A Review in Quality MeasuresA Review in Quality Measuresfor for

Halftoned ImagesHalftoned Images

Student Per-Erik Axelson

04/22/23 Ph.D. Course in Digital Halftoning 2

Image Quality

Subjective QualitySubjective Quality– Subjective test (MOS): Best way so far to assess and judge

image quality– This method is to inconvenient, slow and expensive for

practical usage

Objective Quality MeasuresObjective Quality Measures– The goal of objective image quality assessment research is to

supply quality metrics that can predict perceived image quality automatically

04/22/23 Ph.D. Course in Digital Halftoning 3

Most important demandMost important demand– In General, we want binary image to match continuous-tone

original as closely as possible

Objective Image QualityObjective Image Quality Image quality paradigmImage quality paradigm

Original Image Reproduced Image

04/22/23 Ph.D. Course in Digital Halftoning 4

Objective Image QualityObjective Image Quality

A number of demandsA number of demands

– The method should be able to evaluate all kinds of halftones and provide a meaningful comparison across different types of image distortions

– The method should return measures for several aspects of quality that are well correlated with results from subjective tests

– The method should be easy to calculate and have low computational complexity

04/22/23 Ph.D. Course in Digital Halftoning 5

Objective Image QualityObjective Image Quality

Useful applicationsUseful applications

– Be used to monitor image quality for quality control systems

– Be employed to benchmark halftoning algorithms

– Be embedded into an image processing system to optimize the algorithms and the parameter settings

04/22/23 Ph.D. Course in Digital Halftoning 6

Objective Image QualityObjective Image Quality

Two classes of objective quality assessmentTwo classes of objective quality assessment

1.1. Mathematically defined measuresMathematically defined measures

– Methods based on the Mean Square Error (MSE)

2. Models of the human visual system (HVS)2. Models of the human visual system (HVS)

– Methods using the contrast sensitivity function (CSF)

04/22/23 Ph.D. Course in Digital Halftoning 7

Image Quality Error MetricsImage Quality Error Metrics

FunctionFunction– Derive measure from the point-wise difference between

original and the binary halftone

– In general, using a fixed threshold at midpoint DefinitionDefinition

2

,

)),(),(( ji

jiyjixMSE ji

NMMSERMS,

)(

ji

jiyjixMNDPSNR

,

2

2

10 ),(),(log10)dB(

ji

ji

jiyjix

jixSNR

,

2,

2

10 ),(),(

),(log10)dB(

binary),(original),( jiyjix

04/22/23 Ph.D. Course in Digital Halftoning 8

Image Quality Error MetricsImage Quality Error Metrics

White NoiseSNR = 10 dB

PSNR = 15,7 dB

High-pass NoiseSNR = 10 dBPSNR = 15.7

Correlation between MSE, SNR or PSNR and Correlation between MSE, SNR or PSNR and visual quality is known to be poorvisual quality is known to be poor

– Treats all errors with an equal weight

04/22/23 Ph.D. Course in Digital Halftoning 9

Human Visual SystemHuman Visual System

Complicated Non-linear and spatially varyingComplicated Non-linear and spatially varying

– Assuming linearity and spatial invariance

– The human perception system do not have equal response to all spatial frequencies

– As the spatial frequencies become higher and higher, our ability to perceive the pattern will be lower and lower

– It turns out that our ability to perceive very low frequency patterns also decreases as the frequency decreases

– These characteristics can be captured using a contrast sensitivity function (CSF)

04/22/23 Ph.D. Course in Digital Halftoning 10

– Object image by the eye

Visual angle:

Human Visual ResponseHuman Visual Response– Sensitivity depends on angular frequency subtended at eye– Compute angular frequency from image size (pixels), printed

image size (mm), viewing distance (mm)

radians2

tan2 1

dl

dl

degreecycles360l

dNaf

At Nyquist frequency:

image theacross radians,N

04/22/23 Ph.D. Course in Digital Halftoning 11

Contrast Sensitivity FunctionContrast Sensitivity Function– Band-pass model [Mannos & Sakrison 1974]– Modified to low-pass [Mitsa & Varkur 1993]

1.1)1.0(exp()1.002.0(6,2)( aaa fffH

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– Angular dependence in CSF [Sullivan, Miller & Pios 1993]– Mild-drop in visual sensitivity in diagonal directions– The decreased sensitivity along the diagonals and the flattening at

low angular frequencies are visible

Contrast Sensitivity FunctionContrast Sensitivity Function

04/22/23 Ph.D. Course in Digital Halftoning 13

Weighted SNR MetricWeighted SNR Metric Weighted SNR by CSFWeighted SNR by CSF

– WSNR measures appropriate when noise is additive and signal independent

vu

vu

vuCvuYvuX

vuCvuX

,

2,

2

10),(),(),(

),(),(log10)dB(WSNR

– Where X(u,v), Y(u,v) and C(u,v) represent the DFT of the inputimage, output image and CSF, respectively

04/22/23 Ph.D. Course in Digital Halftoning 14

WSNRWSNR To find WSNRTo find WSNR

– Generate unsharpened halftone using modified error diffusion [Eschbach & Knox 1991]

– Compute WSNR of unsharpened halftone relative to original image

04/22/23 Ph.D. Course in Digital Halftoning 15

A Universal Image Quality IndexA Universal Image Quality Index Main FeaturesMain Features

– New Philosophy: switch from error measurement to structural distortion measurement

– Mathematically defined and no HVS model is explicitly employed

– Universal: Applicable on various image-processing applications and provide a meaningful comparison across different types of image distortions

– Easy to apply on images

– Low computational complexity

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A Universal Image Quality IndexA Universal Image Quality Index Application to ImagesApplication to Images

– Compare difference between the original and the binary image

– Measure statistical features locally and then combine them together

– Sliding window (size 8 8) approach in local region, leading to a quality map

– The index value is the average of the quality map

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A Universal Image Quality IndexA Universal Image Quality Index

22222222

2)()(

2])())[((

4

yx

yx

yx

xy

yx

xy

yxyx

yxyx

Q

DefinitionDefinition

1 2 3

Combination of three factorsCombination of three factors

1. Loss of Correlation (Linear correlation between x and y)

2. Luminance Distortion (Mean luminance between x and y)

3. Contrast Distortion (Variance contrast (signal) between x and y)

Q : Dynamic range [-1, 1]