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The document discusses various types of filters that can be applied in the spatial or frequency domain, including Laplacian filters, unsharp masking, high-boost filtering, homomorphic filtering, and band-pass/band-reject filters. The Laplacian filter can enhance edges by applying a mask that emphasizes differences between center pixels and surrounding pixels. Homomorphic filtering aims to increase contrast and compress dynamic range by separating illumination and reflectance components in the frequency domain after taking the logarithm of pixel intensities. Band-pass and band-reject filters allow isolating certain frequency ranges. Notch filters can perform narrow band-reject filtering using Butterworth filters.

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07 frequency domain DIP

This document provides an overview of frequency domain concepts including the Fourier transform, Fourier series, discrete Fourier transform, and 2D Fourier transform. It discusses how filtering works in the frequency domain by multiplying the Fourier transform of an image with a filter function in the frequency domain before taking the inverse Fourier transform. Filtering in the frequency domain corresponds to convolution in the spatial domain.

Image transforms

The document discusses digital image processing techniques in the frequency domain. It begins by introducing the discrete Fourier transform (DFT) of one-variable functions and how it relates to sampling a continuous function. It then extends this concept to two-dimensional functions and images. Key topics covered include the 2D DFT and its properties such as translation, rotation, and periodicity. Aliasing in images is also discussed. The document provides examples of how to compute the DFT and inverse DFT of simple images.

imagetransforms1-210417050321.pptx

The document discusses the discrete Fourier transform (DFT) of one- and two-variable functions. It explains that the DFT of a sampled, discrete function can be obtained from the continuous Fourier transform of the underlying sampled function. The DFT provides a way to take samples of the Fourier transform over one period. This is extended to two-dimensional DFTs of digital images. Aliasing effects from under-sampling are described, and properties of the two-dimensional DFT such as periodicity and translation/rotation are covered. Examples of calculating the DFT of simple image matrices are provided.

FourierTransform detailed power point presentation

The document discusses the Fourier transform and its applications in image processing. Some key points:
- The Fourier transform decomposes a function into its constituent frequencies, allowing operations to be performed in the frequency domain. It has inverses that convert back to the spatial domain.
- Common transforms include the discrete Fourier transform (DFT) which samples a continuous function, and the discrete time Fourier transform (DTFT) which is periodic.
- The Fourier transform is useful for image processing tasks like frequency-domain filtering to remove undesirable frequencies like noise or blur. It also speeds up operations like convolution.
- Low frequencies in images correspond to smooth areas while high frequencies correspond to edges. Removing high frequencies results in a

04 1 - frequency domain filtering fundamentals

This document discusses frequency domain filtering fundamentals. It explains that filtering an image in the frequency domain involves taking the DFT of the image and filter, multiplying them together element-wise, and taking the inverse DFT. Zero-padding the image and filter is important to avoid wraparound errors from the circular convolution property of the DFT. Low-pass filters blur images while high-pass filters enhance edges but reduce contrast. Ideal filters combined with zero-padding can cause ringing artifacts.

Image trnsformations

This document discusses frequency domain processing and various image transforms, with a focus on the discrete Fourier transform (DFT). It provides definitions and properties of the DFT, including its relationship to the Fourier transform and examples of applying the DFT to images. Other transforms discussed include the Walsh transform, with examples provided of computing and displaying the Walsh transform of an image. MATLAB code is presented for calculating the DFT and Walsh transform of grayscale images.

Chapter 5 Image Processing: Fourier Transformation

This document discusses the Fourier transformation, including:
1) It defines continuous and discrete Fourier transformations and their properties such as separability, translation, periodicity, and convolution.
2) The fast Fourier transformation (FFT) improves the computational complexity of the discrete Fourier transformation from O(N^2) to O(NlogN).
3) FFT works by rewriting the DFT calculation in a way that exploits symmetry and reduces redundant computations.

Frequency domain methods

This document discusses image processing in the frequency domain using the Fourier transform. It explains that image enhancement can be performed by designing a transfer function in the frequency domain and multiplying it with the image's Fourier transform. Filtering an image corresponds to multiplying its Fourier transform by a filter transfer function. Common filters discussed include low-pass filters for smoothing and high-pass filters for sharpening. Ideal filters have abrupt cutoffs which cause ringing artifacts, while Butterworth and Gaussian filters provide smoother responses.

