– Digital image acquisition, classes of images – Image quality assessment – Simple image features and their application – Image filtering in the spatial and spectral domains – Extracting certain features of images (corners, circles, edges) – Exemplary applications

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Advanced Digital Image
Processing:
problems, methods
and applications
Paweł Forczmański
Chair of Multimedia Systems, Faculty of Computer Science and Information Tech-
nology, West Pomeranian University of Technology, Szczecin
Vilnius University, Institute of Mathematics
and Informatics, 18/04/2016

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AgendaAgenda
Introduction (objectives, problems,
image classes, acquisition)
Introduction (objectives, problems,
image classes, acquisition)
Image filtering methodsImage filtering methods
Image quality estimation (concpets,
exemplary metrics)
Image quality estimation (concpets,
exemplary metrics)
Simple image features and their applicationSimple image features and their application

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Computer
graphics
Data processing
Signal
processing
Digital image
processing
Pattern recognition
IntroductionIntroduction

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DIP: Application AreasDIP: Application Areas
OCR
Criminal
Forensic
CAD
Robotics
GIS
Media and
Entertainment
CT
MRI USG
Bar
codes
Text
processing

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ObjectivesObjectives
Image
quality
improvement
compression
Image
representation
transformation
Objective
(computer)
transmission
Subjective
(human)
coding
storing
Image
quality
improvement

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Image classesImage classes

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. . .
M
N
K
. . .
Tyical color image is in a raster form
which has:
M columns
N rows
i K layers:
Sample image with
MxNx3 (YUV color-
space)
Data representation (1)Data representation (1)










 

kNMkM
kNk
k
NM
Kk
xx
xx
X
,,,1,
,,1,1,1




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Light sensors matrixLight sensors matrix
cones cones
cones
rods
Bayer matrix
Human eye

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Bryce Bayer - patent (U.S. Patent No. 3,971,065) - 1976
MegaPixels?MegaPixels?

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Bayer Matrix vs Foveon X3Bayer Matrix vs Foveon X3

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Image acquisitionImage acquisition
quantization
discretization
Digital image
quantization quantization
discretization
discretization

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Nadajnik Trans. channel
Signal quality
estimation
Source
Reconstruction and
presentation
Perception and un-
derstanding
processing, storing and
transmission
Acquisition and
registration
Signal source
Knowlegde
about distortions
Knowlegde about
receiver and application
Knowlwdge about
source and transmitter
Receiver
➔ Imaging systems can introduce certain signal distortions or artifacts, there-
fore, it is an important issue to be able to evaluate the quality.
Quality estimationQuality estimation

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The quality of an image can be reduced during
●
Image acquisition
●
Image transmisson
●
Image processing
Quality measure may be a determinant of quality degradation
Classification of methods I:
perceptual (perceptive, subjective)
objective (calculative).
Classification of methods II:
Scalar-based,
Vector-based (sets of scalars)
Classification of methods III:
Full-reference,
No-reference,
Partial-reference
Image QualityImage Quality

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• Related works
– Pioneering work [Mannos & Sakrison ’74]
– Sarnoff model [Lubin ’93]
– Visible difference predictor [Daly ’93]
– Perceptual image distortion [Teo & Heeger ’94]
– DCT-based method [Watson ’93]
– Wavelet-based method [Safranek ’89, Watson et al. ’97]
Philosophy:
degraded signal = reference signal + error
reference signal → ideal
quantitive estimation of distortions level
Standard model of IQA:
Image Quality AssessmentImage Quality Assessment

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Motivation – simulating elementary characteristics of HVS
Main features:
Channel decomposition  linear transformation
Frequency weigthing  contrast sensitivity function
Masking  intra-channel interactions
Reference
signal
Evaluation
Channel
decomposition
Error
normalization.
.
.
Aggregation
Pre-
processing
.
.
.


/1
, 





 l k
kleE
Evaluated
sugnal
Standard model of IQAStandard model of IQA
(Image Quality Assessment)(Image Quality Assessment)

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+
+
_
= + +...
...
structural
distortion
+
distorted
image
original
image
= + +
+
nonstructural
distortion
cK+1
.
c1
.
cK+2
.
c2
.
cM
.
cK
.+
+
nonstructural distortion
components
structural distortion
components
Standard model of IQA (Image QualityStandard model of IQA (Image Quality
Assessment): Adaptive Linear SystemAssessment): Adaptive Linear System

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Structural content
Normalized Cross-Colerraltion
Peak Absolute Error (PAE)
Image Fidelity
Average Difference

