– 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
This document discusses networks and deep learning, with a focus on their application to analyzing the COVID-19 pandemic. It begins with an overview of networks and graph theory concepts. It then discusses how deep learning, specifically graph neural networks, can be used to analyze networks and learn representations of nodes. Applications discussed include traffic prediction and modeling disease spread. It also introduces the SIR model for modeling epidemics and the basic reproduction number metric.
This document is the curriculum vitae of Eugen Zaharescu, an Associate Professor at Ovidius University in Constanta, Romania. It provides personal details such as his name, date of birth, education history, and employment history. It lists that he received a PhD in Electronics and Telecommunications from Polytechnic University of Bucharest in 1981 and has been teaching courses in image processing, multimedia systems and other topics at Ovidius University since 1992. It also provides details on his research interests and activities in areas such as image processing, data bases and web technologies.
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Pranešimas VII Lietuvos jaunųjų mokslininkų konferencijoje „Operacijų tyrimas ir taikymai“
„Kompiuterininkų dienos – 2015“, Panevėžyje, KTU PTVF 2013-09-18
This document discusses networks and deep learning, with a focus on their application to analyzing the COVID-19 pandemic. It begins with an overview of networks and graph theory concepts. It then discusses how deep learning, specifically graph neural networks, can be used to analyze networks and learn representations of nodes. Applications discussed include traffic prediction and modeling disease spread. It also introduces the SIR model for modeling epidemics and the basic reproduction number metric.
This document is the curriculum vitae of Eugen Zaharescu, an Associate Professor at Ovidius University in Constanta, Romania. It provides personal details such as his name, date of birth, education history, and employment history. It lists that he received a PhD in Electronics and Telecommunications from Polytechnic University of Bucharest in 1981 and has been teaching courses in image processing, multimedia systems and other topics at Ovidius University since 1992. It also provides details on his research interests and activities in areas such as image processing, data bases and web technologies.
Alexander Serov has extensive experience and education in physics, mathematics, engineering, and philosophy. He has developed several numerical simulation methods and software, including for modeling ultrasonic waves, Maxwell's equations, molecular dynamics, and MEMS. His background qualifies him for positions requiring strong analytical skills and experience with computational modeling across various scientific domains.
Pranešimas VII Lietuvos jaunųjų mokslininkų konferencijoje „Operacijų tyrimas ir taikymai“
„Kompiuterininkų dienos – 2015“, Panevėžyje, KTU PTVF 2013-09-18
The document is a presentation about Bitdefender products and solutions. It provides an overview of Bitdefender as a company, highlighting its leadership in antivirus technology and awards. It also summarizes Bitdefender's consumer and business product lines, including solutions for endpoint protection, server security, virtual environments, and cloud security. The presentation aims to demonstrate Bitdefender's comprehensive portfolio for addressing malware evolution across physical, virtual, and mobile platforms.
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Pranešimas XVII mokslinės kompiuterininkų konferencijos
sekcijoje „K9. Saityno technologijų vystymas“
„Kompiuterininkų dienos – 2015“, Panevėžyje, KTU PTVF 2013-09-19
Pranešimas XVII mokslinės kompiuterininkų konferencijos
sekcijoje „K8. Statistiniai metodai, optimizavimas ir prognozavimas“
„Kompiuterininkų dienos – 2015“, Panevėžyje, KTU PTVF 2013-09-19
Pranešimas XVII mokslinės kompiuterininkų konferencijos
sekcijoje „K9. Saityno technologijų vystymas“
„Kompiuterininkų dienos – 2015“, Panevėžyje, KTU PTVF 2013-09-19
Pranešimas sekcijoje
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„Kompiuterininkų dienos – 2015“, Panevėžyje, KTU PTVF 2015-09-19
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sekcijoje „K9. Saityno technologijų vystymas“
„Kompiuterininkų dienos – 2015“, Panevėžyje, KTU PTVF 2013-09-19
1) The document summarizes research on classifying rice grains using digital image analysis of morphological and color features.
2) It outlines procedures for image acquisition of rice seeds, quantifying features like Fourier descriptors, geometry, and color.
3) Future work is to acquire images of 360 rice varieties, analyze contour and color features, and cluster varieties based on morphological and color similarities.
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This document discusses using image processing techniques to detect defects in printed circuit boards during manufacturing. It describes acquiring images of circuit boards using a CCD camera and enhancing the images through techniques like histogram equalization and edge detection. Defects are then detected by subtracting an image of the circuit board from a template image and analyzing the differences to identify defects. The system is able to quickly and accurately detect defects using digital image processing.
