## Similar to Digital Image Processing Module 3 Notess

Lecture 11
Lecture 11
Wael Sharba

DIGITAL IMAGE PROCESSING - Day 4 Image Transform
DIGITAL IMAGE PROCESSING - Day 4 Image Transform
vijayanand Kandaswamy

Frequency Image Processing
Frequency Image Processing
Suhas Deshpande

Fourier image
Fourier image
NGHIPHAM14

Fourier series Introduction
Fourier series Introduction
Rizwan Kazi

Fourier transform
Fourier transform
Naveen Sihag

Lecture 9
Lecture 9
Wael Sharba

lec-4.ppt
lec-4.ppt
AbdullahRafique7

lec-4.ppt
lec-4.ppt
AnchitProch

lec-4.ppt
lec-4.ppt

Filtering in frequency domain
Filtering in frequency domain
GowriLatha1

Nabaa
Digital image processing using matlab: filters (detail)
Digital image processing using matlab: filters (detail)
thanh nguyen

Unit vii
Unit vii
mrecedu

Image processing 2
Image processing 2
Taymoor Nazmy

IVR - Chapter 3 - Basics of filtering II: Spectral filters
IVR - Chapter 3 - Basics of filtering II: Spectral filters
Charles Deledalle

Lecture 10
Lecture 10
Wael Sharba

Norm-variation of bilinear averages
Norm-variation of bilinear averages
VjekoslavKovac1

6.frequency domain image_processing
6.frequency domain image_processing
Nashid Alam

Frequency Domain Filtering 1.ppt
Frequency Domain Filtering 1.ppt
ManishKumawat77

### Similar to Digital Image Processing Module 3 Notess(20)

Lecture 11
Lecture 11

DIGITAL IMAGE PROCESSING - Day 4 Image Transform
DIGITAL IMAGE PROCESSING - Day 4 Image Transform

Frequency Image Processing
Frequency Image Processing

Fourier image
Fourier image

Fourier series Introduction
Fourier series Introduction

Fourier transform
Fourier transform

Lecture 9
Lecture 9

lec-4.ppt
lec-4.ppt

lec-4.ppt
lec-4.ppt

lec-4.ppt
lec-4.ppt

Filtering in frequency domain
Filtering in frequency domain

Nabaa
Nabaa

Digital image processing using matlab: filters (detail)
Digital image processing using matlab: filters (detail)

Unit vii
Unit vii

Image processing 2
Image processing 2

IVR - Chapter 3 - Basics of filtering II: Spectral filters
IVR - Chapter 3 - Basics of filtering II: Spectral filters

Lecture 10
Lecture 10

Norm-variation of bilinear averages
Norm-variation of bilinear averages

6.frequency domain image_processing
6.frequency domain image_processing

Frequency Domain Filtering 1.ppt
Frequency Domain Filtering 1.ppt

## More from shivubhavv

MANASA FINAL PPT 21.pptxxxxxxxxxxxxxxxxxxx
MANASA FINAL PPT 21.pptxxxxxxxxxxxxxxxxxxx
shivubhavv

Government polytechnic college-1.pptxabcd
Government polytechnic college-1.pptxabcd
shivubhavv

AICTE PPT slide of Engineering college kr pete
AICTE PPT slide of Engineering college kr pete
shivubhavv

pptseminar-16-130305074446-phpapp02.pdff
pptseminar-16-130305074446-phpapp02.pdff
shivubhavv

web-scraping-170522083556.pdf.....mmm...
web-scraping-170522083556.pdf.....mmm...
shivubhavv

diabetic Retinopathy. Eye detection of disease
diabetic Retinopathy. Eye detection of disease
shivubhavv

Final presentation of diabetic_retinopathy_vascular
Final presentation of diabetic_retinopathy_vascular
shivubhavv

Diabetic_retinopathy_vascular disease synopsis
Diabetic_retinopathy_vascular disease synopsis
shivubhavv

### More from shivubhavv(8)

MANASA FINAL PPT 21.pptxxxxxxxxxxxxxxxxxxx
MANASA FINAL PPT 21.pptxxxxxxxxxxxxxxxxxxx

Government polytechnic college-1.pptxabcd
Government polytechnic college-1.pptxabcd

AICTE PPT slide of Engineering college kr pete
AICTE PPT slide of Engineering college kr pete

pptseminar-16-130305074446-phpapp02.pdff
pptseminar-16-130305074446-phpapp02.pdff

web-scraping-170522083556.pdf.....mmm...
web-scraping-170522083556.pdf.....mmm...