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Mean Square Error
Zhou Wang and Alan C. Bovik, Mean Squared Error: Love It or
Leave It? A New Look at Signal Fidelity Measures, IEEE Signal
Processing Magazine vol. 26, no. 1, pp. 98-117, Jan. 2009

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Peak Mean Square Error
Normalized Absolute Error
Normalized Mean
Square Error
Lp
norm (Minkowski)
Peak Signal-to-Noise Ratio
Signal-to-Noise Ratio

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RMSE 9.5
(blurred)(blurred)
RMSE 5.2
Pixel by Pixel ComparisonPixel by Pixel Comparison
Prikryl, 1999

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X. Shang, “Structural similarity based image quality assessment: pooling strategies and ap-
plications to image compression and digit recognition” M.S. Thesis, EE Department, The
University of Texas at Arlington, Aug. 2006.
Structural Similarity (SSIM) IndexStructural Similarity (SSIM) Index

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i
k
j
x
xi
+ xj
+ xk
= 0
x - x
O
luminance
change
contrast
change
structural
change
xi
= xj
= xk
),(),(),(),( yxyxyxyx sclSSIM 
1
22
12
),(
C
C
l
yx
yx





yx
c(x , y)=
2 σx σ y+C2
σx
2
+ σ y
2
+C2
3
3
),(
C
C
s
yx
xy





yx
[Wang & Bovik, IEEE Signal Processing Letters, ’02]
[Wang et al., IEEE Trans. Image Processing, ’04]
Structural Similarity (SSIM) IndexStructural Similarity (SSIM) Index

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MSE=0, MSSIM=1 MSE=225, MSSIM=0.949 MSE=225, MSSIM=0.989
MSE=215, MSSIM=0.671 MSE=225, MSSIM=0.688 MSE=225, MSSIM=0.723
Zhou Wang Image Quality Assessment: From Error Visibility to Structural Similarity
MSE vs mSSIMMSE vs mSSIM

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original
image
JPEG2000
compres-
sed image
absolute
error
map
SSIM index
map

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original
image
Gaussian
noise cor-
rupted
image
absolute
error
map
SSIM index
map

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original
image
JPEG com-
pressed
image
absolute
error
map
SSIM index
map

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Zhou Wang and Alan C. Bovik, Mean Squared Error: Love It or Leave It? A New Look at Signal Fidelity Measures, IEEE Signal Processing
Magazine vol. 26, no. 1, pp. 98-117, Jan. 2009
Comparison of quality measuresComparison of quality measures

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Image
2
Image
1
Psychometric
Function
Probability
Summation
Visualisationof
Differences
Amplitude
Nonlinear.
Amplitude
Nonlinear.
Contrast
Sensitivity
Function
Contrast
Sensitivity
Function
+
Cortex
Transform
Cortex
Transform
Masking
Function
Masking
Function
Unidirectional
or Mutual
Masking
[Daly ‘93, Myszkowski ‘98]
Visible Differences Predictor (VDP)Visible Differences Predictor (VDP)
➔ Predicts local differences between images
➔ Takes into account important visual charac-
teristics:
➔ Amplitude compression
➔ Advanced CSF model
➔ Masking
➔ Uses the cortex transform, which is a pyra-
mid-style, invertible & computationally effi-
cient image representation

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VDP: ResultsVDP: Results
Reference
Analysed
Pixel differences:
Reference - Analysed
Pixel differences
The VDP response:
probability of
perceiving
the differences
VDP response

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image
f(x,y)
Conversion
to digital form
Image
pre-processing
Features
extraction
Conversion to output
form
Output image
Features
DIP schemeDIP scheme
local transform
point transform
global transform

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f(x)
x
b
H(b)
180 200 220 240
0
50
100
e
H(e)
180200220240
0
50
100
Histogram stretching along a defined
line changes the distribution of in-
tensities in an image by the alterna-
tion of intensity assignment in each
interval
Each interval changes its width:
where
b –pixel intensity before:
e –pixel intensity after stretching;
f(b) –stretching function.
The tangent of an angle of function
f(b) is the coeficient that changes the
width of each histogram interval
d e= f 'bd b
Histogram modellingHistogram modelling

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The most simple is a linear stretching:
Where a can is equal to:
where
x1
, x2
– boundaries of intensity.
E – maximum possible intensity
f (x)=
{
0 for x<0
ax
E for x>E
a=
E
x2−x1
Simple linear caseSimple linear case
50 100 150 200
0
1000
2000
3000
b
H(b)
f(x)
x
50100150200
0
1000
2000
3000
e
H(e)
x1
x2