Pranešimas XII mokyklinės informatikos konferencijos sekcijoje
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Image and signal processing affect our daily lives in an ever-increasing way. Participate in designing this fascinating technology and shape IT‘s future function in business and society.
https://www.fh-salzburg.ac.at/disziplinen/ingenieurwissenschaften/master-applied-image-and-signal-processing/degree-programme/
The document is a presentation about Bitdefender products and solutions. It provides an overview of Bitdefender as a company, highlighting its leadership in antivirus technology and awards. It also summarizes Bitdefender's consumer and business product lines, including solutions for endpoint protection, server security, virtual environments, and cloud security. The presentation aims to demonstrate Bitdefender's comprehensive portfolio for addressing malware evolution across physical, virtual, and mobile platforms.
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Pranešimas XVII mokslinės kompiuterininkų konferencijos
sekcijoje „K9. Saityno technologijų vystymas“
„Kompiuterininkų dienos – 2015“, Panevėžyje, KTU PTVF 2013-09-19
Pranešimas XVII mokslinės kompiuterininkų konferencijos
sekcijoje „K8. Statistiniai metodai, optimizavimas ir prognozavimas“
„Kompiuterininkų dienos – 2015“, Panevėžyje, KTU PTVF 2013-09-19
Pranešimas XVII mokslinės kompiuterininkų konferencijos
sekcijoje „K9. Saityno technologijų vystymas“
„Kompiuterininkų dienos – 2015“, Panevėžyje, KTU PTVF 2013-09-19
Pranešimas sekcijoje
K10&M4. Informacinės technologijos studijų ir mokymo(-si) procese
„Kompiuterininkų dienos – 2015“, Panevėžyje, KTU PTVF 2015-09-19
Pranešimas XVII mokslinės kompiuterininkų konferencijos
sekcijoje „K9. Saityno technologijų vystymas“
„Kompiuterininkų dienos – 2015“, Panevėžyje, KTU PTVF 2013-09-19
1) The document summarizes research on classifying rice grains using digital image analysis of morphological and color features.
2) It outlines procedures for image acquisition of rice seeds, quantifying features like Fourier descriptors, geometry, and color.
3) Future work is to acquire images of 360 rice varieties, analyze contour and color features, and cluster varieties based on morphological and color similarities.
The document provides an agenda and overview for a Bitdefender sales team tour in the United States. It introduces the Bitdefender team members participating in the tour and stops in New York, Washington, and Chicago. The agenda includes an introduction to Bitdefender, its technologies, and the Bitdefender Partner Advantage Network program. It also outlines Bitdefender's history of innovation, growth protecting over 500 million users, and the benefits of partnering with Bitdefender given the growing cybersecurity market.
This document discusses using image processing techniques to detect defects in printed circuit boards during manufacturing. It describes acquiring images of circuit boards using a CCD camera and enhancing the images through techniques like histogram equalization and edge detection. Defects are then detected by subtracting an image of the circuit board from a template image and analyzing the differences to identify defects. The system is able to quickly and accurately detect defects using digital image processing.
Pranešimas XII mokyklinės informatikos konferencijos sekcijoje
M5. Inovatyvūs mokymo metodai ir priemonės
„Kompiuterininkų dienos – 2015“, Panevėžyje, KTU PTVF 2013-09-19
Dieses Abschluss Master-Programm bietet den Studierenden des Vollzeitstudiums an der Fachhochschule in Puch eine eingehende fachliche und wissenschaftlichen Ausbildung. Basierend auf dem Bachelor Studium, bietet dieser Studiengang in Ingenieurwissenschaften eine gründliche technische Ausbildung in Verbindung mit Forschung getriebenen Lehren. Es werden einleitende und fortgeschrittene Themen in den Bereichen Bild und Signalverarbeitung, formale und methodische Grundlagen und den unterschiedlichsten Anwendungsgebieten gelehrt.
Image and signal processing affect our daily lives in an ever-increasing way. Participate in designing this fascinating technology and shape IT‘s future function in business and society.
https://www.fh-salzburg.ac.at/disziplinen/ingenieurwissenschaften/master-applied-image-and-signal-processing/degree-programme/
This document outlines the units of study for a Digital Image Processing course. The five units cover topics such as image enhancement in the spatial domain, image restoration, color image processing, image compression, morphological image processing, and image segmentation. Unit 1 introduces digital image processing and fundamentals. Unit 2 discusses spatial enhancement methods and spatial filtering. Unit 3 covers color image processing techniques. Unit 4 addresses image compression standards. Unit 5 examines morphological operations and image segmentation methods. The course utilizes a primary textbook and lists additional reference materials.
Kern Fairburn has a BSc in Imaging Science and Electronic Engineering. He has experience in various part-time jobs and has received awards for Imaging Science Excellence. He is looking for a role where he can apply his knowledge of electronics and improve his skills in areas like computer science. His interests include astrophotography, extreme sports, and tinkering.
