rate Control
Bit-stream Organization (Tier 2 Coding)
Compressed Image Data (Code-stream)
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JPEG2000 Irreversible/Reversible Path
Image samples
Level Offset
Irreversible Path
ICT RGB gt YCbCr
Irreversible DWT Daubechies 9/7 Filter
Scalar, Uniform, Deadzone Quantizer
Reversible Path
RCT RGB gt YDbDr
Reversible DWT Le Gall 5/3 Filter
Ranging
To block coder
ROI Coding (Max-shift)
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Coding Efficiency of Mammograms

• EZW Embedded Zerotree Wavelets
• J2K IR JPEG2000 Irreversible Path
• J2K R JPEG2000 Reversible Path
• SPIHT R -- Set Partitioning in Hierarchical Trees
  using Reversible SP Transform
• SPIHT IR -- Set Partitioning in Hierarchical
  Trees using Irreversible wavelet Transform

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CBC Strategies

• Previous Approach (EZW AAC)
• AAC Adaptive Arithmetic Coding
• EZW Embedded Zerotree Wavelets

• Second Approach (J2K BZIP2)
• J2K IR JPEG2000 Irreversible Path
• BZIP2 a freely available, patent free,
  high-quality data compressor

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CBC Strategies

• Third Approach (J2K ONLY)
• J2K R JPEG2000 Reversible Path
• Max-Shift ROI Coding Method

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Region of Interest Mask Generation

• Process to transform ROI shape from spatial
  domain to WT domain
• Indicates which wavelet coefficients are
  responsible to reconstruct the shape losslessly
• ROI mask is calculated by tracing the DWT
  backward
• ROI grows a bit larger in shape in each
  resolution level

Inverse Le Gall 5x3 Wavelet Transform
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ROI Coding

• Two ROI coding methods
• the general scaling-based method (part 2)
• the max-shift method (part 1)

• General Scaling
• Method down-shifting BG quantized wavelet
  coefficients by an arbitrary number
• of bit-plane (say, s). Different ROI can have
  different scaling value, s.
• Pros Cons
• The importance of ROI and BG coefficients can be
  controlled by s.
• Multiple ROI with different quality differential
  are possible.
• Need ROI shape information during encoding.
• Limited ROI shape to rectangles and ellipse.

• Max-shift
• Method down-shifting BG coefficients in such a
  way that the maximum shifted BG
• is smaller than the un-shifted ROI coefficients.
• Pros Cons
• No need to put ROI shape information in
  code-stream
• Arbitrary-shape ROI is possible.
• Reduce coding efficiency by doubling the number
  of bit-plane for ROI code-block.
• No control over the ROI/BG quality differential.

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Problems on ROI Coding
Original mammogram
ROI Shape Generated by Fractal Encoding
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Problems on ROI Coding
Compressed with max-shift not applied on the
highest DWT level at CR 201, PSNR 40.15 dB,
ROI MSE 2.39
Compressed with max-shift applied on the entire
wavelet domain and reversible transform at CR
201, PSNR10.69dB, ROI MSE 2.34
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Lossless ROI with Max-shift ROI Coding
ROI coding passes
- K_max of bit-plane after max-shift - K_max
of bit-plane before max-shift
To ensure lossless ROI 1) Encoder should
distinguish ROI code-block from BG code-block 2)
ROI coding passes should prevent from truncation
in tier 2 entropy coding

• To ensure certain BG quality
• Max-shift is not applied on highest DWT level
• Truncation is not allowed in the LL subband
• For the other three subbands (i.e., HL, LH and HH
  subbands), truncation of the BG bit-stream is
  determined by EBCOT, while there is no truncation
  in the bit-stream of ROI code-blocks.

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Summary of J2K ONLY

• No Max-Shift
• No Truncation

3-Level, DWT
HL1
HL2
HL3
LL3

• No Max-Shift
• ROI bit-streams are not truncated
• BG bit-streams are truncated with EBCOT

HH3
LH3
HH2
LH2

• Perform Max-Shift
• ROI coding passes are not truncated
• -BG coding passes are truncated with EBCOT

LH1
HH1
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Content-based Compression with Modified JPEG 2000
Compressed with modified JPEG 2000 at CR 201
PSNR 40.42 dB ROI MSE 0
Arithmetic difference of original/compressed
images with histogram equalization.
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Results

• Three CBC Strategies
• EZW AAC
• J2K BZIP2
• J2K ONLY
• Three Sets of Mammograms
• Fifty, 10-Bit, digitized mammograms with
  microcalcifications from the University of
  Chicago
• 130, 12-Bit, digitized mammograms with masses
  from the University of South Florida
• Fifteen, 8-Bit, digital mammograms from the
  University of North Carolina