diabetic Retinopathy. Eye detection of disease
diabetic Retinopathy. Eye detection of disease

Final presentation of diabetic_retinopathy_vascular
Final presentation of diabetic_retinopathy_vascular

Diabetic_retinopathy_vascular disease synopsis
Diabetic_retinopathy_vascular disease synopsis

leewayhertz.com-AI in predictive maintenance Use cases technologies benefits ...
leewayhertz.com-AI in predictive maintenance Use cases technologies benefits ...
alexjohnson7307

System Design Case Study: Building a Scalable E-Commerce Platform - Hiike
System Design Case Study: Building a Scalable E-Commerce Platform - Hiike
Hiike

Nordic Marketo Engage User Group_June 13_ 2024.pptx
Nordic Marketo Engage User Group_June 13_ 2024.pptx
MichaelKnudsen27

A Comprehensive Guide to DeFi Development Services in 2024
A Comprehensive Guide to DeFi Development Services in 2024
Intelisync

Ocean lotus Threat actors project by John Sitima 2024 (1).pptx
Ocean lotus Threat actors project by John Sitima 2024 (1).pptx
SitimaJohn

Presentation of the OECD Artificial Intelligence Review of Germany
Presentation of the OECD Artificial Intelligence Review of Germany
innovationoecd

UI5 Controls simplified - UI5con2024 presentation
UI5 Controls simplified - UI5con2024 presentation
Wouter Lemaire

Columbus Data & Analytics Wednesdays - June 2024
Columbus Data & Analytics Wednesdays - June 2024
Jason Packer

Skybuffer AI: Advanced Conversational and Generative AI Solution on SAP Busin...
Skybuffer AI: Advanced Conversational and Generative AI Solution on SAP Busin...
Tatiana Kojar

Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdf
Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdf

Serial Arm Control in Real Time Presentation
Serial Arm Control in Real Time Presentation
tolgahangng

Let's Integrate MuleSoft RPA, COMPOSER, APM with AWS IDP along with Slack
Let's Integrate MuleSoft RPA, COMPOSER, APM with AWS IDP along with Slack
shyamraj55

HCL Notes and Domino License Cost Reduction in the World of DLAU
HCL Notes and Domino License Cost Reduction in the World of DLAU
panagenda

Monitoring and Managing Anomaly Detection on OpenShift.pdf
Monitoring and Managing Anomaly Detection on OpenShift.pdf
Tosin Akinosho

Your One-Stop Shop for Python Success: Top 10 US Python Development Providers
Your One-Stop Shop for Python Success: Top 10 US Python Development Providers
akankshawande

Choosing The Best AWS Service For Your Website + API.pptx
Choosing The Best AWS Service For Your Website + API.pptx
Brandon Minnick, MBA

Artificial Intelligence for XMLDevelopment
Artificial Intelligence for XMLDevelopment

Trusted Execution Environment for Decentralized Process Mining
Trusted Execution Environment for Decentralized Process Mining
LucaBarbaro3

Main news related to the CCS TSI 2023 (2023/1695)
Main news related to the CCS TSI 2023 (2023/1695)
Jakub Marek

Overcoming the PLG Trap: Lessons from Canva's Head of Sales & Head of EMEA Da...
Overcoming the PLG Trap: Lessons from Canva's Head of Sales & Head of EMEA Da...
saastr

leewayhertz.com-AI in predictive maintenance Use cases technologies benefits ...
leewayhertz.com-AI in predictive maintenance Use cases technologies benefits ...

System Design Case Study: Building a Scalable E-Commerce Platform - Hiike
System Design Case Study: Building a Scalable E-Commerce Platform - Hiike

Nordic Marketo Engage User Group_June 13_ 2024.pptx
Nordic Marketo Engage User Group_June 13_ 2024.pptx

A Comprehensive Guide to DeFi Development Services in 2024
A Comprehensive Guide to DeFi Development Services in 2024

Ocean lotus Threat actors project by John Sitima 2024 (1).pptx
Ocean lotus Threat actors project by John Sitima 2024 (1).pptx

Presentation of the OECD Artificial Intelligence Review of Germany
Presentation of the OECD Artificial Intelligence Review of Germany

UI5 Controls simplified - UI5con2024 presentation
UI5 Controls simplified - UI5con2024 presentation

Columbus Data & Analytics Wednesdays - June 2024
Columbus Data & Analytics Wednesdays - June 2024

Skybuffer AI: Advanced Conversational and Generative AI Solution on SAP Busin...
Skybuffer AI: Advanced Conversational and Generative AI Solution on SAP Busin...

Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdf
Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdf

Serial Arm Control in Real Time Presentation
Serial Arm Control in Real Time Presentation

Let's Integrate MuleSoft RPA, COMPOSER, APM with AWS IDP along with Slack
Let's Integrate MuleSoft RPA, COMPOSER, APM with AWS IDP along with Slack

HCL Notes and Domino License Cost Reduction in the World of DLAU
HCL Notes and Domino License Cost Reduction in the World of DLAU

Monitoring and Managing Anomaly Detection on OpenShift.pdf
Monitoring and Managing Anomaly Detection on OpenShift.pdf

Your One-Stop Shop for Python Success: Top 10 US Python Development Providers
Your One-Stop Shop for Python Success: Top 10 US Python Development Providers

Choosing The Best AWS Service For Your Website + API.pptx
Choosing The Best AWS Service For Your Website + API.pptx

Artificial Intelligence for XMLDevelopment
Artificial Intelligence for XMLDevelopment

Trusted Execution Environment for Decentralized Process Mining
Trusted Execution Environment for Decentralized Process Mining

Main news related to the CCS TSI 2023 (2023/1695)
Main news related to the CCS TSI 2023 (2023/1695)

Overcoming the PLG Trap: Lessons from Canva's Head of Sales & Head of EMEA Da...
Overcoming the PLG Trap: Lessons from Canva's Head of Sales & Head of EMEA Da...

