Image Processing involves the immense utilisation of Wavelet Transforms, and to apply on images require the knowledge of its application two dimensions.
Image Processing involves the immense utilisation of Wavelet Transforms, and to apply on images require the knowledge of its application two dimensions.
DISTINGUISH BETWEEN WALSH TRANSFORM AND HAAR TRANSFORMDip transformsNITHIN KALLE PALLY
walsh transform-1D Walsh Transform kernel is given by:
n - 1
g(x, u) = (1/N) ∏ (-1) bi(x) bn-1-i(u)
i = 0
where, N – no. of samples
n – no. of bits needed to represent x as well as u
bk(z) – kth bits in binary representation of z.
Thus, Forward Discrete Walsh Transformation is
N - 1 n - 1
W(u) = (1/N) Σ f(x) ∏ (-1) bi(x) b(u) x = 0 i = 0
Removing noise from the Medical image is still a challenging problem for researchers. Noise added is not easy to remove from the images. There have been several published algorithms and each approach has its assumptions, advantages, and limitations. This paper summarizes the major techniques to denoise the medical images and finds the one is better for image denoising. We can conclude that the Multiwavelet technique with Soft threshold is the best technique for image denoising.
Image Denoising Using Wavelet TransformIJERA Editor
In this project, we have studied the importance of wavelet theory in image denoising over other traditional methods. We studied the importance of thresholding in wavelet theory and the two basic thresholding method i.e. hard and soft thresholding experimentally. We also studied why soft thresholding is preferred over hard thresholding, three types of soft thresholding (Bayes shrink, Sure shrink, Visu shrink) as well as advantages and disadvantage of each of them
Describes Pulse Compression in Radar Systems.
For comments please contact me at solo.hermelin@gmail.com.
For more presentations on different subjects visit my website at http://solohermelin.com.
Since some figures were not downloaded, I recommend to see this presentation on my website under RADAR Folder, Signal Processing subfolder.
What is Fourier Transform
Spatial to Frequency Domain
Fourier Transform
Forward Fourier and Inverse Fourier transforms
Properties of Fourier Transforms
Fourier Transformation in Image processing
DISTINGUISH BETWEEN WALSH TRANSFORM AND HAAR TRANSFORMDip transformsNITHIN KALLE PALLY
walsh transform-1D Walsh Transform kernel is given by:
n - 1
g(x, u) = (1/N) ∏ (-1) bi(x) bn-1-i(u)
i = 0
where, N – no. of samples
n – no. of bits needed to represent x as well as u
bk(z) – kth bits in binary representation of z.
Thus, Forward Discrete Walsh Transformation is
N - 1 n - 1
W(u) = (1/N) Σ f(x) ∏ (-1) bi(x) b(u) x = 0 i = 0
Removing noise from the Medical image is still a challenging problem for researchers. Noise added is not easy to remove from the images. There have been several published algorithms and each approach has its assumptions, advantages, and limitations. This paper summarizes the major techniques to denoise the medical images and finds the one is better for image denoising. We can conclude that the Multiwavelet technique with Soft threshold is the best technique for image denoising.
Image Denoising Using Wavelet TransformIJERA Editor
In this project, we have studied the importance of wavelet theory in image denoising over other traditional methods. We studied the importance of thresholding in wavelet theory and the two basic thresholding method i.e. hard and soft thresholding experimentally. We also studied why soft thresholding is preferred over hard thresholding, three types of soft thresholding (Bayes shrink, Sure shrink, Visu shrink) as well as advantages and disadvantage of each of them
Describes Pulse Compression in Radar Systems.
For comments please contact me at solo.hermelin@gmail.com.
For more presentations on different subjects visit my website at http://solohermelin.com.
Since some figures were not downloaded, I recommend to see this presentation on my website under RADAR Folder, Signal Processing subfolder.