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histogramSource image
Non-linear cases (examples)Non-linear cases (examples)

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It usually increases the global contrast of images, especially when the usable
data of the image is represented by close contrast values.
Through this adjustment, the intensities can be better distributed on the histo-
gram. Areas of lower local contrast gain a higher contrast.
Histogram equalizationHistogram equalization
0 2 4 6 8
0
1
2
3
b
H(b)
mean
0 2 4 6 8
0
1
2
3
e
H(e)
mean

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Work in RGB spaceWork in RGB space
originalRGB equalized

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Work in HSL spaceWork in HSL space
HSL equalized

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RGB and HSL comparisonRGB and HSL comparison
original RGB equalized HSL equalized

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One-dimensional histogram if defined by function f :
f : X×Y  Z
f
−1
: Z  2
X ×Y
f
−1
: {x , y∣f x , y=z }
1D vs 2D histogram1D vs 2D histogram
Two-dimensional histogram if defined by functions f and g :
f : X×Y  Z
g : X ×Y  V
f −1
: Z  2 X ×Y
g−1
: V  2 X ×Y
f −1
: {x , y∣f x , y=z }
g−1
: {x , y∣gx , y=v}

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There are many 2D histograms! One of the most useful is coocur-
rence matrix
M 1=
[
0 0 0 0
0 1 1 1
0 1 2 2
0 1 2 3
];
z=[0123] ;
H1(z)=[7531];
M 2 =
[
1 3 2 0
2 0 1 0
1 0 2 0
0 0 1 1
];
z=[0 1 2 3 ];
H 2z=[7 5 3 1];
Co-occurrence matrixCo-occurrence matrix
r={x , y,x , y1};
Cr=H fg z ,v;
f x , y=gx , y1;
Cr1
=
[
3 3 0 0
0 2 2 0
0 0 1 1
0 0 0 0
]; Cr2
=
[
1 2 1 0
2 1 0 1
3 0 0 0
0 0 1 0
];
← 1D Histograms →
← 2D Histograms →

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Example of calculation on real image – it helps when we want to
tell if the image is crisp or blurred
ExampleExample

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exampleexample
Intensity thresholding
for
for

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In digital image processing convolutional filtering plays an
important role in:
➔
Edge detection and related processes;
➔
Sharpening;
➔
Blurring;
➔
Special effects (motion blur)
➔
Etc...
Traditional computing (sequential programming);
Parallel computing (mult processors/cores, GPU: „stencil
computing”).
Convolutional filteringConvolutional filtering

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In practice, f and g are vectors or matrices with discrete values, and integral
operator is changed into sum.
Convolutional filteringConvolutional filtering
h[ x]=∑
t=t1
t=tn
f [x−t]g [t ]
f1
f2
f3
f4
f5
f6
f7
f8
g3
g2
g1
* * *
h1
h2
h3
h4
h5
h6

norm
(window .*mask)
norm
f ∗g=∫−∞
∞
f (x−t)g(t)dt

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1
1
1
1 1
1 1
1 1
Norm=9
1
1
1
1 1
2 1
1 1
Norm=10
1
1
1
1 1
3 1
1 1
Norm=11
0
1
0
0 0
1 1
0 0
Norm=3
Averaging filterAveraging filter
1
1
1 1
1
Norm=5
1
1
1
1
1
Norm=5
1
1
1
1 1
1 1
1 1
1
1
1
1 1
1 1
1 1
Norm=21
1
1
1

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An image f is filtered with a mask gσ which is a discrete appro-
ximation of two-dimensional Gauss function:
Gauss filteringGauss filtering
decides about
blurring effect

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Edge detectionEdge detection
Edges can be detected using various gradient operators:
➔
First derivative of an image shows the edge and its direction
➔
Point of sign change of second derivative (zero crossing), can also be
used to detect edges
The main problem is false detection, which comes from the amplification of
noise!
Second
derivative
image
Intensty
projection
First
derivative
The edge is a local change in image intensity and its vertical (or
horizontal) projection can look like that presented above

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8 2 222
Horizontal lines Vertical lines+45o -45opoint detection
Line detectionLine detection

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ow( j ,k)=√[ A4− A8 ]
2
+[A5− A7 ]
2 0
Roberts vs PrewittRoberts vs Prewitt
A0
A1
A2
A3
A4
A5
A6
A7
A8
ow  j ,k =X 2
Y 2
X =A2 2 A3 A4 −A0 2 A7 A6 
Y =A0 2 A1 A2 − A6 2 A5  A4 
ow
(j,k)
ow
(j,k)
Roberts filtering
Prewitt filtering