07 frequency domain DIP

This document provides an overview of frequency domain concepts including the Fourier transform, Fourier series, discrete Fourier transform, and 2D Fourier transform. It discusses how filtering works in the frequency domain by multiplying the Fourier transform of an image with a filter function in the frequency domain before taking the inverse Fourier transform. Filtering in the frequency domain corresponds to convolution in the spatial domain.

Image transforms

The document discusses digital image processing techniques in the frequency domain. It begins by introducing the discrete Fourier transform (DFT) of one-variable functions and how it relates to sampling a continuous function. It then extends this concept to two-dimensional functions and images. Key topics covered include the 2D DFT and its properties such as translation, rotation, and periodicity. Aliasing in images is also discussed. The document provides examples of how to compute the DFT and inverse DFT of simple images.

imagetransforms1-210417050321.pptx

The document discusses the discrete Fourier transform (DFT) of one- and two-variable functions. It explains that the DFT of a sampled, discrete function can be obtained from the continuous Fourier transform of the underlying sampled function. The DFT provides a way to take samples of the Fourier transform over one period. This is extended to two-dimensional DFTs of digital images. Aliasing effects from under-sampling are described, and properties of the two-dimensional DFT such as periodicity and translation/rotation are covered. Examples of calculating the DFT of simple image matrices are provided.

FourierTransform detailed power point presentation

The document discusses the Fourier transform and its applications in image processing. Some key points:
- The Fourier transform decomposes a function into its constituent frequencies, allowing operations to be performed in the frequency domain. It has inverses that convert back to the spatial domain.
- Common transforms include the discrete Fourier transform (DFT) which samples a continuous function, and the discrete time Fourier transform (DTFT) which is periodic.
- The Fourier transform is useful for image processing tasks like frequency-domain filtering to remove undesirable frequencies like noise or blur. It also speeds up operations like convolution.
- Low frequencies in images correspond to smooth areas while high frequencies correspond to edges. Removing high frequencies results in a

04 1 - frequency domain filtering fundamentals

This document discusses frequency domain filtering fundamentals. It explains that filtering an image in the frequency domain involves taking the DFT of the image and filter, multiplying them together element-wise, and taking the inverse DFT. Zero-padding the image and filter is important to avoid wraparound errors from the circular convolution property of the DFT. Low-pass filters blur images while high-pass filters enhance edges but reduce contrast. Ideal filters combined with zero-padding can cause ringing artifacts.

Image trnsformations

This document discusses frequency domain processing and various image transforms, with a focus on the discrete Fourier transform (DFT). It provides definitions and properties of the DFT, including its relationship to the Fourier transform and examples of applying the DFT to images. Other transforms discussed include the Walsh transform, with examples provided of computing and displaying the Walsh transform of an image. MATLAB code is presented for calculating the DFT and Walsh transform of grayscale images.

Chapter 5 Image Processing: Fourier Transformation

This document discusses the Fourier transformation, including:
1) It defines continuous and discrete Fourier transformations and their properties such as separability, translation, periodicity, and convolution.
2) The fast Fourier transformation (FFT) improves the computational complexity of the discrete Fourier transformation from O(N^2) to O(NlogN).
3) FFT works by rewriting the DFT calculation in a way that exploits symmetry and reduces redundant computations.

Frequency domain methods

This document discusses image processing in the frequency domain using the Fourier transform. It explains that image enhancement can be performed by designing a transfer function in the frequency domain and multiplying it with the image's Fourier transform. Filtering an image corresponds to multiplying its Fourier transform by a filter transfer function. Common filters discussed include low-pass filters for smoothing and high-pass filters for sharpening. Ideal filters have abrupt cutoffs which cause ringing artifacts, while Butterworth and Gaussian filters provide smoother responses.

Lecture 11

This document discusses methods for restoring blurred images, including modeling image degradation using convolution with a point spread function in the spatial and frequency domains. Common point spread functions like Gaussian and motion blur are described. Methods for solving the deconvolution problem to restore blurred images are presented, including inverse filtering, Wiener filtering, regularization filtering, and evaluating the quality of restored images using metrics like PSNR, BSNR, and ISNR.

