This document summarizes spatial filtering techniques for image enhancement, including smoothing and sharpening filters. It discusses neighbourhood operations and different types of spatial filters like averaging filters and median filters that can be used to smooth images. Techniques for sharpening images like the Laplacian filter and highboost filter are also covered. The document provides examples and equations to demonstrate how various spatial filters work to enhance images.
Image Enhancement: Introduction to Spatial Filters, Low Pass Filter and High Pass Filters. Here Discussed Image Smoothing and Image Sharping, Gaussian Filters
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
Digital image processing is the use of computer algorithms to perform image processing on digital images. As a subcategory or field of digital signal processing, digital image processing has many advantages over analog image processing.
Image Enhancement: Introduction to Spatial Filters, Low Pass Filter and High Pass Filters. Here Discussed Image Smoothing and Image Sharping, Gaussian Filters
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
Digital image processing is the use of computer algorithms to perform image processing on digital images. As a subcategory or field of digital signal processing, digital image processing has many advantages over analog image processing.
Image processing, Noise, Noise Removal filtersKuppusamy P
Basics of images, Digital Images, Noise, Noise Removal filters
Reference:
Richard Szeliski, Computer Vision: Algorithms and Applications, Springer 2010
Spatial filtering using image processingAnuj Arora
spatial filtering in image processing (explanation cocept of
mask),lapace filtering and filtering process of image for extract information and reduce noise
Image Restoration And Reconstruction
Mean Filters
Order-Statistic Filters
Spatial Filtering: Mean Filters
Adaptive Filters
Adaptive Mean Filters
Adaptive Median Filters
Image processing, Noise, Noise Removal filtersKuppusamy P
Basics of images, Digital Images, Noise, Noise Removal filters
Reference:
Richard Szeliski, Computer Vision: Algorithms and Applications, Springer 2010
Spatial filtering using image processingAnuj Arora
spatial filtering in image processing (explanation cocept of
mask),lapace filtering and filtering process of image for extract information and reduce noise
Image Restoration And Reconstruction
Mean Filters
Order-Statistic Filters
Spatial Filtering: Mean Filters
Adaptive Filters
Adaptive Mean Filters
Adaptive Median Filters
This presentation describes briefly about the image enhancement in spatial domain, basic gray level transformation, histogram processing, enhancement using arithmetic/ logical operation, basics of spatial filtering and local enhancements.
A simple introduction to network programming using Python 3 socket module. This material was used in a 2-day summer training at Mansoura University in August 2016.
The examples included come from other tutorials with some changes. The source code of these and other examples can be found here:
https://github.com/ksonbol/socket_examples
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
morphological tecnquies in image processingsoma saikiran
it describes you about different types of morphological techniques in image processing and what is the function and applications of morphological tecniques in image processing
MedicalSpatial filtering is a process by which we can alter properties of an optical image by selectively removing certain spatial frequencies that make up an object, for example, filtering video data received from satellite and space probes, or removal of raster from a television picture or scanned image. Image processing, digital images slides spatial filters. Filters are divided into two types: linear (also called convolution) and nonlinear. A convolution is an algorithm that consists of recalculating the value of a pixel based on its own pixel value and the pixel values of its neighbors weighted by the coefficients of a convolution kernel. Spatial filtering is commonly used to "clean up" the output of lasers, removing aberrations in the beam due to imperfect, dirty, or damaged optics, or due to variations in the laser gain medium itself.
You can find the video recording here: https://www.youtube.com/watch?v=lYoHh19RNy4
Heiko Behrens and Matthew Hungerford present advanced programming techniques for Pebble. This presentation focused on graphics techniques including run-time dithering, offline dithering, pixel manipulations, and frame-buffer drawing.
This talk featured the amiga boing ball dithering demo.
Day 1 - Video 3B
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.
UiPath Test Automation using UiPath Test Suite series, part 4DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 4. In this session, we will cover Test Manager overview along with SAP heatmap.