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Prewitt vs SobelPrewitt vs Sobel
PrewittPrewitt SobelSobel

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Laplace operator (Laplasian) is defined as a second derivative
of image f at the location (x,y)
Z1
Z2
Z3
Z4
Z5
Z6
Z7
Z8
Z9
Laplace operatorLaplace operator
or

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ow( j ,k)=max
{1, max
i∈〈0 ;7〉
∣5Si −3Ti∣
}
Si =Ai + Ai+1+ Ai +2
Ti= Ai+3+ Ai+ 4+ Ai+ 5+ Ai+6+ Ai+7
i∈〈0 ;7〉
indexes change modulo 8
KirschKirsch
where

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Szczecin
Canny edge detectorCanny edge detector
➔
multi-stage algorithm to detect a wide range of edges in
images
➔
developed by John F. Canny in 1986
➔
Canny also produced a computational theory of edge
detection explaining why the technique works.
An "optimal" edge detector means:
good detection – the algorithm should mark as many real
edges in the image as possible.
good localization – edges marked should be as close as
possible to the edge in the real image.
minimal response – a given edge in the image should only
be marked once, and where possible, image noise should not
create false edges.

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Faculty of Computer
Science and
Information
Technology
West Pomeranian
University of
Technology,
Szczecin
1. Image smoothing using Gaussian
2. Derivatives calulation using masks: [-1 0 1] i [-10
1]'.
Canny Edge DetectorCanny Edge Detector

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Faculty of Computer
Science and
Information
Technology
West Pomeranian
University of
Technology,
Szczecin
3. Non-maximum suppression as an edge thin-
ning technique.
A 3x3 filter is moced over an image and at every lo-
cation, it suppresses the edge strength of the center
pixel (by setting its value to 0) if its magnitude is
not greater than the magnitude of the two neigh-
bors in the gradient direction
4. Tracing edges through the image and hy-
steresis thresholding
Canny Edge DetectorCanny Edge Detector

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Faculty of Computer
Science and
Information
Technology
West Pomeranian
University of
Technology,
Szczecin
Non-linear filteringNon-linear filtering
Output image's pixels result from a nonlinear
transform of input image's pixels and a filter
mask
Example: Media filter
Input set: A={9,88,1,15,43,100,2,34,102} Sort elements in A (increasing➔
order): B=sort(A)
B={1,2,9,15,34,43,88,100,102} Select median of B (middle element):➔
median(B)=34

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Faculty of Computer
Science and
Information
Technology
West Pomeranian
University of
Technology,
Szczecin
Non-linear filteringNon-linear filtering

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Faculty of Computer
Science and
Information
Technology
West Pomeranian
University of
Technology,
Szczecin
Adaptive filteringAdaptive filtering

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Faculty of Computer
Science and
Information
Technology
West Pomeranian
University of
Technology,
Szczecin
Detecting charactersitic pointsDetecting charactersitic points
Objects/scene detection can be based on detecting charac-
teristic points
●Matching point Pij
in the image j to the point Pik
in the image k
●Removing false candidates
● Certain points Pij
in the image j have no corresponding points Pik
in the image k
●Ambiguity
● Several points Pij
in the image j correspond to a point Pik
●Noise

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Faculty of Computer
Science and
Information
Technology
West Pomeranian
University of
Technology,
Szczecin
How?How?
Corner operator is one solution...

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Faculty of Computer
Science and
Information
Technology
West Pomeranian
University of
Technology,
Szczecin
IdeaIdea
It is a possibility that such interesting point may be
detected by looking at the image through some
small window.
By sliding this window over the image we can de-
tect significant changes in intensity in a certain di-
rection
●
Morevec detector
●
Harris detector

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Faculty of Computer
Science and
Information
Technology
West Pomeranian
University of
Technology,
Szczecin
Moravec detectorMoravec detector
There are 3 cases:
●
If an area is uniform (flat), the dif-
ferences calculated in all directions
will be not significant
●
If it is an edge, the diferences
along its direction will be small,
while in the perpendicular direction
– large
●
If there is an isolated point, the di-
ferences in most of directions will
be significant
●
Finally, the maxima of points with
the highest differences are selected
flat edge
corner
isolated point

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Faculty of Computer
Science and
Information
Technology
West Pomeranian
University of
Technology,
Szczecin
Harris detectorHarris detector
R(x,y)=det(M) - (trace(M))
2

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Faculty of Computer
Science and
Information
Technology
West Pomeranian
University of
Technology,
Szczecin
ComparisonComparison
Harris Moravec