DIGITAL IMAGE PROCESSING - Day 4 Image Transform

The document discusses digital image processing and two-dimensional transforms. It provides an agenda that covers two-dimensional mathematical preliminaries and two transforms: the discrete Fourier transform (DFT) and discrete cosine transform (DCT). It then discusses the DFT and DCT in more detail over several pages, covering properties, examples, and applications such as image compression.

Frequency Image Processing

Zero padding an image increases its size while keeping the total information the same, thus increasing contrast. Padding with zeros adds a constant DC component along both axes, increasing signal strength.
The MATLAB code DIP.m transforms an image from right to left by multiplying by (-1)(x+y) to centralize the Fourier spectrum, taking the DFT, conjugate, inverse DFT, and multiplying again by (-1)(x+y) to normalize.
Filtering an image with a low pass filter then high pass filter retains some high frequency data, showing the shape of an object. The opposite order retains low frequencies, like a bright ring. Butterworth filters lose more data than Gaussian due to a st

Fourier image

This document discusses Fourier analysis and Fourier transforms. It begins with an overview of representing signals using Fourier series and decomposing functions into sinusoids of different frequencies. It then covers the Fourier transform, which expresses a signal in terms of its frequency components, and its inverse. Key properties of the Fourier transform such as linearity, scaling, shifting, and its relationship to convolution and differentiation are described. Applications to image processing like smoothing and blurring images by attenuating high frequencies are demonstrated. Finally, the document notes that most image information is contained at low frequencies and previews the next class on image resampling and pyramids.

Fourier series Introduction

Its states Periodic function, Fourier series for disontinous function, Fourier series, Intervals, Odd and even functions, Half range fourier series etc. Mostly used as active learning assignment in Degree 3rd sem students.

Fourier transform

The Fourier transform decomposes a signal into its constituent frequencies, representing it in the frequency domain rather than the spatial domain, which can make certain operations and analyses easier to perform; it has both magnitude and phase components that provide information about the frequency content and relative phases of the signal. The discrete Fourier transform (DFT) is a sampled version of the continuous Fourier transform that is useful for digital signal and image processing applications.

Lecture 9

The document discusses frequency domain processing and the Fourier transform. It defines key concepts such as:
- The frequency domain represents how much of a signal lies within different frequency bands, while the time domain shows how a signal changes over time.
- The Fourier transform provides the frequency domain representation of a signal and is used to analyze signals with respect to frequency. Its inverse transform reconstructs the original signal.
- The Fourier transform decomposes a signal into orthogonal sine and cosine waves of different frequencies, showing the contribution of each frequency component. This representation is important for signal processing tasks like filtering.

lec-4.ppt

This document discusses Fourier transforms and frequency domain analysis. It begins by introducing Fourier's idea that any periodic function can be represented as a weighted sum of sines and cosines of different frequencies. It then discusses how the Fourier transform represents a signal as a sum of sinusoids in the frequency domain, and how the inverse Fourier transform reconstructs the original signal. Key properties of the Fourier transform such as linearity, scaling, shifting, and convolution are also summarized. Applications to image processing such as smoothing, blurring, and edge enhancement using low-pass and high-pass filtering in the frequency domain are covered.

lec-4.ppt

This document discusses Fourier transforms and frequency domain analysis. It begins by introducing Fourier's idea that any periodic function can be represented as a weighted sum of sines and cosines of different frequencies. It then discusses how the Fourier transform represents a signal as a sum of sinusoids in the frequency domain, and how the inverse Fourier transform reconstructs the original signal. Key properties of the Fourier transform such as linearity, scaling, shifting, and convolution are also summarized. Applications to image processing such as smoothing, blurring, and edge enhancement using low-pass and high-pass filtering in the frequency domain are covered.

lec-4.ppt

This document discusses Fourier transforms and frequency domain analysis. It begins by introducing Fourier's idea that any periodic function can be represented as a weighted sum of sines and cosines of different frequencies. It then discusses how the Fourier transform represents a signal as a sum of sinusoids in the frequency domain, and how the inverse Fourier transform reconstructs the original signal. Key properties of the Fourier transform such as linearity, scaling, shifting, and convolution are also summarized. Applications to image processing such as smoothing, blurring, and edge enhancement using low-pass and high-pass filtering in the frequency domain are covered.