The UiPath Test Manager overview with SAP heatmap webinar offers a concise yet comprehensive exploration of the role of a Test Manager within SAP environments, coupled with the utilization of heatmaps for effective testing strategies.
Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
What will you get from this session?
1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
Topics covered:
Execution from the test manager
Orchestrator execution result
Defect reporting
SAP heatmap example with demo
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
SAP Sapphire 2024 - ASUG301 building better apps with SAP Fiori.pdfPeter Spielvogel
Building better applications for business users with SAP Fiori.
• What is SAP Fiori and why it matters to you
• How a better user experience drives measurable business benefits
• How to get started with SAP Fiori today
• How SAP Fiori elements accelerates application development
• How SAP Build Code includes SAP Fiori tools and other generative artificial intelligence capabilities
• How SAP Fiori paves the way for using AI in SAP apps
GraphRAG is All You need? LLM & Knowledge GraphGuy Korland
Guy Korland, CEO and Co-founder of FalkorDB, will review two articles on the integration of language models with knowledge graphs.
1. Unifying Large Language Models and Knowledge Graphs: A Roadmap.
https://arxiv.org/abs/2306.08302
2. Microsoft Research's GraphRAG paper and a review paper on various uses of knowledge graphs:
https://www.microsoft.com/en-us/research/blog/graphrag-unlocking-llm-discovery-on-narrative-private-data/
Elevating Tactical DDD Patterns Through Object CalisthenicsDorra BARTAGUIZ
After immersing yourself in the blue book and its red counterpart, attending DDD-focused conferences, and applying tactical patterns, you're left with a crucial question: How do I ensure my design is effective? Tactical patterns within Domain-Driven Design (DDD) serve as guiding principles for creating clear and manageable domain models. However, achieving success with these patterns requires additional guidance. Interestingly, we've observed that a set of constraints initially designed for training purposes remarkably aligns with effective pattern implementation, offering a more ‘mechanical’ approach. Let's explore together how Object Calisthenics can elevate the design of your tactical DDD patterns, offering concrete help for those venturing into DDD for the first time!
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
Welcome to the first live UiPath Community Day Dubai! Join us for this unique occasion to meet our local and global UiPath Community and leaders. You will get a full view of the MEA region's automation landscape and the AI Powered automation technology capabilities of UiPath. Also, hosted by our local partners Marc Ellis, you will enjoy a half-day packed with industry insights and automation peers networking.
📕 Curious on our agenda? Wait no more!
10:00 Welcome note - UiPath Community in Dubai
Lovely Sinha, UiPath Community Chapter Leader, UiPath MVPx3, Hyper-automation Consultant, First Abu Dhabi Bank
10:20 A UiPath cross-region MEA overview
Ashraf El Zarka, VP and Managing Director MEA, UiPath
10:35: Customer Success Journey
Deepthi Deepak, Head of Intelligent Automation CoE, First Abu Dhabi Bank
11:15 The UiPath approach to GenAI with our three principles: improve accuracy, supercharge productivity, and automate more
Boris Krumrey, Global VP, Automation Innovation, UiPath
12:15 To discover how Marc Ellis leverages tech-driven solutions in recruitment and managed services.
Brendan Lingam, Director of Sales and Business Development, Marc Ellis
State of ICS and IoT Cyber Threat Landscape Report 2024 previewPrayukth K V
The IoT and OT threat landscape report has been prepared by the Threat Research Team at Sectrio using data from Sectrio, cyber threat intelligence farming facilities spread across over 85 cities around the world. In addition, Sectrio also runs AI-based advanced threat and payload engagement facilities that serve as sinks to attract and engage sophisticated threat actors, and newer malware including new variants and latent threats that are at an earlier stage of development.