The Faculty of Applied Mathematics and Telecommunications at Vyatka State University consists of three departments: Higher Mathematics, Applied Mathematics and Informatics, and Radioelectronic Equipment. The Radioelectronic Equipment Department implements educational programs in communication networks, secure communications, mobile communication technologies, and information security. The department's research includes algorithms for image compression, filtering, and segmentation, as well as work on self-organizing wireless networks and design of recursive digital filters. Key areas of research include nonlinear image processing, video compression, and cognitive radio technologies for ad hoc networks.
It is a distinct pleasure for me to write in support of my student, Jackie Pang. He studied in my lab for about three years, during which time I witnessed his research achievement and outstanding leadership.
Jackie entered my lab when he was a junior student. At first He had difficulty accepting the strict attendance and assignments. But soon, he learned to manage his time, work in group situations and enjoyed the opportunity to learn from his older peers.
In the past two years, Jackie took a great deal of work in the projects. Even so, he spent most of the rest of time doing research and published several technical reports and papers including one journal paper in both scientific visualization and information visualization.
Jackie is an outstanding student of wide interests. He has won many awards on math, physics and informatics. He also received many honors from many cities, colleges and societies.
Jackie has a lively and enquiring mind. When he comes up with a new idea, he always writes it down and discusses its feasibility with his peers. He also has strong practice ability and done a lot of pioneering work in team building and infrastructure construction. Last year, he developed a website for us to review papers online and created a wiki site for his group to share their experience.
Jackie is also very kind and willing to help his classmates. He always collects materials from the web and sends them to others after putting these materials in order. He is also careful and responsible, and can express clearly.
Since Jackie has long since become the most valuable member of my lab, and a role model for his newer classmates, I recommend him to your fellowship program with absolute confidence.
Thank you for the opportunity of correspondence.
Face Recognition System using Self Organizing Feature Map and Appearance Base...ijtsrd
Face Recognition has develop one of the most effective presentations of image analysis. This area of research is important not only for the applications in human computer interaction, biometric and security but also in other pattern classification problem. To improve face recognition in this system, two methods are used PCA Principal component analysis and SOM Self organizing feature Map .PCA is a subspace projection method is used compress the input face image. SOM method is used to classify DCT based feature vectors into groups to identify if the subject in the input image is "present" or "not present" in the image database. The aim of this system is that input image has to compare with stored images in the database using PCA and SOM method. An image database of 100 face images is evaluated containing 10 subjects and each subject having 10 images with different facial expression. This system is evaluated by measuring the accuracy of recognition rate. This system has been implemented by MATLAB programming. Thaung Yin | Khin Moh Moh Than | Win Tun "Face Recognition System using Self-Organizing Feature Map and Appearance-Based Approach" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26691.pdfPaper URL: https://www.ijtsrd.com/computer-science/cognitive-science/26691/face-recognition-system-using-self-organizing-feature-map-and-appearance-based-approach/thaung-yin
Blind detection of image manipulation @ PoliMiGiorgio Sironi
The document discusses various techniques for the blind detection of image manipulation without the use of digital watermarks. It outlines pixel-based, format-based, camera-based, physics-based, and geometric-based approaches. It focuses on the use of projective geometry tools and geometric-based techniques like analyzing the assumptions of manual text selection and rectification to known fonts or objects to detect tampering. Key steps involve finding keypoints with SIFT feature detection, matching keypoint pairs with RANSAC, and comparing rectified images to reference samples to judge manipulation.
Presentation of the InVID tools for image forensics analysisInVID Project
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This document is a resume for Tomas Singliar, a PhD candidate at the University of Pittsburgh studying machine learning and artificial intelligence. It outlines his education, research interests in statistical machine learning and complex dynamic networks, work experience including internships at Intel researching clustering algorithms and Bayesian networks, and publications in top AI conferences. The resume provides contact information and lists qualifications for Tomas Singliar as a candidate.
This document provides information about a Digital Image Processing course, including:
1. The course details such as the teaching scheme, examination scheme, and importance of the course.
2. The course objectives which are to familiarize students with digital image fundamentals and processing techniques like enhancement, segmentation, compression, and restoration.
3. The course outcomes which are for students to apply image processing concepts and design algorithms for tasks like enhancement, segmentation, compression, and object recognition.
This curriculum vitae summarizes Francesco Conti's education and work experience. He has a PhD in theoretical physics from the University of Pavia and currently works as a Quantitative Risk Analyst for UniCredit Group. He has extensive experience developing financial models and risk management methodologies using C++, Python, and other programming languages.
