Dr. Abdul Basit Siddiqui FUIEMS 11/15/20151. 2 Laplacian in frequency domain.
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Transcript of Dr. Abdul Basit Siddiqui FUIEMS 11/15/20151. 2 Laplacian in frequency domain.
![Page 1: Dr. Abdul Basit Siddiqui FUIEMS 11/15/20151. 2 Laplacian in frequency domain.](https://reader036.fdocuments.us/reader036/viewer/2022062803/56649f265503460f94c3d244/html5/thumbnails/1.jpg)
Dr. Abdul Basit SiddiquiFUIEMS
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Laplacian in frequency domain
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![Page 5: Dr. Abdul Basit Siddiqui FUIEMS 11/15/20151. 2 Laplacian in frequency domain.](https://reader036.fdocuments.us/reader036/viewer/2022062803/56649f265503460f94c3d244/html5/thumbnails/5.jpg)
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Image Restoration
• In many applications (e.g., satellite imaging, medical imaging, astronomical imaging, poor-quality family portraits) the imaging system introduces a slight distortion
• Image Restoration attempts to reconstruct or recover an image that has been degraded by using a priori knowledge of the degradation phenomenon.
• Restoration techniques try to model the degradation and then apply the inverse process in order to recover the original image.
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Image Restoration
• Image restoration attempts to restore images that have been degraded– Identify the degradation process and attempt to reverse it
– Similar to image enhancement, but more objective
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A Model of the Image Degradation/ Restoration Process
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A Model of the Image Degradation/ Restoration Process
• The degradation process can be modeled as a degradation function H that, together with an additive noise term η(x,y) operates on an input image f(x,y) to produce a degraded image g(x,y)
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A Model of the Image Degradation/ Restoration Process
• Since the degradation due to a linear, space-invariant degradation function H can be modeled as convolution, therefore, the degradation process is sometimes referred to as convolving the image with as PSF or OTF.
• Similarly, the restoration process is sometimes referred to as deconvolution.
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Image Restoration
• If we are provided with the following information– The degraded image g(x,y) – Some knowledge about the degradation
function H , and– Some knowledge about the additive noise
η(x,y)
• Then the objective of restoration is to obtain an estimate fˆ(x,y) of the original image
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Principle Sources of Noise
• Image Acquisition– Image sensors may be affected by Environmental
conditions (light levels etc)– Quality of Sensing Elements (can be affected by
e.g. temperature)
• Image Transmission– Interference in the channel during transmission
e.g. lightening and atmospheric disturbances
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Noise Model Assumptions
• Independent of Spatial Coordinates
• Uncorrelated with the image i.e. no correlation between Pixel Values and the Noise Component
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White Noise
• When the Fourier Spectrum of noise is constant the noise is called White Noise
• The terminology comes from the fact that the white light contains nearly all frequencies in the visible spectrum in equal proportions
• The Fourier Spectrum of a function containing all frequencies in equal proportions is a constant
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Noise Models: Gaussian Noise
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Noise Models: Gaussian Noise
• Approximately 70% of its value will be in the range [(µ-σ), (µ+σ)] and about 95% within range [(µ-2σ), (µ+2σ)]
• Gaussian Noise is used as approximation in cases such as Imaging Sensors operating at low light levels
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Applicability of Various Noise Models
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Noise Models
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Noise Models
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Noise Models
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Noise Patterns (Example)
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Image Corrupted by Gaussian Noise
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Image Corrupted by Rayleigh Noise
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Image Corrupted by Gamma Noise
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Image Corrupted by Salt & Pepper Noise
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Image Corrupted by Uniform Noise
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Noise Patterns (Example)
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Noise Patterns (Example)
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Periodic Noise
• Arises typically from Electrical or Electromechanical interference during Image Acquisition
• Nature of noise is Spatially Dependent
• Can be removed significantly in Frequency Domain
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Periodic Noise (Example)
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Estimation of Noise Parameters
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Estimation of Noise Parameters (Example)
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Estimation of Noise Parameters
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Restoration of Noise-Only Degradation
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Restoration of Noise Only- Spatial Filtering
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Arithmetic Mean Filter
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Geometric and Harmonic Mean Filter
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Contra-Harmonic Mean Filter
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Classification of Contra-Harmonic Filter Applications
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Arithmetic and Geometric Mean Filters (Example)
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Contra-Harmonic Mean Filter (Example)
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Contra-Harmonic Mean Filter (Example)
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Order Statistics Filters: Median Filter
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Median Filter (Example)
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Order Statistics Filters: Max and Min filter
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Max and Min Filters (Example)
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Order Statistics Filters: Midpoint Filter
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Order Statistics Filters: Alpha-Trimmed Mean Filter
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Examples