The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
Le nuove frontiere dell'AI nell'RPA con UiPath Autopilot™UiPathCommunity
In questo evento online gratuito, organizzato dalla Community Italiana di UiPath, potrai esplorare le nuove funzionalità di Autopilot, il tool che integra l'Intelligenza Artificiale nei processi di sviluppo e utilizzo delle Automazioni.
📕 Vedremo insieme alcuni esempi dell'utilizzo di Autopilot in diversi tool della Suite UiPath:
Autopilot per Studio Web
Autopilot per Studio
Autopilot per Apps
Clipboard AI
GenAI applicata alla Document Understanding
👨🏫👨💻 Speakers:
Stefano Negro, UiPath MVPx3, RPA Tech Lead @ BSP Consultant
Flavio Martinelli, UiPath MVP 2023, Technical Account Manager @UiPath
Andrei Tasca, RPA Solutions Team Lead @NTT Data
Essentials of Automations: The Art of Triggers and Actions in FMESafe Software
In this second installment of our Essentials of Automations webinar series, we’ll explore the landscape of triggers and actions, guiding you through the nuances of authoring and adapting workspaces for seamless automations. Gain an understanding of the full spectrum of triggers and actions available in FME, empowering you to enhance your workspaces for efficient automation.
We’ll kick things off by showcasing the most commonly used event-based triggers, introducing you to various automation workflows like manual triggers, schedules, directory watchers, and more. Plus, see how these elements play out in real scenarios.
Whether you’re tweaking your current setup or building from the ground up, this session will arm you with the tools and insights needed to transform your FME usage into a powerhouse of productivity. Join us to discover effective strategies that simplify complex processes, enhancing your productivity and transforming your data management practices with FME. Let’s turn complexity into clarity and make your workspaces work wonders!
In his public lecture, Christian Timmerer provides insights into the fascinating history of video streaming, starting from its humble beginnings before YouTube to the groundbreaking technologies that now dominate platforms like Netflix and ORF ON. Timmerer also presents provocative contributions of his own that have significantly influenced the industry. He concludes by looking at future challenges and invites the audience to join in a discussion.
The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
Pushing the limits of ePRTC: 100ns holdover for 100 daysAdtran
At WSTS 2024, Alon Stern explored the topic of parametric holdover and explained how recent research findings can be implemented in real-world PNT networks to achieve 100 nanoseconds of accuracy for up to 100 days.
Securing your Kubernetes cluster_ a step-by-step guide to success !KatiaHIMEUR1
Today, after several years of existence, an extremely active community and an ultra-dynamic ecosystem, Kubernetes has established itself as the de facto standard in container orchestration. Thanks to a wide range of managed services, it has never been so easy to set up a ready-to-use Kubernetes cluster.
However, this ease of use means that the subject of security in Kubernetes is often left for later, or even neglected. This exposes companies to significant risks.
In this talk, I'll show you step-by-step how to secure your Kubernetes cluster for greater peace of mind and reliability.
2. 2
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19
Contents
Next, we will look at spatial filtering
techniques:
– What is spatial filtering?
– Smoothing Spatial filters.
– Sharpening Spatial Filters.
– Combining Spatial Enhancement Methods
3. 3
of
19
Neighbourhood Operations
Neighbourhood operations simply operate
on a larger neighbourhood of pixels than
point operations
Neighbourhoods are
mostly a rectangle
around a central pixel
Any size rectangle
and any shape filter
are possible
Origin x
y Image f (x, y)
(x, y)
Neighbourhood
4. 4
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19
Neighbourhood Operations
For each pixel in the origin image, the
outcome is written on the same location at
the target image.