What is Fourier Transform
Spatial to Frequency Domain
Fourier Transform
Forward Fourier and Inverse Fourier transforms
Properties of Fourier Transforms
Fourier Transformation in Image processing
A Review on Image Denoising using Wavelet Transformijsrd.com
this paper proposes different approaches of wavelet based image denoising methods. The search for efficient image denoising methods is still a valid challenge at the crossing of functional analysis and statistics. Wavelet algorithms are very useful tool for signal processing such as image denoising. The main of modify the coefficient is remove the noise from data or signal. In this paper, the technique was extended up to almost remove noise Gaussian.
WEBINAR ON FUNDAMENTALS OF DIGITAL IMAGE PROCESSING DURING COVID LOCK DOWN by by K.Vijay Anand , Associate Professor, Department of Electronics and Instrumentation Engineering , R.M.K Engineering College, Tamil Nadu , India
Image and Audio Signal Filtration with Discrete Heap Transformsmathsjournal
Filtration and enhancement of signals and images by the discrete signal-induced heap transform (DsiHT) is described in this paper. The basic functions of the DsiHT are orthogonal waves that are originated from the signal generating the transform. These waves with their specific motion describe a process of elementary rotations or Givens transformations of the processed signal. Unlike the discrete Fourier transform which performs rotations of all data of the signalon each stage of calculation, the DsiHT sequentially rotates only two components of the data and accumulates a heap in one of the components with the maximum energy. Because of the nature of the heap transform, if the signal under process is mixed with a wave which is similar to the signal-generator then this additive component is eliminated or vanished after applying the heap transformation. This property can effectively be used for noise removal, noise detection, and image enhancement.
Similar to Digital Image Processing_ ch3 enhancement freq-domain (20)
Dev Dives: Train smarter, not harder – active learning and UiPath LLMs for do...UiPathCommunity
💥 Speed, accuracy, and scaling – discover the superpowers of GenAI in action with UiPath Document Understanding and Communications Mining™:
See how to accelerate model training and optimize model performance with active learning
Learn about the latest enhancements to out-of-the-box document processing – with little to no training required
Get an exclusive demo of the new family of UiPath LLMs – GenAI models specialized for processing different types of documents and messages
This is a hands-on session specifically designed for automation developers and AI enthusiasts seeking to enhance their knowledge in leveraging the latest intelligent document processing capabilities offered by UiPath.
Speakers:
👨🏫 Andras Palfi, Senior Product Manager, UiPath
👩🏫 Lenka Dulovicova, Product Program Manager, UiPath
Accelerate your Kubernetes clusters with Varnish CachingThijs Feryn
A presentation about the usage and availability of Varnish on Kubernetes. This talk explores the capabilities of Varnish caching and shows how to use the Varnish Helm chart to deploy it to Kubernetes.
This presentation was delivered at K8SUG Singapore. See https://feryn.eu/presentations/accelerate-your-kubernetes-clusters-with-varnish-caching-k8sug-singapore-28-2024 for more details.
Search and Society: Reimagining Information Access for Radical FuturesBhaskar Mitra
The field of Information retrieval (IR) is currently undergoing a transformative shift, at least partly due to the emerging applications of generative AI to information access. In this talk, we will deliberate on the sociotechnical implications of generative AI for information access. We will argue that there is both a critical necessity and an exciting opportunity for the IR community to re-center our research agendas on societal needs while dismantling the artificial separation between the work on fairness, accountability, transparency, and ethics in IR and the rest of IR research. Instead of adopting a reactionary strategy of trying to mitigate potential social harms from emerging technologies, the community should aim to proactively set the research agenda for the kinds of systems we should build inspired by diverse explicitly stated sociotechnical imaginaries. The sociotechnical imaginaries that underpin the design and development of information access technologies needs to be explicitly articulated, and we need to develop theories of change in context of these diverse perspectives. Our guiding future imaginaries must be informed by other academic fields, such as democratic theory and critical theory, and should be co-developed with social science scholars, legal scholars, civil rights and social justice activists, and artists, among others.