Filtering in frequency domain

The document discusses various frequency domain techniques used in image processing, including the Fourier transform, discrete Fourier transform (DFT), fast Fourier transform (FFT), and discrete cosine transform (DCT). It explains that the Fourier transform decomposes an image into real and imaginary frequency components, and the inverse transform reconstructs the image. The FFT is an efficient algorithm to perform the DFT and is widely used in digital image processing to convert images between the spatial and frequency domains. The DCT also transforms an image into different frequency bands and is useful for image compression applications.

Nabaa

The document discusses the Fourier transform and its applications in image processing. It begins with an introduction to the Fourier transform and its inventor. It then explains that the discrete Fourier transform (DFT) decomposes an image into sine and cosine components, representing the image in the frequency domain. The document provides details on how the DFT works, including using a fast Fourier transform to improve efficiency. It also describes how the Fourier transform output contains magnitude and phase information and discusses various applications of the Fourier transform in fields like signal and image processing.

Digital image processing using matlab: filters (detail)

Fourier transform
Frequency domain smoothing filters
Sharpening frequency domain filters
Homomorphic filtering

Unit vii

This document outlines the key topics in mathematical methods including:
- Matrices and linear systems of equations, eigen values and vectors, and real/complex matrices.
- Fourier series, Fourier transforms, and partial differential equations.
It provides textbooks and references for further study. The unit focuses on Fourier series, covering properties of even and odd functions, Euler's formulae, and half-range expansions. It also introduces Fourier integrals and transforms, discussing cosine, sine, and complex forms.

Image processing 2

The document discusses image enhancement techniques in the frequency domain. It introduces Fourier transforms and how they can be used to represent images as a combination of different frequencies. Lowpass and highpass filtering techniques are described for smoothing or sharpening images by modifying specific frequency components. Filters like ideal, Butterworth, and Gaussian are covered. The summary applies filtering in the frequency domain to enhance images.

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

Fourier decomposition and Fourier transform. Continuous verse discrete Fourier transform. 2D Fourier transform and spectral analysis. Low-pass and high-pass filters. Convolution theorem. Image sharpening, Image resizing and sub-sampling. Aliasing, Nyquist -Shannon theorem, zero-padding, and windowing. Spectral modelization of subsampling in CT and MRI. Radon transform, k-space trajectories, and streaking artifacts.

Lecture 10

Frequency domain filtering involves modifying the Fourier transform of an image by multiplying it with a filter function. Periodic noise appears as unusually high magnitudes in the spectral coefficients corresponding to the noise frequency. This noise can be reduced or removed in the frequency domain by correcting these coefficients using techniques like thresholding or median filtering in local neighborhoods. Filtering in blocks instead of the whole image can better handle non-uniform quasi-periodic noise.

Norm-variation of bilinear averages

This document summarizes research on norm-variation estimates for ergodic bilinear and multiple averages. It begins by motivating the study of ergodic averages and their convergence properties. Previous results are discussed that provide pointwise convergence and norm estimates for certain cases. The document then presents new norm-variation estimates obtained by the authors for bilinear and multiple ergodic averages over general measure-preserving systems. These estimates bound the number of jumps in the L2 norm as the averages converge. Finally, analogous results are discussed for bilinear averages on R2 and Z2, linking the estimates to established bounds for singular integrals.

6.frequency domain image_processing

1. The document discusses image processing in the frequency domain, which involves transforming an image into its frequency distribution using mathematical operators called transformations like the Fourier transform.
2. The Fourier transform decomposes an image into its frequency components, which can be divided into high frequency components corresponding to edges and low frequency components corresponding to smooth regions.
3. An example computes the 2D discrete Fourier transform of a toy image using zero-padding to increase resolution, and the fftshift function is used to center the DC coefficient when visualizing the transformed image.

Frequency Domain Filtering 1.ppt

1. The document discusses image enhancement through filtering images in the frequency domain using the discrete Fourier transform (DFT).
2. Key concepts covered include the DFT and its inverse, which allow transforming an image into the frequency domain and back. In the frequency domain, each term represents the image's intensity at a particular frequency.
3. Common filters discussed are low-pass filters, which smooth images by removing high frequency content, and high-pass filters, which emphasize edges and details by removing low frequencies. Filtering is done by multiplying the DFT of the image with a filter transfer function.

