Adaptive Median Filters
Elements of visual perception
Representing Digital Images
Spatial and Intensity Resolution
cones and rods
Brightness Adaptation
Spatial and Intensity Resolution
Image Acquisition and Representation
A Simple Image Formation Model
Image Sampling and Quantization
Image Interpolation
Image quantization
Nearest Neighbor Interpolation
Adaptive Median Filters
Elements of visual perception
Representing Digital Images
Spatial and Intensity Resolution
cones and rods
Brightness Adaptation
Spatial and Intensity Resolution
Image Acquisition and Representation
A Simple Image Formation Model
Image Sampling and Quantization
Image Interpolation
Image quantization
Nearest Neighbor Interpolation
Image Interpolation Techniques with Optical and Digital Zoom Concepts -semina...mmjalbiaty
full details about Spatial and Intensity Resolution , optical and digital zoom concepts and the common three interpolation algorithms for implementing zoom in image processing
An image can be seen as a matrix I, where I(x, y) is the brightness of the pixel located at coordinates (x, y). In the Convolutional neural network, the kernel is nothing but a filter
that is used to extract the features from the images.
Image Interpolation Techniques with Optical and Digital Zoom Concepts -semina...mmjalbiaty
full details about Spatial and Intensity Resolution , optical and digital zoom concepts and the common three interpolation algorithms for implementing zoom in image processing
An image can be seen as a matrix I, where I(x, y) is the brightness of the pixel located at coordinates (x, y). In the Convolutional neural network, the kernel is nothing but a filter
that is used to extract the features from the images.
Image segmentation is a computer vision task that involves dividing an image into multiple segments or regions, where each segment corresponds to a distinct object, region, or feature within the image. The goal of image segmentation is to simplify and analyze an image by partitioning it into meaningful and semantically relevant parts. This is a crucial step in various applications, including object recognition, medical imaging, autonomous driving, and more.
Key points about image segmentation:
Semantic Segmentation: This type of segmentation assigns each pixel in an image to a specific class, essentially labeling each pixel with the object or region it belongs to. It's commonly used for object detection and scene understanding.
Instance Segmentation: Here, individual instances of objects are separated and labeled separately. This is especially useful when multiple objects of the same class are present in the image.
Boundary Detection: Some segmentation methods focus on identifying the boundaries that separate different objects or regions in an image.
Methods: Image segmentation can be achieved through various techniques, including traditional methods like thresholding, clustering, and region growing, as well as more advanced techniques involving deep learning, such as using convolutional neural networks (CNNs) and fully convolutional networks (FCNs).
Challenges: Image segmentation can be challenging due to variations in lighting, color, texture, and object shape. Overlapping objects and unclear boundaries further complicate the task.
Applications: Image segmentation is used in diverse fields. For example, in medical imaging, it helps identify organs or abnormalities. In autonomous vehicles, it aids in identifying pedestrians, other vehicles, and obstacles.
Evaluation: Measuring the accuracy of segmentation methods can be complex. Metrics like Intersection over Union (IoU) and Dice coefficient are often used to compare segmented results to ground truth.
Data Annotation: Creating ground truth annotations for segmentation can be labor-intensive, as each pixel must be labeled. This has led to the development of datasets and tools to facilitate annotation.
Semantic Segmentation Networks: Deep learning architectures like U-Net, Mask R-CNN, and Deeplab have significantly improved the accuracy of image segmentation by effectively learning complex patterns and features.
Image segmentation plays a fundamental role in understanding and processing images, enabling computers to "see" and interpret visual information in ways that mimic human perception.
Image segmentation is a computer vision task that involves dividing an image into meaningful and distinct segments or regions. The goal is to partition an image into segments that represent different objects or areas of interest within the image. Image segmentation plays a crucial role in various applications, such as object detection, medical imaging, autonomous vehicles, and more.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
SINGLE‐PHASE TO THREE‐PHASE DRIVE SYSTEM USING TWO PARALLEL SINGLE‐PHASE RECT...ijiert bestjournal
Now a days digital image processing is rapid emerging field with fast growing
applications in sciences and engineering technologies. Digital image processing has broad
spectrum of applications such as remote sensing, medical processing, radar, sonar,
robotics, sport field and automated processes [1-2]. Edge detection techniques are
employed for the detecting the edges of the primitive picture. Earlier some primitive
methods were used for the image processing. H. C. Andrew et.al. gave the method of
digital image restoration [3-5], A. K. Jain and et.al put forwarded the partial difference
equations and finite differences in image processing [6]. Image process, image models and
estimation regarding the edge detection has been flourished during last decade [7-9]. Most
modules in practical vision system depend, directly or indirectly, on the performance of an
edge detector and digital image processing.