DevOps and Testing slides at DASA ConnectKari Kakkonen
My and Rik Marselis slides at 30.5.2024 DASA Connect conference. We discuss about what is testing, then what is agile testing and finally what is Testing in DevOps. Finally we had lovely workshop with the participants trying to find out different ways to think about quality and testing in different parts of the DevOps infinity loop.
Neuro-symbolic is not enough, we need neuro-*semantic*Frank van Harmelen
Neuro-symbolic (NeSy) AI is on the rise. However, simply machine learning on just any symbolic structure is not sufficient to really harvest the gains of NeSy. These will only be gained when the symbolic structures have an actual semantics. I give an operational definition of semantics as “predictable inference”.
All of this illustrated with link prediction over knowledge graphs, but the argument is general.
Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
The publishing industry has been selling digital audiobooks and ebooks for over a decade and has found its groove. What’s changed? What has stayed the same? Where do we go from here? Join a group of leading sales peers from across the industry for a conversation about the lessons learned since the popularization of digital books, best practices, digital book supply chain management, and more.
Link to video recording: https://bnctechforum.ca/sessions/selling-digital-books-in-2024-insights-from-industry-leaders/
Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
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UiPath Test Automation using UiPath Test Suite series, part 3DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 3. In this session, we will cover desktop automation along with UI automation.
Topics covered:
UI automation Introduction,
UI automation Sample
Desktop automation flow
Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
PHP Frameworks: I want to break free (IPC Berlin 2024)Ralf Eggert
In this presentation, we examine the challenges and limitations of relying too heavily on PHP frameworks in web development. We discuss the history of PHP and its frameworks to understand how this dependence has evolved. The focus will be on providing concrete tips and strategies to reduce reliance on these frameworks, based on real-world examples and practical considerations. The goal is to equip developers with the skills and knowledge to create more flexible and future-proof web applications. We'll explore the importance of maintaining autonomy in a rapidly changing tech landscape and how to make informed decisions in PHP development.
This talk is aimed at encouraging a more independent approach to using PHP frameworks, moving towards a more flexible and future-proof approach to PHP development.
2. Introduction
The spatial domain refers to the representation of an
image as the array of gray-level intensity.
The electromagnetic spectrum consist of sinusoidel
waves of different wavelengths (frequencies).
The frequency content of an image refers to the rate at
which the gray levels change in the image
Rapidly changing brightness values correspond to
high frequency terms, slowly changing brightness
values correspond to low frequency terms
The Fourier transform is a mathematical tool that
analyses a signal (e.g. images) into its spectral
components depending on its wavelength (i.e.
frequency) content.
3. Fourier Transforms
In 1822, Jean B. Fourier has shown that any function f(x) that
have bounded area with the x-axis can be expressed as a linear
combination of sine and/or cosine waves of different
frequencies.
This is also applicable functions of 2 variables, e.g. images.
+
+
=
+
Q. Can we recover the different
frequencies of this signal?
5. Illustration of Fourier Theory for images
Every row is Sine wave of
frequncy 1
Sine wave with frequncy 2
Combined waves frequncy 1+2+3
Sine wave with frequncy 3
Mixed waves with frequncy 5, 2 &1
6. MATLAB generated images
MATLAB can be used to generate images with patterns of and
desired rate of change of brightness.
For this we need to use trigonometric functions of 2 variables as
indicated by the following example code:
clear all;
A=zeros(256,256);
B=A;
for i=1:1:256
for j=1:1:256
A(i,j)=a1*sin(pi*(a2*i+a3*j)/m);
B(i,j)=b1cos(pi*(b2*i+b3*j)/n); //m and n are to be powers of 2.
end
end
C=A+B;
imshow(C);
imwrite(C, 'SinoPattern2.bmp')
8. Fourier Transform - Definition
The Discrete Fourier Transform (DFT) of f(x) is defined as:
1
F(u) =
M
M −1
∑
x =0
2π u x
f ( x) cos(
)
M
− 1 M −1
2π u x
∑ f ( x) sin( M )
M x =0
And the inverse DFT (IDFT) is defined as:
2π u x M −1
2π u x
f(x) = ∑ R (u ) cos(
) − ∑ I (u ) sin(
)
M
M
u =0
u =0
M −1
The u values u = 0, 1, ..., M-1) is the frequency domain of f(x).