Origin x
y Image f (x, y)
(x, y)
Neighbourhood
TargetOrigin
5. 5
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19
Simple Neighbourhood Operations
Simple neighbourhood operations example:
– Min: Set the pixel value to the minimum in
the neighbourhood
– Max: Set the pixel value to the maximum in
the neighbourhood
6. 6
of
19
The Spatial Filtering Process
j k l
m n o
p q r
Origin x
y Image f (x, y)
eprocessed = n*e +
j*a + k*b + l*c +
m*d + o*f +
p*g + q*h + r*i
Filter (w)
Simple 3*3
Neighbourhood
e 3*3 Filter
a b c
d e f
g h i
Original Image
Pixels
*
The above is repeated for every pixel in the
original image to generate the filtered image
7. 7
of
19
Spatial Filtering: Equation Form
∑∑−= −=
++=
a
as
b
bt
tysxftswyxg ),(),(),(
Filtering can be given
in equation form as
shown above
Notations are based
on the image shown
to the left
ImagestakenfromGonzalez&Woods,DigitalImageProcessing(2002)
8. 8
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19
Smoothing Spatial Filters
One of the simplest spatial filtering
operations we can perform is a smoothing
operation
– Simply average all of the pixels in a
neighbourhood around a central value
– Especially useful
in removing noise
from images
– Also useful for
highlighting gross
detail
1
/9
1
/9
1
/9
1
/9
1
/9
1
/9
1
/9
1
/9
1
/9
Simple
averaging
filter
9. 9
of
19
Smoothing Spatial Filtering
1
/9
1
/9
1
/9
1
/9
1
/9
1
/9
1
/9
1
/9
1
/9
Origin x
y Image f (x, y)
e = 1
/9*106 +
1
/9*104 + 1
/9*100 + 1
/9*108 +
1
/9*99 + 1
/9*98 +
1
/9*95 + 1
/9*90 + 1
/9*85
= 98.3333
Filter
Simple 3*3
Neighbourhood
106
104
99
95
100 108
98
90 85
1
/9
1
/9
1
/9
1
/9
1
/9
1
/9
1
/9
1
/9
1
/9
3*3 Smoothing
Filter
104 100 108
99 106 98
95 90 85
Original Image
Pixels
*
The above is repeated for every pixel in the
original image to generate the smoothed image
10. 10
of
19
Image Smoothing Example
The image at the top left
is an original image of
size 500*500 pixels
The subsequent images
show the image after
filtering with an averaging
filter of increasing sizes
– 3, 5, 9, 15 and 35
Notice how detail begins
to disappear
ImagestakenfromGonzalez&Woods,DigitalImageProcessing(2002)
17. 17
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19
Weighted Smoothing Filters
More effective smoothing filters can be
generated by allowing different pixels in the
neighbourhood different weights in the
averaging function
– Pixels closer to the
central pixel are more
important
– Often referred to as a
weighted averaging
1
/16
2
/16
1
/16
2
/16
4
/16
2
/16
1
/16
2
/16
1
/16
Weighted
averaging filter
18. 18
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19
Another Smoothing Example
By smoothing the original image we get rid
of lots of the finer detail which leaves only
the gross features for thresholding
ImagestakenfromGonzalez&Woods,DigitalImageProcessing(2002)
Original Image Smoothed Image Thresholded Image
* Image taken from Hubble Space Telescope
19. 19
of
19
Averaging Filter Vs. Median Filter
Example
Filtering is often used to remove noise from
images
Sometimes a median filter works better than
an averaging filter
Original Image
With Noise
Image After
Averaging Filter
Image After
Median Filter
ImagestakenfromGonzalez&Woods,DigitalImageProcessing(2002)
20. 20
of
19
Averaging Filter Vs. Median Filter
Example
ImagestakenfromGonzalez&Woods,DigitalImageProcessing(2002)
Original
21. 21
of
19
Averaging Filter Vs. Median Filter
Example
ImagestakenfromGonzalez&Woods,DigitalImageProcessing(2002)
Averaging
Filter
22. 22
of
19
Averaging Filter Vs. Median Filter
Example
ImagestakenfromGonzalez&Woods,DigitalImageProcessing(2002)
Median
Filter
23. 23
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19
Strange Things Happen At The Edges!
Origin x
y Image f (x, y)
e
e
e
e
At the edges of an image we are missing
pixels to form a neighbourhood
e e
e
24. 24
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19
Strange Things Happen At The Edges!