Neighbourhood operations
What is spatial filtering?
Smoothing operations
What happens at the edges?
Correlation and convolution
Sharpening filters
Combining filtering techniques
Some simple neighbourhood operations include:
Min: Set the pixel value to the minimum in the neighbourhood
Max: Set the pixel value to the maximum in the neighbourhood
Median: The median value of a set of numbers is the midpoint value in that set (e.g. from the set [1, 7, 15, 18, 24] 15 is the median). Sometimes the median works better than the average
Spatial smoothing may be viewed as a process for estimating the value of a pixel from its neighbours.
What is the value that “best” approximates the intensity of a given pixel given the intensities of its neighbours?
We have to define “best” by establishing a criterion.
A spatial filter is an image operation where each pixel value I(u; v) is changed by a function of the intensities of pixels in a neighborhood of (u; v).
It involves moving the filter mask from point to point in an image.
At each point (x,y), the response of the filter at that point is calculated using a predefined relationship
The area of machine learning has enabled experts to reveal
bits of knowledge from the useful information and past
occasions. One of the familiar histories in the world is Titanic
disaster. The main aim is to anticipate the passengers who have
survived using the machine learning techniques. To make the
correct predictions about the disaster various parameters are
included such as Name, Sex, Age, PassengerID, Embarked etc.
Initially the dataset has collected.
The dataset has been contemplated and deselected utilizing
different machine learning calculations like SVM, Random
forest and so forth. The methods are used in this are decision
tree, linear SVM, and logistic regression. Evaluating the Titanic
disaster to decide a relationship between the survival of
passengers and attributes of the travelers utilizing different
machine learning calculations is the main goal of this project.
Hence, various algorithms can be compared based on the
accuracy of a test dataset [1].
The overall accuracy can be calculated by undergoing
several stages as depicted by the below Fig. 1 using aforesaid
machine learning approaches.
A. Dataset
Kaggle website provides the dataset for this work [10]. The
data comprises of 891 rows in the prepare set which is a
traveller test with their related names. The Passenger class,
Ticket number, Age, Sex, name of the passenger, Decision tree characterization procedure is a standout
amongst the most prevalent systems in the developing field of
information mining. A method of building a decision tree from
the set of samples is the method involved in the implementing
decision tree algorithm. It is the form of flow chart where
every non-terminal node represents the test on a particular
attribute and class labels are held with the terminal node [2].
Here, the chance of survival can be calculated
Deep learning is a technique that basically mimics the human brain. So, the Scientist and Researchers taught can we make machines learn in the same way so, there is where the deep learning concept came that led to the invention called the neural network
Deep learning is a technique that basically mimics the human brain. So, the Scientist and Researchers taught can we make machines learn in the same way so, there is where the deep learning concept came that lead to the invention called Neural Network
Deep neural networks & computational graphsRevanth Kumar
To improve the performance of a Deep Learning model. The goal is to reduce the optimization function which can be divided based on the classification and the regression problems.
To begin, a self-driving car (driverless, autonomous, robotic car) is a vehicle that is capable of sensing its environment and navigating without human input.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
3. Introduction
Convolutions are mathematical operations between two functions
that create a third function. In image processing, it happens by
going through each pixel to perform a calculation with the pixel and
its neighbours.
In Convolutional neural network, the kernel is nothing but a filter
that is used to extract the features from the images.
A convolution lets you do many things, like calculate derivatives,
detect edges, apply blurs, etc. A very wide variety of things. And all
of this is done with a ”convolution kernel”.
The kernels will define the size of the convolution, the weights
applied to it, and an anchor point usually positioned at the center.
December 28, 2020 3 / 20
4. Convolution filters
An image can be seen as a matrix I, where I(x, y) is the brightness
of the pixel located at coordinates (x, y).
A convolution product is computed between the matrix I and a
kernel matrix K which represents the type of filter.
K can be of size 3 × 3 or 5 × 5. The result of this product will be
the new brightness of the pixel (x, y).
I∗K =
I(1, 1) I(1, 2) ... I(1, n)
. . .
. . .