One can use Excel to implement Fourier tranforms.
9. Fourier Transform - continued
Unlike f(x), F(u) is a complex valued function, i.e. is a pair of
functions involving trigonometric functions:
1
R(u) =
M
I(u) = −
1
M
M −1
∑ f ( x) cos(2πux / M ),
called the real part, and
x =0
M −1
∑ f ( x) sin(2πux / M ),
called the imaginary part.
x =0
i.e. F(u) ≡ [ R(u ) I (u )].
F is represented by its MAGNITUDE and PHASE rather that its
REAL and IMAGINARY parts,
where: MAGNITUDE(u) = SQRT( R(u)^2+IMAGINARY(u)^2 )
The phase angle of the transform is:
I (u )
φ (u ) = tan (
).
R(u )
−1
PHASE(u) = ATAN( IMAGINARY(u)/REAL(u) )
10. The 2-dimensional DFT
The DFT of a digitised function f(x,y) (i.e. an image) is defined as:
1
F(u, v) =
MN
M −1 N −1
∑∑ f ( x, y) cos(2π (u x / M + v y / N )
x =0 y =0
∑∑ f ( x, y) sin(2π (u x / M + v y / N )
x =0 y =0
and the inverse DFT is defined in a similar manner as before.
1
−
MN
M −1 N −1
f ( x, y) = ∑ ∑ R(u, v) cos(2π (u x / M + v y / N ) −
N −1M −1
u =0 v =0
N −1M −1
∑ ∑ I (u , v) sin( 2π (u x / M + v y / N )
u =0 v =0
Note that, F(0,0) = the average value of f(x,y) and is refered to as
the DC component of the spectrum.
It is a common practice to multiply the image f(x,y) by (-1) x+y. In
this case, the DFT of (f(x,y)(-1)x+y) has its origin located at the
centre of the image, i.e. at (u,v)=(M/2,N/2).
12. The Fourier spectrum – in 2D
• The original image
contains two principal
features: edges run
approximately at ±45ο .
•
The Fourier spectrum
shows important
components in the
same directions.
13. Fourier Spectrum
Original image
Log enhanced version
of Fourier Spectrum
Inverse Fourier
The FTs also tend to have bright lines that are
perpendicular to lines in the original letter. If the
letter has circular segments, then so does the FT.
16. The Notch filter
A simple filter that forces the average image value to become 0.
The average value of an image f(x,y) is the DC component of the
DFT spectrum i.e. F(0,0). The Notch filter is defined as follows:
0
H (u, v) =
1
Original
image
if (u, v) = (M/2, N/2)
otherwise.
Image after
Notch filter
application
Note that the edges stand out more than before filtering.
When the average value is 0, some values of the filtered image
are negative, but for display purposes pixel values are shifted.
17. Low-pass and High-pass filtering
Low frequencies in the DFT spectrum correspond to image
values over smooth areas, while high frequencies
correspond to detailed features such as edges & noise.
A filter that suppresses high frequencies but allows low ones
is called Low-pass filter, while a filter that reduces low
frequencies and allows high ones is called High-pass filter.
Examples of such filters are obtained from circular Gaussian
functions of 2 variables (see next slide)
1
−( u 2 + v 2 ) / 2σ 2
H ( u ,v ) =
e
,
- Lowpass filter,
2
2πσ
1
−( u 2 + v 2 ) / 2σ 2
H ( u ,v ) =
(1 − e
) - Highpass filter .
2
2πσ
18. Low-pass & High-pass filtering - Example
Low pass filtering
High pass filtering
Low pass filtering results in blurring effects, while High pass
filtering results in sharper edges.