### Digital Image Processing Module 3 Notess

• 2. Laplacian in Spatial Domain ● Laplacian – – Isotropic Rotation Invariant 𝑄2 f = f (x +1, y) + f (x - 1, y) + f (x, y +1) + f (x, y - 1) - 4 f (x, y) g(x, y) = f (x, y) +c[𝑄2 f (x, y)] 2 2 ∂t + ∂z2 ∂2 f ∂2 f 𝑄 f = 2
• 3. Laplacian in Frequency Domain 2 2 ∂t + ∂z2 ∂2 f ∂2 f 𝑄 f = 3
• 4. Laplacian in Frequency Domain H(u,v) =-4𝑢2 (u2 +v2 ) With respect to center of frequency rectangle : H(u,v) =-4π2 [(u - M /2)2 +(v - N /2)2 )] =-4 π 2 D2 (u,v) Laplacian of an image: 4
• 5. Laplacian in Frequency Domain ●Enhancement Eq: g(x, y) = f (x, y) +c[▽2 f (x, y)] c =- 1 ● Scales of f (x, y) & ▽ 2 f (x, y) as computed by DFT differ widely due to the DFT process ● Normalize f (x, y) to [0,1] before DFT ● Normalize ▽2 f (x, y) to [-1,1] 5
• 7. Comparative Laplacian in Spatial & Frequency Domains 7
• 8. Unsharp Mask, Highboost Filtering & High- Frequency-Emphasis Filtering ● In spatial domain: gmask (x, y) = f (x, y) - f (x, y) g(x, y) = f (x, y) +k * gmask (x, y) k =1: Unsharp Masking k >1: Highboost Filtering k ∈1: De- emphasized Unsharp Masking 8
• 9. Unsharp Mask, Highboost Filtering & High- Frequency-Emphasis Filtering 9 [ 1+ k*Hhp (u,v)] F(u,v) }
• 10. Unsharp Mask, Highboost Filtering & High- Frequency-Emphasis Filtering ● In frequency domain: High- Frequency Emphasis Filter k1>=0: Controlsthe offset from origin k2 >=0: Controlsthe contribution of high frequencies 10 g(x,y)= {[ k1+k2 * Hhp (u,v)] F(u,v) }
• 12. Homomorphic Filtering ● Homomorphic filtering is a FDS that aims at a simultaneous increase in contrast & dynamic range compression. ● It is mainly utilized for non-uniformly illuminated images in medical, sonar images etc. for edge enhancement that makes the image details clear to the observer. ● Certain situations where the image is subjected to the multiplicative interference or noise as depicted ● f(x,y)= i(x,y) . r(x,y) 12
• 13. Homomorphic Filtering… ● Illumination-Reflectance Model in FDS ● Illumination Component – – Slow Spatial Variations & Attenuate contributions by illumination ● Reflectance Component – – Varies abruptly – junctions of dissimilar objects Amplify contributions by reflectance ● Simultaneous dynamic range compression & contrast enhancement ● We cannot easily use the product i & r to operate separately on the frequency components of illumination & reflection because the FT of f ( x , y) is not separable; 1 3
• 14. H F…. • F[f(x,y)) not equal to F[i(x, y)].F[r(x, y)]. 14 ln f(x,y) = ln i(x, y) + ln r(x, y). We can separate them by taking logarithm F[ln f(x,y)} = F[ln i(x, y)} + F[ln r(x, y)] F(x,y) = I(x,y) + R(x,y), where F, I & R are the FTs ln f(x,y),ln i(x, y) , & ln r(x, y). respectively. F is FT of the sum of 2 images: a low-freq illumination image (suppress) & a high freq reflectance (enhance)image 0 < i(x,y) < a, It indicate the perfect black body 0 < r(x,y) < 1, It indicate the perfect white body
• 15. H.F… 15  Since i & r combine multiplicatively, they can be added by taking log of the image intensity,  so that they can be separated in the FD.  i variations can be thought as a multiplicative noise & can be reduced by filtering in the log domain.  To make the i of an image more even, the HF components are increased and the LF Components are filtered  Because the HF are assumed as reflectance in the scene whereas the LF as the illumination in the scene.i.e.,  High pass filter is used to suppress LF’s & amplify HF’s in the log intensity domain.  i component tends to vary slowly across the image & the reflectance tends to vary rapidly.  Therefore, by applying a FD filter the intensity variation across the image can be reduced while highlighting detail.
• 16. H.F…. • Z(x,y) = ln[f(x,y)] = ln[i(x,y)] + ln[r(x,y)] eq-1 • DFT[z(x,y)] • = DFT{ln[f(x,y)]} • = DFT{ln[i(x,y)] + ln[r(x,y)]} • = DFT{ln[i(x,y)]} + DFT{ln[r(x,y)]} eq-2 • Since DFT[f(x,y)] = F(u,v), eq-2 becomes, • Z(u,v) = Fi(u,v) + Fr(u,v) eq-3 • The function Z represents the FT of the sum of two images: a low frequency illumination image & a high frequency reflectance image 16
• 17. H.F…. • Thus ,FT of o/p by multiplying the DFT of the i/p with the filter H(u,v). i.e., S(u,v) = H(u,v) Z(u,v) eq-4 • where S(u,v) is the FT of o/p. Substitute eq-3 in 4, • we get S(u,v) = H(u,v) [ Fi(u,v) + Fr(u,v) ] • = H(u,v) Fi(u,v) + H(u,v) Fr(u,v) eq-5 • Applying IDFT to eq-6, • we get, T -1 [S(u,v)] = T-1 [ H(u,v) Fi(u,v) + H(u,v) Fr(u,v)] • = T-1 [ H(u,v) Fi(u,v)] + T-1 [H(u,v) Fr(u,v)] • s(x,y) = i’(x,y) + r’(x,y) eq-6 • The Enhanced image is obtained by taking exponential of the IDFT s(x,y), i.e., 17 g(x, y) =es(x,y) =ei'( x,y) er'( x,y) =i (x, y)r (x, y) 0 0 io(x,y) = e i’(x,y) , ro(x,y) = e r’(x,y) Where, are the I & r components of the enhanced o/p
• 18. Homomorphic Filtering g(x, y) =es(x,y) =ei'( x,y) er'( x,y) =i (x, y)r (x, y) 0 0 18
• 19. Homomorphic Filtering ● Illumination Component – – Slow Spatial Variations Low Frequencies log of illumination – attenuate contributions by illumination – – – Varies abruptly – junctions of dissimilar objects High frequencies log of reflectance amplify contributions by reflectance ●Refle c Lta ∈ nc 1e Component ● Simultaneous dynamic range compression & contrast e n h a n H c e >m 1e n t 19
• 20. L L H 2 0 2 -c[D (u,v)/D ] ( - )[ 1-e ]+ H(u,v)= Homomorphic Filtering 20
• 21. Image: 1 62x746 γL=0.25, γH=2, c=1, D0=80 21
• 22. Band-reject & Band-pass Filters HBP (u,v) =1- HBR (u,v) 22
• 24. Notch Filters – Narrow Filtering Q k=1 HNR (u,v) = Hk (u,v)H- k (u,v) ] 1/2 2 2 1/2 2 2 k k k k k N / 2 +v ) ] M / 2 +u ) +(v - [(u - D (u,v) = +(v - N / 2 - v ) [(u - M / 2 - u ) D (u,v) = - k 24
• 25. - k k 2n 0k 3 k=1 2n 0k / D (u,v)] 1+[D 1 / D (u,v)] 1+[D 1 Butterworth Notch Reject Filters HNR (u,v) = HNP (u,v) =1- HNR (u,v) 25
• 27. 27
• 28. 28
Current LanguageEnglish
Español
Portugues
Français
Deutsche