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Digital Image Processing
Image Restoration Digital Image Processing
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Content Introduction Image degradation/restoration model Noise models
Restoration by spatial filtering Estimation of degradation functions Inverse filtering Wiener filtering Geometric transformation
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Introduction Objective of image restoration The distortion is due to
to recover a distorted image to the original form based on idealized models. The distortion is due to Image degradation in sensing environment e.g. random atmospheric turbulence Noisy degradation from sensor noise. Blurring degradation due to sensors e.g. camera motion or out-of-focus Geometric distortion e.g. earth photos taken by a camera in a satellite
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Introduction Enhancement Restoration
Concerning the extraction of image features Difficult to quantify performance Subjective; making an image “look better” Restoration Concerning the restoration of degradation Performance can be quantified Objective; recovering the original image
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Image degradation / restoration model
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Noise models Assuming that noise is
independent of spatial coordinates, and uncorrelated with respect to the image content
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Noise models
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Adding Gaussian Noise at Matlab
t_gaus = imnoise (t, ‘gaussian’); imshow(t_gaus);
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Noise models
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Adding Salt and Pepper Noise at Matlab
t_sp = imnoise (t, ‘salt & pepper’); imshow(t_sp);
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Noise models Other common noise models Rayleigh noise Gamma noise
Exponential noise Uniform noise
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Noise Models Rayleigh Noise Gamma(Erlang) Noise Exponential Noise
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Noise models paper salt -3-levels -simple constant areas
(spans from black to white) paper salt
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Additive Noise Histograms
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Additive Noise Histograms
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Periodic Noise Noise components
Are generated due to electrical or electromechanical interference during image acquisition Periodic noise can be reduced in via frequency domain
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Adding Periodic Noise at Matlab
tw = imread(filename); t = rgb2gray(tw); s = size(t); [x,y] = meshgrid(1:s(1), 1:s(2)); p = sin(x/3+y/5)+1; t_pn = (im2double(t)+p’/2)/2; imshow(t_pn);
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Restoration by spatial filtering
Noise is unknown Spatial filtering is appropriate when only additive noise is present
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Restoration of Salt and Pepper Noise by LPF
a3 = fspecial(‘average’); t_sp_a3 = filter2 (a3, t_sp); a7 = fspecial(‘average’, [7,7]); t_sp_a7 = filter2 (a7, t_sp);
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Restoration of Salt and Pepper Noise by Median Filter
T_sp_m3 = medfilt2(t_sp);
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Restoration by spatial filtering
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Restoration by spatial filtering
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Restoration by spatial filtering
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Restoration by spatial filtering
Q is the order of filter
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Restoration by spatial filtering
Noise level is Mean =0 Variance = 400
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Restoration by spatial filtering
Mean filters (noise reduced by blurring) Arithmetic mean filter and geometric mean filter are well suited for random noise such as Gaussian noise Contraharmonic mean filter is well suited for impulse noise Disadvantage: must know pepper noise or salt noise in advance
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Restoration by spatial filtering
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Restoration by spatial filtering
wrong
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Restoration by spatial filtering
-- Repeated passes of median filter tend to blur the image. -- Keep the number of passes as low as possible.
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Restoration by spatial filtering
Fig. 8 next page
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Restoration by spatial filtering
Pepper noise Salt noise
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Median and alpha-trimmed filter performed better
High level of noise large filter Median and alpha-trimmed filter performed better Alpha-trimmed did better than median filter
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Restoration by spatial filtering
Filters discussed so far Do not consider image characteristics Adaptive filters to be discussed Behaviors based on statistical characteristics of the subimage under a filter window Better performance More complicated Adaptive, local noise reduction filter Adaptive median filter
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Restoration by spatial filtering
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Restoration by spatial filtering
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Restoration by spatial filtering
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Restoration by spatial filtering
Adaptive filtering
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Restoration by spatial filtering
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Restoration by spatial filtering
Is Z_med impulse? Is Z_xy impulse?
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Restoration by spatial filtering
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Periodic Noise Reduction (Frequency Domain Filtering)
Band-Reject Filters Ideal Band-reject Filter -D(u,v) =distance from the origin of the centered freq. rectangle -W =width of the band -D0=Radial center of the band.
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Periodic Noise Reduction (Frequency Domain Filtering)
Butterworth Band-Reject Filter of order n Gaussian Band-Reject Filter
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Periodic Noise Reduction (Frequency Domain Filtering)
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Periodic Noise Reduction (Frequency Domain Filtering)
Band-Pass Filters Opposite operation of a band-reject fiter
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Periodic Noise Reduction (Frequency Domain Filtering)
Notch Filters Rejects (or passes) frequencies in predefined neighborhoods about a center frequency Ideal Must appear in symmetric pairs about the origin. Butterworth Gaussian
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Periodic Noise Reduction (Frequency Domain Filtering)
Notch Filters Ideal Center frequency components Shift with respect to the center
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Notch pass filter Horizontal lines of the noise pattern I can be seen
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Optimum Notch Filtering
Several pairs of components are present more than just one sinusoidal component
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Optimum Notch Filtering
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Estimation of degradation functions
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Estimation of degradation functions
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Estimation of degradation functions
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Estimation of degradation functions
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Estimation of degradation functions
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Estimation of degradation functions (model bases)
Mathematical model for uniform linear motion between the image and the sensor during image acquisition Let x0(t) and y0(t) denote time varying components of motion in the x- and y-directions Degradation model
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Estimation of degradation functions (model bases)
Uniform Linear motion in the x and y direction x0(t)=at/T and y0(t)=bt/T where the image has been displaced by a total distance a in the x-direction and b in the y-direction
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Estimation of degradation functions (model bases)
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Inverse filtering
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Inverse filtering
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Inverse filtering Degradation function Curtain of noise
Cutting off values of the ratio outside a radius of 40, 70,85.
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Wiener filtering
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Wiener filtering
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Wiener filtering White noinse
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Wiener filtering
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Geometric transformations
Objective: to eliminate geometric distortion that occurs when an image is captured Examples of geometric distortion Pincushion distortion (associated with zoom lenses)
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Geometric transformations
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Geometric transformations
Two steps in geometric transformation Spatial transformation: rearrangement of pixels on the image plane Gray-level interpolation: assignment of gray levels to pixels in the spatially transformed image
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Geometric transformations
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Geometric transformations
• Solution To formulate the spatial relocation of pixels by the use of the corresponding tiepoints Tiepoints: a subset of pixels whose locations in the input (distorted) and output (restored) images are known.
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Geometric transformations
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Geometric transformations
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Geometric transformations
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Geometric transformations
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Geometric transformations
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