I(m, 1) I(m, 2) ... I(m, n)
∗
K(1, 1) K(1, 2) K(1.3)
K(2, 1) K(2, 2) K(2, 3)
K(3, 1) K(3, 2) K(3, 3)
Where
I ∗ Kx ,y =
1
i=−1
1
j=−1
I(x + i, y + j) ∗ K(i, j)
December 28, 2020 4 / 20
5. Edge Detection
Edge detection refers to the process of identifying and locating sharp
discontinuities in an image.
Edges are significant local changes in the image and are important
features for analyzing images.
An edge point is a point in an image with coordinates [i,j] at the
location of a significant local intensity change in the image.
Different Methods of edge detection are available in computer
vision. They are:
1. Sobel Operator
2. Prewitt Operator
3. Laplacian Operator
4. Canny’s Edge Detection Algorithm
December 28, 2020 5 / 20
6. Continue...
Main steps in Edge Detection
Smoothing: Suppress as much noise as possible, without destroying
true edges.
Enhancement: Apply differentiation to enhance the quality of edges
(i.e., sharpening).
Threshold: Determine which edge pixels should be discarded as noise
and which should be retained (i.e., threshold edge magnitude).
Localization: Determine the exact edge location. Edge thinning and
linking are usually required in this step.
December 28, 2020 6 / 20
7. Edge Detection using Derivative (Gradient)
Edge detection is essentially the operation of detecting significant
local changes in an image.
The gradient is a measure of change in a function, and an image can
be considered to be an array of samples of some continuous function
of image intensity.
The first derivate of an image can be computed using the gradient.
f or G[f (x, y)] =
∂f
∂x
∂f
∂y
There are two important properties associated with the gradient: (1)
the vector G[f(x, y)] points in the direction of the maximum rate of
increase of the function f(x, y), and (2) the magnitude of the
gradient, given by
December 28, 2020 7 / 20
8. Continue...
G[f (x, y)] =
∂f 2
∂x
+
∂f 2
∂y
equals the maximum rate of increase of f(x, y) per unit distance in the
direction G
From vector analysis, the direction of the gradient is defined as:
α(x, y) = tan−1
∂f
∂x
∂f
∂y
where the angle α is measured with respect to the x axis.
Gx (x, y) → ∂f
∂x
Gy (x, y) → ∂f
∂y
December 28, 2020 8 / 20
9. Continue...
Consider the arrangement of pixels about the pixel [i, j]:
3x3 Neighbourhood :
a0 a1 a2
a7 [i, j] a3
a6 a5 a4
The partial derivatives ∂f
∂x , ∂f
∂y can be computed by:
Gx =(a2+ca3+a4)-(a0+ca7+a6)
Gy =(a0+ca1+a2)-(a6+ca5+a4)
December 28, 2020 9 / 20
10. Sobel Operator
The Sobel filter is used for edge detection. It works by calculating
the gradient of image intensity at each pixel within the image. It
finds the direction of the largest increase from light to dark and the
rate of change in that direction.
To avoid having the gradient calculated about an interpolated point
between pixels is to use a 3 x 3 neighborhood for the gradient
calculations.
The Sobel operator is the magnitude of the gradient computed by:
M = G2
x + G2
y
where the partial derivatives are computed by
Gx =(a2+ca3+a4)-(a0+ca7+a6)
Gy =(a0+ca1+a2)-(a6+ca5+a4)
December 28, 2020 10 / 20
11. Continue...
With the constant c = 2.
Gx and Gy can be implemented using convolution masks:
Gx :
-1 0 1
-2 0 2
-1 0 1
Gy :
1 2 1
0 0 0
-1 -2 -1
Note that this operator places an emphasis on pixels that are closer
to the center of the mask.
The Sobel operator is one of the most commonly used edge
detectors.
December 28, 2020 11 / 20
12. Prewitt operator
The operator calculates the gradient of the image intensity at each
point, giving the direction of the largest possible increase from light
to dark and the rate of change in that direction.