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Results

• Fixing T, varying BG quality

Film-based Digitized Mammograms
Percentage of FAR Avg. (13.72), Max (44.57),
Min (5.18) Average 93.15 microcalcification
coverage
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Results
Film-based Digitized Mammograms
Percentage of FAR Avg. (14.54), Max (44.33),
Min (2.77) Over 83 of images have at least
the mass boundaries covered
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Results
Digital Mammograms
Percentage of FAR Avg. (15.71), Max (29.32),
Min (4.17)
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Results
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Results
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Results
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Results
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Pros Cons of Our Modifications

• J2K BZIP2
• Full control of the background quality through
  specifying the final bit-rate for the JPEG2000
  irreversible path.
• An overall good PSNR-CR performance for both
  digitized and digital mammograms.
• Lossless and lossy compression engines are
  independent and, thus, there is no control over
  the final bit-rate.
• More complicated compression/decompression
  processes, since it has independent compression
  engines.

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Pros Cons of Our Modifications

• J2K ONLY
• Achieves lossless coding of FAR and lossy coding
  of the background within a single compression
  engine.
• Code-stream conforms to the JPEG2000 standard
  and, thus, any JPEG2000 decoder can be used for
  decompression.
• Preserves all the merits of the JPEG2000 standard
• Has excellent performance on digital mammograms.
• There is an upper bound on CR since the ROI
  coding passes are prevented from truncation.
• The PSNR performance is not as good as the J2K
  BZIP2 for digitized mammograms with lower
  percentage of FAR or at higher compression ratios.

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Future Work

• Investigate a reversible wavelet filter that has
  better coding efficiency than the current Le Gall
  5/3 wavelet filter.
• Explore newer ROI coding methods to replace
  max-shift 1) BbBShift (Bitplane-by-Bitplane
  Shift), and 2) PSB Shift (Partial Significant
  Bitplanes Shift).
• Restrict FAR to only the breast regions.
• Perform observer studies on the CBC results.

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Questions?
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1-Level DWT
LL1
LH1
HL1
HH1
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2-Level DWT
LH2
LL2
LH1
HH2
HL2
HH1
HL1
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3-Level DWT
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Uniform Quantizer with Deadzone
Quantization Rule

• qbn - the output quantization index in subband
  b
• ybn - the input wavelet coefficient in subband
  b
• ?b - the quantization index in subband b
• ? - the base step size adjusted to achieve a
  desired overall compressed bit-rate
• Gb - the squared norm of the DWT synthesis basis
  vectors for subband b

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Uniform Quantizer with Deadzone
Dequantization Rule
When qbn?0
When qbn0

• qbn - the input quantization index in subband b
• ?bn - the output wavelet coefficient in subband
  b
• ?b - the quantization index in subband b
• ?b lies on the range of 0,1) and ?b ½
  corresponds to a mid-point reconstruction
• If p least significant bit is truncated, the step
  size ?b.2p

Wavelet coeff.83, ?b 4 qbn 83/4 20
00010100 ?bn(200.5)482 If six bit was
coded qbn 0001015 ?bn(50.5)4.2288 ?bn
(50.3)4.2284.8
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Embedded Block Coder (Tier 1)
Context-based Adaptive Binary Arithmetic Coder
Code-block
64x64 samples
Compressed bit-stream
Significant propagation pass
Magnitude Refinement Pass
Clean-up Pass

• Three sub-bitplane coding passes are generated
  for each bitplane of each code-block
• Totally 3k-2 coding passes for each bit-stream (k
  - the no. of bitplane for a code-block)
• Lz, the length in bytes of including coding pass,
  z, is calculated using the internal state
• of the arithmetic coder
• Dz, the distortion (MSE) by which including
  coding pass Pi(z,k) reduces in distortion,
• is estimated

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Post-Compression Rate-Distortion Optimization
(Tier 2)
Total distortion after truncating z passes
Length Constraint
To find a set of possible truncation points zi,
? for each bit-stream
?gt0
The quantity, ?, can be defined as the
interpretation of distortion-length slope
0 ? zlt z

• To find the set of feasible truncation points
• is equivalent to find the convex hull of the
• Distortion-Length curve.
• The truncation points are optimal in the
• sense that the distortion, D, cannot be further
• reduced without also increasing the length, L.
• The encoder iteratively tries different values
• of ? such that the length constraint is met.

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Quality Layers (Tier 2)

• a collection of some consecutive coding passes
  from each code-block in each
• subband and component
• Each code-block can contribute an arbitrary
  number of coding passes to a layer
• and each layer successively increases the image
  quality.
• in some quality layers, the contribution of
  certain code-blocks can be empty

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Precinct and Packets (Tier 2)

• A precinct contains one or more code-blocks
• Precinct is the basic unit of the packet
• The code-block size from a resolution level is
  constrained by precinct size
• Packet contains compressed data from a specific
  tile, layer, component, resolution level and
  precinct.

Packet Progression Layer resolution level
component position Resolution level layer
component position Component position
resolution level layer Resolution level
position component layer Position
component resolution level layer