19. Wavelet Transforms
Wavelet analysis allows the use of long time intervals for
more precise low-frequency information, and shorter
intervals for high-frequency information.
A wavelet (i.e. small wave) is a mathematical function
used to analyse a continuous-time signal into different
frequency components at different resolution scale.
A wavelet transform of a function is a representation of f
wavelets. The wavelets are scaled and translated copies
of a finite-length or fast-decaying oscillating waveform
ψ(t), known as the mother wavelet.
There are many wavelet filters to choose from. Here we
only discuss the Discrete Wavelet Transform.
20. Wavelet Transforms -Properties
The Wavelet transform is a short time anlysis tool
of finite energy quasi-stationary signals at multiresolutions.
The Discrete wavelet transform (DWT) provide a
compact representation of a signal’s frequency
commponents with strong spatial support.
DWT decomposes a signal into frequency subbands
at different scales from which it can be perfectly
recontructed.
2D-signals such as images can be decomposed in
many different ways.
21. The Haar Wavelet
The Haar wavelet is a
discontinuous, and
resembles a step function.
It is a crude version of the
Truncated cosine.
The Haar wavelet
0.6
0.4
0.2
0
-2
-0.2 0
2
4
6
8
10
-0.4
-0.6
It can be implemented using a simple filter:
If X={x1,x2,x3,x4 ,x5 ,x6 ,x7 ,x8 } is a time-signal of length 8, then
the Haar wavelet decomposes X into an aproximation
subband containing the Low frequencies and a detail
subband containing the high frequencies:
Low= {x2+x1, x4+x3 , x6+x5 , x8+x7 }/√2
High= {x2-x1, x4-x3 , x6-x5 , x8-x7 }/√2
23. Wavelet Decomposition of Images
A Haar wavelet decompose images first on the rows and then on the
columns resulting in 4 subbands, the LL-subband which an approximation of
the original image while the other subbands contain the missing details
The LL-subband output from any stage can be decomposed further.
Original
Image
1 stage Transformation
After 2 stages
…
24. Different Decomposition Schemes.
The previous 2 decomposition scheme is known as
the Pyrimad scheme, whereby at successive stages
only the LL subband is wavelet transdormed.
Other decomposition schemes include:
The standard scheme – At every stage all the
image is wavelet transformd
The wavelet packet – After stage 1, a non-LL
subband is transformed only if it satisfied
certain condition.
The Quincux – During each stage, the columns
decomposition is only applied on the L-subband
25. Statistical Properties of Wavelet subbands
LL subband
HL subband
700
6000
600
5000
500
4000
400
3000
300
2000
200
100
1000
0
0
1
LH subband
Original pixels distribution of Mandrill
3000
2500
frequency
2000
1500
1000
500
1
20
39
58
77
96
115
134
153
172
191
210
229
248
0
coefficient value
1 25 49 73 97 121 145 169 193 217 241
25 49 73 97 121 145 169 193 217 241
8000
7000
6000
5000
4000
3000
2000
1000
0
HH subband
6000
5000
4000
3000
2000
1000
0
1 25 49 73 97 121 145 169 193 217 241
1 25 49 73 97 121 145 169 193 217 241
The distribution of the LL-subband approximate that of the original but all nonLL subbands have a Laplacian distribution. This remains valid at all depths.
26. Applications of Wavelet Transforms
The list of applications is growing fast. These include:
Image and video Compression
Feature detection and recognition
Image denoising
Face Recognition
Signal interpulation
Most applications benefit from the statistical propererty
of the non-LL subbands (The laplacian distribution of
the wavelet coefficients in these subbands).
27. Wavelet-based Feature detection
Non-LL subbands of a wavelet decomposed image contains high
frequencies (i.e. image features) which are highlighted. These
significant coefficients are the furthest away from the mean.
Thresholding reveals the main features.
Horizontal features
σ
Vertical features