(cont…)
There are a few approaches to dealing with
missing edge pixels:
– Omit missing pixels
• Only works with some filters
• Can add extra code and slow down processing
– Pad the image
• Typically with either all white or all black pixels
– Replicate border pixels
– Truncate the image
25. 25
of
19
Correlation & Convolution
The filtering we have been talking about so
far is referred to as correlation with the filter
itself referred to as the correlation kernel
Convolution is a similar operation, with just
one subtle difference
For symmetric filters it makes no difference
eprocessed = v*e +
z*a + y*b + x*c +
w*d + u*e +
t*f + s*g + r*h
r s t
u v w
x y z
Filter
a b c
d e e
f g h
Original Image
Pixels
*
26. 26
of
19
Sharpening Spatial Filters
Previously we have looked at smoothing
filters which remove fine detail
Sharpening spatial filters seek to highlight
fine detail
– Remove blurring from images
– Highlight edges
Sharpening filters are based on spatial
differentiation
29. 29
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19
1st
Derivative
The formula for the 1st
derivative of a
function is as follows:
It’s just the difference between subsequent
values and measures the rate of change of
the function
)()1( xfxf
x
f
−+=
∂
∂
31. 31
of
19
2nd
Derivative
The formula for the 2nd
derivative of a
function is as follows:
Simply takes into account the values both
before and after the current value
)(2)1()1(2
2
xfxfxf
x
f
−−++=
∂
∂
34. 34
of
19
Using Second Derivatives For Image
Enhancement
The 2nd
derivative is more useful for image
enhancement than the 1st
derivative
– Stronger response to fine detail
– Simpler implementation
– We will come back to the 1st
order derivative
later on
The first sharpening filter we will look at is
the Laplacian
– Isotropic
– One of the simplest sharpening filters
– We will look at a digital implementation
35. 35
of
19
The Laplacian
The Laplacian is defined as follows:
where the partial 1st
order derivative in the x
direction is defined as follows:
and in the y direction as follows:
y
f
x
f
f 2
2
2
2
2
∂
∂
+
∂
∂
=∇
),(2),1(),1(2
2
yxfyxfyxf
x
f
−−++=
∂
∂
),(2)1,()1,(2
2
yxfyxfyxf
y
f
−−++=
∂
∂
36. 36
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19
The Laplacian (cont…)
So, the Laplacian can be given as follows:
We can easily build a filter based on this
),1(),1([2
yxfyxff −++=∇
)]1,()1,( −+++ yxfyxf
),(4 yxf−
0 1 0
1 -4 1
0 1 0
37. 37
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19
The Laplacian (cont…)
Applying the Laplacian to an image we get a
new image that highlights edges and other
discontinuities
ImagestakenfromGonzalez&Woods,DigitalImageProcessing(2002)
Original
Image
Laplacian
Filtered Image
Laplacian
Filtered Image
Scaled for Display
38. 38
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19
But That Is Not Very Enhanced!