The document discusses Karel Perutka, a senior lecturer at Tomas Bata University in Zlin, Czech Republic. It describes his educational background, areas of teaching which include MATLAB programming, and research interests which center around adaptive control, real-time control, and creating educational games and tools using MATLAB. It also provides details about four games he has created to help students learn programming concepts through a gaming format, including Labyrinth of MATLAB, LUDO, Automtest, and Riskuj.
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The document discusses object detection using YOLOv5 models of varying sizes on different hardware platforms. It evaluates the mAP, inference time, parameters, and GFLOPS of YOLOv5s, YOLOv5m, YOLOv5l, and YOLOv5x models on a reduced COCO dataset. It also measures the average inference time of the optimized Int8 versions of these models on an iPhone 12's Neural Engine, GPU, and CPU. The results show that optimized YOLOv5 models can run real-time object detection at up to 100 images per second on the iPhone 12's Neural Engine.
This document summarizes research on supervised environmental data classification using spatial auto-beta models. The data consists of random fields with attribute values and class labels. A training set is used to classify new observations using generative classification methods. Specifically, attribute values fall within an interval and class labels take one of two values. Transformations are applied to make the data distribution normal. The best fitting distribution is selected to best describe the data. Classification accuracy is evaluated using actual error rates estimated from the data.
This document summarizes a presentation on analyzing Lombard speech and its acoustic properties. It discusses an experiment where 8 speakers recorded words in two rooms, one with acoustic treatment and one without, both with and without noise. Acoustic features were extracted from the speech samples and analyzed based on noise type, room type, and speaker gender. Key findings included identifying features that distinguish Lombard speech from normal speech and vary based on noise level. Future work will use these findings to automatically monitor and improve speech quality and intelligibility in noise.
This document discusses the history and development of hypertext and markup languages. It begins with early methods of calculating and writing before discussing the development of printing press and moveable type in the 15th century. It then outlines important developments in hypertext standards and systems from 1945 to the present, including XML, HTML, CSS and the creation of the World Wide Web in 1990. It also discusses early limitations and issues with HTML and predictions for the future of hypertext.
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ABSTRACT: A prima vista, un mattoncino Lego e la backdoor XZ potrebbero avere in comune il fatto di essere entrambi blocchi di costruzione, o dipendenze di progetti creativi e software. La realtà è che un mattoncino Lego e il caso della backdoor XZ hanno molto di più di tutto ciò in comune.
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Enchancing adoption of Open Source Libraries. A case study on Albumentations.AI
Pawel FORCZMANSKI (West Pomeranian University of Technology) "Advanced digital image processing methods"
1. Erasmus+seminar,18/04/2016
1 / 64
Faculty of Computer
Science and
Information
Technology
West Pomeranian
University of
Technology,
Szczecin
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
2. Erasmus+seminar,18/04/2016
2 / 64
Faculty of Computer
Science and
Information
Technology
West Pomeranian
University of
Technology,
Szczecin
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
3. Erasmus+seminar,18/04/2016
3 / 64
Faculty of Computer
Science and
Information
Technology
West Pomeranian
University of
Technology,
Szczecin
Computer
graphics
Data processing
Signal
processing
Digital image
processing
Pattern recognition
IntroductionIntroduction
4. Erasmus+seminar,18/04/2016
4 / 64
Faculty of Computer
Science and
Information
Technology
West Pomeranian
University of
Technology,
Szczecin
DIP: Application AreasDIP: Application Areas
OCR
Criminal
Forensic
CAD
Robotics
GIS
Media and
Entertainment
CT
MRI USG
Bar
codes
Text
processing
5. Erasmus+seminar,18/04/2016
5 / 64
Faculty of Computer
Science and
Information
Technology
West Pomeranian
University of
Technology,
Szczecin
ObjectivesObjectives
Image
quality
improvement
compression
Image
representation
transformation
Objective
(computer)
transmission
Subjective
(human)
coding
storing
Image
quality
improvement
6. Erasmus+seminar,18/04/2016
6 / 64
Faculty of Computer
Science and
Information
Technology
West Pomeranian
University of
Technology,
Szczecin
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 'bd 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∣gx , 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 2z=[7 5 3 1];
Co-occurrence matrixCo-occurrence matrix
r={x , y,x , y1};
Cr=H fg z ,v;
f x , y=gx , y1;
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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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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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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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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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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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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Non-linear filteringNon-linear filtering
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Adaptive filteringAdaptive filtering
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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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How?How?
Corner operator is one solution...
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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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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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Harris detectorHarris detector
R(x,y)=det(M) - (trace(M))
2
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West Pomeranian
University of
Technology,
Szczecin
ComparisonComparison
Harris Moravec