The Prewitt operator uses the same equations as the Sobel operator,
except that the constant c = 1. Therefore:
Gx :
-1 0 1
-1 0 1
-1 0 1
Gy :
1 1 1
0 0 0
-1 -1 -1
December 28, 2020 12 / 20
13. Laplacian Operator
The Laplacian is the two-dimensional equivalent of the second
derivative. The formula for the Laplacian of a function f (x, y) is
2
f =
∂2
f
∂x2
+
∂2
f
∂y2
The simplest gradient approximation is
Gx
∼= f [i, j + 1] − f [i, j]
Gy
∼= f [i, j] − f [i + 1, j]
∂2
f
∂x2 = ∂Gx
∂x ; ∂2
f
∂y2 =
∂Gy
∂x
December 28, 2020 13 / 20
14. Continue...
∂2
f
∂x2
= f [i, j + 1] − 2f [i, j] + f [i, j − 1]
which is the desired approximation to the second partial derivative
centered about [i,j]. Similarly
∂2
f
∂y2
= f [i + 1, j] − 2f [i, j] + f [i − 1, j]
By combining these two equations into a single operator, the
following mask can be used to approximate the Laplacian:
Laplacian :
∂2
f
∂x2
+
∂2
f
∂y2
≈ fi+1,j + fi−1,j + fi,j+1 + fi,j−1 − 4fi,j
2
=
0 1 0
1 -4 1
0 1 0
December 28, 2020 14 / 20
15. Linear Filter
Linear smoothing filters are for removing Gaussian noise and, in
most cases, the other types of noise as well.
same pattern of weights is used in each window, which means that
the linear filter is spatially invariant and can be implemented using a
convolution mask.
The simplest linear filters is implemented by a local averaging
operation where the value of each pixel is replaced by the average of
all the values in the local neighborhood:
h[i, j] =
1
M
(k,l)∈N
f [k, l] ;
1
9
X
1 1 1
1 1 1
1 1 1
where M is the total number of pixels in the neighborhood N.
December 28, 2020 15 / 20
16. Gaussian Kernel
In image processing filters are mainly used to suppress either the
high frequencies in the image, i.e. smoothing the image, or the low
frequencies, i.e. enhancing or detecting edges in the image.
An image can be filtered either in the frequency or in the spatial
domain.
The corresponding process in the spatial domain is to convolve the
input image f(i,j) with the filter function h(i,j). This can be written
as:
g(i, j) = h(i, j) f (i, j)
The discrete convolution can be defined as a ‘shift and multiply’
operation, where we shift the kernel over the image and multiply its
value with the corresponding pixel values of the image. For a square
kernel with size M× M, we can calculate the output image with the
following formula:
December 28, 2020 16 / 20
17. Calculating Gaussian Convolution Kernels
The Gaussian filter uses the Gaussian function in the kernel of the
filter:
G(x, y) =
1
2πσ2
e− x2
+ y2
2σ2
This filter is a weighted filter which gives more importance to the
central pixels. The parameter σ controls the weight given to the
center.
where,
G(x,y) =The variables referenced as x and y relate to pixel
coordinates within an image.
e = represents the value of Euler’s number has been defined as a
mathematical constant equating to 2.718.
σ = represents a threshold or factor value, as specified by the user.
December 28, 2020 17 / 20
18. Continue...
When calculating the kernel elements, the coordinate values
expressed by x and y should reflect the distance in pixels from the
middle pixel.
In order to gain a better grasp on the Gaussian kernel formula we
can implement the formula in steps.
If we were to create a 3×3 kernel and specified a weighting value of
5.5 our calculations can start off as indicated by the following
illustration:
1
2π(5.5)2 e− 12
+12
2(5.5)2
1
2π(5.5)2 e− 02
+12
2(5.5)2
1
2π(5.5)2 e− 12
+12
2(5.5)2
1
2π(5.5)2 e− 12
+02
2(5.5)2
1
2π(5.5)2 e− 02
+02
2(5.5)2
1
2π(5.5)2 e− 12
+02
2(5.5)2
1
2π(5.5)2 e− 12
+12
2(5.5)2
1
2π(5.5)2 e− 02
+12
2(5.5)2
1
2π(5.5)2 e− 12
+12
2(5.5)2
December 28, 2020 18 / 20
19. Continue...
The calculated values of each kernel element:
0.00509 0.00517 0.0521
0.00517 0.00526 0.00517
0.00509 0.00517 0.00509
An important requirement to take note of at this point being that
the sum total of all the elements contained as part of a
kernel/matrix must equate to one.
At this point the sum total of the kernel equates to .046322.
The kernel values should be updated by multiplying each element by
one divided by the current kernel sum.
k =
0.1098 0.1117 0.1098
0.1117 0.1135 0.1117
0.1098 0.1117 0.1098
Now, successfully calculated a 3×3 Gaussian Blur kernel matrix
which implements a weight value of 5.5.
December 28, 2020 19 / 20