The result of a Laplacian filtering
is not an enhanced image
We have to do more work in
order to get our final image
Subtract the Laplacian result
from the original image to
generate our final sharpened
enhanced image
Laplacian
Filtered Image
Scaled for Display
ImagestakenfromGonzalez&Woods,DigitalImageProcessing(2002)
fyxfyxg 2
),(),( ∇−=
39. 39
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19
Laplacian Image Enhancement
In the final sharpened image edges and fine
detail are much more obvious
ImagestakenfromGonzalez&Woods,DigitalImageProcessing(2002)
- =
Original
Image
Laplacian
Filtered Image
Sharpened
Image
41. 41
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19
Simplified Image Enhancement
The entire enhancement can be combined
into a single filtering operation
),1(),1([),( yxfyxfyxf −++−=
)1,()1,( −+++ yxfyxf
)],(4 yxf−
fyxfyxg 2
),(),( ∇−=
),1(),1(),(5 yxfyxfyxf −−+−=
)1,()1,( −−+− yxfyxf
42. 42
of
19
Simplified Image Enhancement (cont…)
This gives us a new filter which does the
whole job for us in one step
0 -1 0
-1 5 -1
0 -1 0
ImagestakenfromGonzalez&Woods,DigitalImageProcessing(2002)
44. 44
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19
Variants On The Simple Laplacian
There are lots of slightly different versions of
the Laplacian that can be used:
0 1 0
1 -4 1
0 1 0
1 1 1
1 -8 1
1 1 1
-1 -1 -1
-1 9 -1
-1 -1 -1
Simple
Laplacian
Variant of
Laplacian
ImagestakenfromGonzalez&Woods,DigitalImageProcessing(2002)
45. 45
of
19
Unsharp Mask & Highboost Filtering
Using sequence of linear spatial filters in
order to get Sharpening effect.
-Blur
- Subtract from original image
- add resulting mask to original image
47. 47
of
19
1st
Derivative Filtering
Implementing 1st
derivative filters is difficult in
practice
For a function f(x, y) the gradient of f at
coordinates (x, y) is given as the column
vector:
∂
∂
∂
∂
=
=∇
y
f
x
f
G
G
y
x
f
48. 48
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19
1st
Derivative Filtering (cont…)
The magnitude of this vector is given by:
For practical reasons this can be simplified as:
)f(∇=∇ magf
[ ] 2
1
22
yx GG +=
2
1
22
∂
∂
+
∂
∂
=
y
f
x
f
yx GGf +≈∇
49. 49
of
19
1st
Derivative Filtering (cont…)
There is some debate as to how best to
calculate these gradients but we will use:
which is based on these coordinates
( ) ( )321987 22 zzzzzzf ++−++≈∇
( ) ( )741963 22 zzzzzz ++−+++
z1 z2 z3
z4 z5 z6
z7 z8 z9
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Sobel Operators
Based on the previous equations we can
derive the Sobel Operators
To filter an image it is filtered using both
operators the results of which are added
together
-1 -2 -1
0 0 0
1 2 1
-1 0 1
-2 0 2
-1 0 1
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19
Sobel Example
Sobel filters are typically used for edge
detection
ImagestakenfromGonzalez&Woods,DigitalImageProcessing(2002)
An image of a
contact lens which
is enhanced in
order to make
defects (at four
and five o’clock in
the image) more
obvious
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19
1st
& 2nd
Derivatives
Comparing the 1st
and 2nd
derivatives we can
conclude the following:
– 1st
order derivatives generally produce thicker
edges
– 2nd
order derivatives have a stronger response
to fine detail e.g. thin lines
– 1st
order derivatives have stronger response
to grey level step
– 2nd
order derivatives produce a double
response at step changes in grey level
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19
Combining Spatial Enhancement
Methods
Successful image
enhancement is typically
not achieved using a single
operation
Rather we combine a range
of techniques in order to
achieve a final result
This example will focus on
enhancing the bone scan to
the right
ImagestakenfromGonzalez&Woods,DigitalImageProcessing(2002)
54. 54
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19
Combining Spatial Enhancement
Methods (cont…)
ImagestakenfromGonzalez&Woods,DigitalImageProcessing(2002)
Laplacian filter of
bone scan (a)
Sharpened version of
bone scan achieved
by subtracting (a)
and (b) Sobel filter of bone
scan (a)
(a)
(b)
(c)
(d)
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19
Combining Spatial Enhancement
Methods (cont…)
ImagestakenfromGonzalez&Woods,DigitalImageProcessing(2002)
The product of (c)
and (e) which will be
used as a mask
Sharpened image
which is sum of (a)
and (f)
Result of applying a
power-law trans. to
(g)
(e)
(f)
(g)
(h)
Image (d) smoothed with
a 5*5 averaging filter