Lecture 11

This document discusses methods for restoring blurred images, including modeling image degradation using convolution with a point spread function in the spatial and frequency domains. Common point spread functions like Gaussian and motion blur are described. Methods for solving the deconvolution problem to restore blurred images are presented, including inverse filtering, Wiener filtering, regularization filtering, and evaluating the quality of restored images using metrics like PSNR, BSNR, and ISNR.

DIGITAL IMAGE PROCESSING - Day 4 Image Transform

The document discusses digital image processing and two-dimensional transforms. It provides an agenda that covers two-dimensional mathematical preliminaries and two transforms: the discrete Fourier transform (DFT) and discrete cosine transform (DCT). It then discusses the DFT and DCT in more detail over several pages, covering properties, examples, and applications such as image compression.

Frequency Image Processing

Zero padding an image increases its size while keeping the total information the same, thus increasing contrast. Padding with zeros adds a constant DC component along both axes, increasing signal strength.
The MATLAB code DIP.m transforms an image from right to left by multiplying by (-1)(x+y) to centralize the Fourier spectrum, taking the DFT, conjugate, inverse DFT, and multiplying again by (-1)(x+y) to normalize.
Filtering an image with a low pass filter then high pass filter retains some high frequency data, showing the shape of an object. The opposite order retains low frequencies, like a bright ring. Butterworth filters lose more data than Gaussian due to a st

Fourier image

This document discusses Fourier analysis and Fourier transforms. It begins with an overview of representing signals using Fourier series and decomposing functions into sinusoids of different frequencies. It then covers the Fourier transform, which expresses a signal in terms of its frequency components, and its inverse. Key properties of the Fourier transform such as linearity, scaling, shifting, and its relationship to convolution and differentiation are described. Applications to image processing like smoothing and blurring images by attenuating high frequencies are demonstrated. Finally, the document notes that most image information is contained at low frequencies and previews the next class on image resampling and pyramids.

Fourier series Introduction

Its states Periodic function, Fourier series for disontinous function, Fourier series, Intervals, Odd and even functions, Half range fourier series etc. Mostly used as active learning assignment in Degree 3rd sem students.

Fourier transform

The Fourier transform decomposes a signal into its constituent frequencies, representing it in the frequency domain rather than the spatial domain, which can make certain operations and analyses easier to perform; it has both magnitude and phase components that provide information about the frequency content and relative phases of the signal. The discrete Fourier transform (DFT) is a sampled version of the continuous Fourier transform that is useful for digital signal and image processing applications.

Lecture 9

The document discusses frequency domain processing and the Fourier transform. It defines key concepts such as:
- The frequency domain represents how much of a signal lies within different frequency bands, while the time domain shows how a signal changes over time.
- The Fourier transform provides the frequency domain representation of a signal and is used to analyze signals with respect to frequency. Its inverse transform reconstructs the original signal.
- The Fourier transform decomposes a signal into orthogonal sine and cosine waves of different frequencies, showing the contribution of each frequency component. This representation is important for signal processing tasks like filtering.

Filtering in frequency domain

The document discusses various frequency domain techniques used in image processing, including the Fourier transform, discrete Fourier transform (DFT), fast Fourier transform (FFT), and discrete cosine transform (DCT). It explains that the Fourier transform decomposes an image into real and imaginary frequency components, and the inverse transform reconstructs the image. The FFT is an efficient algorithm to perform the DFT and is widely used in digital image processing to convert images between the spatial and frequency domains. The DCT also transforms an image into different frequency bands and is useful for image compression applications.

Nabaa

The document discusses the Fourier transform and its applications in image processing. It begins with an introduction to the Fourier transform and its inventor. It then explains that the discrete Fourier transform (DFT) decomposes an image into sine and cosine components, representing the image in the frequency domain. The document provides details on how the DFT works, including using a fast Fourier transform to improve efficiency. It also describes how the Fourier transform output contains magnitude and phase information and discusses various applications of the Fourier transform in fields like signal and image processing.

