Refined Measurement of Digital Image Texture Loss 

Peter D. BurnsBurns Digital Imaging

IS&T and SPIE Electronic Imaging Symposium, Jan. 2013

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Reference:P.D. Burns, Refined Measurement of Digital Image Texture Loss, Proc. SPIE Vol. 8653, Image Quality and System Performance X, 86530H, 2013

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Introduction

Texture-loss MTF using targets with random objects• Dead-leaves target analysis based on noise-power spectrum

Previously applied to image detail loss during; image capture, noise-cleaning, image compression

Method is based on noise-power spectrum (NPS) estimation

Practical measurement introduces random and bias estimation-error, e.g. non-stationary statistics

Common source can be corrected for, reducing measurement error

NPS, Texture MTF and computed acutance measures are improved

Acknowledgements: Uwe Artmann, Donald Baxter, Frédéric Cao, Herve Hornung, Norman Koren, Don Williams and Dietmar Wueller

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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

filterednoisy

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Texture MTF using Noise-power Spectrum*

Printed Test chart

Digital image

One-dimensional noise-power spectra

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Input target

JPEG 2000

Digital camera, image processing

____________________* Also called power spectral density

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Texture MTF

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Proposed method for camera evaluation (basic steps)

Acutancemetric

Camera under test

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Compute or model input NPS

Texture MTF(NPSout/NPSin )0.5 MTFtxt

Printed target

Transform to luminance

Dead leavestarget

Digitalimage

Compute output NPS*

___________________________* Computed NPS includes 2D FFT

and radial integration

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Noise-power Spectrum: meaning and measurement

• Noise-Power spectrum: for a random process, the NPS describes the fluctuations as a function of spatial frequency

Technically: Fourier transform of the spatial autocovariance

• Measurement: Average square of the Discrete Fourier Transform of a nominally uniform data array

Select data array

Compute2D FFT

Compute modulus squared

Basic steps for NPS estimation

1 or 2D

Vari

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frequencyo

FineCoarse

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Noise-power spectrum measurement

• Noise-power spectrum is a second-order parameter of a stochastic process

• NPS measurement is a statistical estimate that relies on stable (stationary) statistics

- constant mean and variance• Image nonuniformity (falloff) causes a bias error in

NPS estimates• Lens shading, lighting variation etc.

NPS error MTF error

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Variance estimation bias

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iii fxx 'Random signal plus trend

bias

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222 1Biased variance estimate

0.43 0.23Standard deviation

large ,22 Ns Variance estimate

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Bias error and improving estimation

•Estimation error can be measured

•If sources are known, estimates can be improvedExamples; instrument calibration, seasonal adjustments

•Nonuniform mean value biases noise estimatesVariance, standard deviation, noise-power spectrum

•Objective: design improved NPS estimate that is simple and benign (does not over-compensate)

•Instead of subtracting the sample mean value, subtract a 2D plane (linear fit) function

2D surface fit

Subtractsurface

Compute NPS

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Low-frequency NPS Bias

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2D surface fit

Subtractsurface

Compute NPS

Example for uniformStep noise field

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Signal

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After subtraction of 2d fit, plane, computed RMS noise reduced 7%

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output

2D fit

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Noise-corrected Texture NPS

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Texture signal

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Noise-corrected dead leaves NPS, with and without 2D linear trend removal

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Texture-MTF Results from Camera Testing

Mean relative error reduction (N=5 replicates) • All frequencies [0, 0.5 cy/pixel] 20%. • Low frequencies [0, 2.5 cy/pixel] 26%.

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no trend removal 2D-linear fit and subtraction

Final scaling was done at 0.02 cy/pixel

NPS error MTF error

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Summary

1. Noise-power spectrum (NPS) is a (second-order) statistical measure

2. Measuring a statistic is estimation

3. Good estimation relies on stable (stationary) population statistics

4. Image nonuniformity leads to NPS bias (positive at low frequencies) and variation

5. Simple 2D detrending (subtract a plane rather than a sample mean value) reduces bias and variation in the NPS estimate.

6. This is a pre-processing step that can be done before NPS estimation

7. This leads to reduced estimation error in the texture MTF, which is computed from (is a function of) two NPS estimates

NPS error Texture MTF error

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Conclusions

Proposed texture MTF analysis relies on noise-power spectrum (NPS) estimation

We investigated error introduced into NPS by non-stationary (mean) signal

Benign and simple correction two-dimensional by de-trending of image data array

Reduction in low-frequency bias and variation (20%)

pdburns@ieee.org

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Mobile camera example (not presented at EI)

• Test image files from N. Koren• NPS estimation with and without detrending• Very little difference

Camera A

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Camera B

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Camera comparison by texture MTF

Effective texture MTF, camera A is the reference (input). Acutance = 0.73

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NPS