Presentation at the Electronic Imaging Symposium, Jan. 2012

1. Measurement of Texture Loss
for JPEG 2000 Compression
Peter D. Burns and Don Williams*
Burns Digital Imaging and *Image Science Associates
Full paper available here
Presented at IS&T and SPIE Electronic Imaging Symposium, Jan. 2012
© copyright 2012 Peter D. Burns

2. Introduction
MTF established as a metric for the capture and
retention of image detail
Texture-loss MTF using targets with random objects
• Dead-leaves target analysis based on noise-power
spectrum
We apply this method to image detail loss during
image compression
Adapt method when printed test target is not used
Compare results for JPEG2000 and JPEG with
Structured Similarity Index (SSIM)
IS&T and SPIE Electronic Imaging 2012 2

3. Dead-Leaves MTF Measurement
Aimed at providing an effective MTF for image fluctuations (signals)
influenced by adaptive or signal-dependent image processing
• e.g., adaptive noise cleaning, which could leave edge untouched, but
reduce detail in important ‘textured regions’
Being developed as part of the CPIQ Initiative
Based on input and output Noise-power spectrum
noisy filtered
IS&T and SPIE Electronic Imaging 2012 3

4. Texture MTF using Noise-power Spectrum*
Printed Digital
Test image
Digital camera,
chart image processing
4
10
Input target
JPEG 2000
Texture MTF
3
10
Power Spectrum
2
1
10
0.8
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
MTFtxt
Frquency, cy/mm 0.6
One-dimensional Noise-power 0.4
spectra
0.2
____________________ 0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
* Also called power spectral density Frquency, cy/mm
IS&T and SPIE Electronic Imaging 2012 4

5. Noise-power Spectrum: meaning and measurement
• Noise-Power spectrum: for a random process, the NPS describes
the fluctuations as a function of spatial frequency
Variance/frequency
Technically: Fourier transform of the
spatial autocovariance
• Measurement:
Average square of the Discrete Coarse Fine
Fourier Transform of a nominally o frequency
uniform data array
Basic steps for NPS estimation
Select data Compute Compute modulus
array 2D FFT squared
1 or 2D
IS&T and SPIE Electronic Imaging 2012 5

6. Proposed Dead-Leaves MTF Measurement
Recipe:
Transform the captured image data to luminance
Compute the power-spectral density as the square of
the amplitude of the two-dimensional DFT of the
array
Divide this array, frequency-by-frequency, by the
spectrum for the input target
Compute the square-root, frequency-by-frequency
Radial-average of this array is the one-dimensional
MTF vector
Compute (visually -weighted) acutance measure
IS&T and SPIE Electronic Imaging 2012 6

7. Proposed method for camera evaluation (basic steps)
Printed target Transform to
Digital image
luminance
Model target signal 1. Compute corrected
spectrum, Starget signal spectrum
signal spectrum
1
2. Texture MTF
0.8
MTFtxt
0.6
0.4
0.2
texture MTF 0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Frquency, cy/mm
3. Texture acutance Acutance
metric metric
IS&T and SPIE Electronic Imaging 2012 7

8. Modified method (details)
Input image
Transform to
Output image
luminance
Measured input signal
spectrum, Starget 2D FFT 2D FFT 10
4
Input target
JPEG 2000
Signal Noise
spectrum spectrum
1. Compute corrected 10
3
Power Spectrum
signal spectrum S signal − S noise
2
10
Radial integration 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Frquency, cy/mm
2. Texture MTF Corrected signal spectrum
'
R = S signal / Starget 1
0.8
MTFtxt
0.6
R( v ) 0.4
0.2
MTFrad ( v ) 0
0 0.05 0.1 0.15 0.2 0.25 0.3
Frquency, cy/mm
0.35 0.4 0.45 0.5
3. Texture acutance v max
∑ MTFrad ( v ) M ( v ) CSF ( v ) Acutance
metric v =1 metric
Visually-weighted summation*
___________
* Display MTF and viewing distance IS&T and SPIE Electronic Imaging 2012 8

9. Application to Image Compression
Input ideal
image
Optical MTF
CFA Detector CFA Image
3 subsampling 1 noise 1 interpolation 3 Compression
Simulated
Image capture simulation captured image
IS&T and SPIE Electronic Imaging 2012 9

10. JPEG 2000 and JPEG compression
JPEG2000: kdu_compress, from Kakadu Software
JPEG: as implemented in Matlab
Default settings for 24-bit color images
Compression ratios: up to 140:1
Example:
input 40:1 100:1
IS&T and SPIE Electronic Imaging 2012 10

11. Example texture MTF
4
10
Input target
JPEG 2000
1
3 0.8
10
Power Spectrum
txt
0.6
MTF
0.4
2
10
0.2
0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Frquency, cy/mm Frquency, cy/mm
Results for 100:1 compression, and the corresponding texture MTF.
acutance = 0.82
IS&T and SPIE Electronic Imaging 2012 11

12. Comparison with Structured Similarity Index, SSIM
1.05
JPEG 2000
1 JPEG
• objective measure of image quality
0.95
• based on image differences
0.9
• visual-difference map, based on a
Texture acutance
0.85
model of visually information
0.8
• average value of the difference image
0.75
is reported as the SSIM.
0.7
Wang, Z., Bovik, A.., Sheikh, H., and Simonelli, E.,
IEEE Trans. Image Processing, (2004) 0.65
0.6
0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
SIMM value
JPEG 2000 JPEG
Compression Bits/pixel/ Texture SSI index Texture SSIM index
rate color acutance acutance
30 0.80 0.986 0.939 1.02 0.939
40 0.60 0.950 0.924 0.991 0.922
50 0.48 0.951 0.920 0.961 0.904
60 0.40 0.859 0.908 0.930 0.886
80 0.30 0.826 0.884 0.890 0.844
100 0.24 0.819 0.865 0.841 0.790
120 0.2 0.796 0.835 0.777 0.742
140 0.17 0.731 0.799 0.667 0.667
IS&T and SPIE Electronic Imaging 2012 12

13. Summary
Many practical objective image quality measurements can be
considered as estimates, with bias error and variation
The proposed texture MTF analysis relies on noise-power
spectrum estimation
We investigated texture-loss due to JPEG 2000 and JPEG
compression
Modified method was developed;
• Direct input signal spectrum measurement (estimation)
• Not dependent on known printed target spectrum
Results indicated stable texture MTF and acutance without date
smoothing or fitting
Compared well with Structured Similarity Index, SSIM
• an offset between the JPEG and JPEG 2000 images sets
pdburns@ieee.org
IS&T and SPIE Electronic Imaging 2012 13

14. Appendix: Example MTF based on Edge SFR and texture NPS
inp t
u
Edge SFR
ou u
tp t
1 1
0.8 0.8
FR
TF
0.6 0.6
M
S
0.4 0.4
0.2 0.2
0 0
0 0 5
.0 0.1 0.15 0 .2 0 5 0
.2 .3 0.3 5 0.4 0 5
.4 0.5 0 0 5
.0 0.1 0.15 0 .2 0 5 0
.2 .3 0.3 5 0.4 0 5
.4 0.5
Sp l fre e cy, cy/pixe
atia qu n l Sp l fre e cy, cy/pixe
atia qu n l
___ Texture
Comparison with Texture 1 - - - Edge
MTF: Results for 100:1
compression ratio
0.8
txt
0.6
MTF
0.4
0.2
0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Frquency, cy/mm
IS&T and SPIE Electronic Imaging 2012 14