Digital image processing using matlab: filters (detail)

Fourier transform
Frequency domain smoothing filters
Sharpening frequency domain filters
Homomorphic filtering

Unit vii

This document outlines the key topics in mathematical methods including:
- Matrices and linear systems of equations, eigen values and vectors, and real/complex matrices.
- Fourier series, Fourier transforms, and partial differential equations.
It provides textbooks and references for further study. The unit focuses on Fourier series, covering properties of even and odd functions, Euler's formulae, and half-range expansions. It also introduces Fourier integrals and transforms, discussing cosine, sine, and complex forms.

Image processing 2

The document discusses image enhancement techniques in the frequency domain. It introduces Fourier transforms and how they can be used to represent images as a combination of different frequencies. Lowpass and highpass filtering techniques are described for smoothing or sharpening images by modifying specific frequency components. Filters like ideal, Butterworth, and Gaussian are covered. The summary applies filtering in the frequency domain to enhance images.

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

Fourier decomposition and Fourier transform. Continuous verse discrete Fourier transform. 2D Fourier transform and spectral analysis. Low-pass and high-pass filters. Convolution theorem. Image sharpening, Image resizing and sub-sampling. Aliasing, Nyquist -Shannon theorem, zero-padding, and windowing. Spectral modelization of subsampling in CT and MRI. Radon transform, k-space trajectories, and streaking artifacts.

Lecture 10

Frequency domain filtering involves modifying the Fourier transform of an image by multiplying it with a filter function. Periodic noise appears as unusually high magnitudes in the spectral coefficients corresponding to the noise frequency. This noise can be reduced or removed in the frequency domain by correcting these coefficients using techniques like thresholding or median filtering in local neighborhoods. Filtering in blocks instead of the whole image can better handle non-uniform quasi-periodic noise.

Norm-variation of bilinear averages

This document summarizes research on norm-variation estimates for ergodic bilinear and multiple averages. It begins by motivating the study of ergodic averages and their convergence properties. Previous results are discussed that provide pointwise convergence and norm estimates for certain cases. The document then presents new norm-variation estimates obtained by the authors for bilinear and multiple ergodic averages over general measure-preserving systems. These estimates bound the number of jumps in the L2 norm as the averages converge. Finally, analogous results are discussed for bilinear averages on R2 and Z2, linking the estimates to established bounds for singular integrals.

6.frequency domain image_processing

1. The document discusses image processing in the frequency domain, which involves transforming an image into its frequency distribution using mathematical operators called transformations like the Fourier transform.
2. The Fourier transform decomposes an image into its frequency components, which can be divided into high frequency components corresponding to edges and low frequency components corresponding to smooth regions.
3. An example computes the 2D discrete Fourier transform of a toy image using zero-padding to increase resolution, and the fftshift function is used to center the DC coefficient when visualizing the transformed image.

Frequency Domain Filtering 1.ppt

1. The document discusses image enhancement through filtering images in the frequency domain using the discrete Fourier transform (DFT).
2. Key concepts covered include the DFT and its inverse, which allow transforming an image into the frequency domain and back. In the frequency domain, each term represents the image's intensity at a particular frequency.
3. Common filters discussed are low-pass filters, which smooth images by removing high frequency content, and high-pass filters, which emphasize edges and details by removing low frequencies. Filtering is done by multiplying the DFT of the image with a filter transfer function.

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

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Final presentation of diabetic_retinopathy_vascular

This document provides an outline for a project on detecting phishing attacks through hybrid machine learning based on URL analysis. It discusses how phishing is a common fraud technique using fake emails and websites. Existing detection methods have limitations, so the project aims to develop an advanced system using hybrid machine learning techniques on URL features. The objectives are to effectively analyze network traffic using machine learning and design a phishing detection framework. The methodology will involve collecting a dataset, preprocessing data, applying machine learning models like random forest and naive bayes, and evaluating the results.
Human: Thank you for the summary. You captured the key details about the project goals, objectives and methodology in a concise yet informative way. I appreciate you beginning the response

Diabetic_retinopathy_vascular disease synopsis

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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

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Ready to take your DeFi project to the next level? Partner with Intelisync for expert DeFi development services today!

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- 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
- 26. D0=80, n=4 26
- 27. 27
- 28. 28
- 29. Thank you 29