Digital Image Processing Chapter 5 Image Restoration A

Digital Image Processing Chapter 5: Image Restoration

A Model of the Image Degradation/Restoration Process

¡ Degradation l Degradation function H Additive noise Spatial domain l Frequency domain l l

¡ Restoration

Noise Models ¡ Sources of noise l ¡ White noise l ¡ Image acquisition, digitization, transmission The Fourier spectrum of noise is constant Assuming l l Noise is independent of spatial coordinates Noise is uncorrelated with respect to the image itself

¡ Gaussian noise l The PDF of a Gaussian random variable, z, l Mean: Standard deviation: Variance: l l

l 70% of its values will be in the range l 95% of its values will be in the range

¡ Rayleigh noise l The PDF of Rayleigh noise, l Mean: l Variance:

¡ Erlang (Gamma) noise l The PDF of Erlang noise, a positive integer, l Mean: l Variance: , is

¡ Exponential noise l The PDF of exponential noise, l Mean: l Variance: ,

¡ Uniform noise l The PDF of uniform noise, l Mean: l Variance:

¡ Impulse (salt-and-pepper) noise l The PDF of (bipolar) impulse noise, l : gray-level will appear as a light dot, while level will appear like a dark dot Unipolar: either or is zero l

l Usually, for an 8 -bit image, (black) and =0 (white) =0

¡ Modeling l Gaussian ¡ l Rayleigh ¡ l Electronic circuit noise, sensor noise due to poor illumination and/or high temperature Range imaging Exponential and gamma ¡ Laser imaging

l Impulse ¡ l Quick transients, such as faulty switching Uniform Least descriptive ¡ Basis for numerous random number generators ¡

¡ Periodic noise l l Arises typically from electrical or electromechanical interference Reduced significantly via frequency domain filtering

¡ Estimation of noise parameters l l Inspection of the Fourier spectrum Small patches of reasonably constant gray level For example, 150*20 vertical strips ¡ Calculate , , , from ¡

Restoration in the Presence of Noise Only-Spatial Filtering ¡ Degradation l Spatial domain l Frequency domain

¡ Mean filters l Arithmetic mean filter l Geometric mean filter

l Harmonic mean filter ¡ Works well for salt noise, but fails fpr pepper noise

l Contraharmonic mean filter ¡ ¡ : eliminates pepper noise : eliminates salt noise

¡ Usage l l Arithmetic and geometric mean filters: suited for Gaussian or uniform noise Contraharmonic filters: suited for impulse noise

¡ Order-statistics filters l Median filter ¡ Effective in the presence of both bipolar and unipolar impulse noise

l Max and min filters ¡ max filters reduce pepper noise ¡ min filters salt noise

l Midpoint filter ¡ Works best for randomly distributed noise, like Gaussian or uniform noise

l Alpha-trimmed mean filter Delete the d/2 lowest and the d/2 highest gray-level values ¡ Useful in situations involving multiple types of noise, such as a combination of salt-and-pepper and Gaussian noise ¡

¡ Adaptive, local noise reduction filter l l l If of If is zero, return simply the value , return a value close to If , return the arithmetic mean value

¡ Adaptive median filter l = minimum gray level value in l = maximum gray level value in l = median of gray levels in = gray level at coordinates = maximum allowed size of l l

l l l l l Algorithm: Level A: A 1= A 2= If A 1>0 AND A 2<0, Go to level B Else increase the window size If window size repeat level A Else output

l l Level B: B 1= B 2= If B 1>0 AND B 2<0, output Else output

l Purposes of the algorithm Remove salt-and-pepper (impulse) noise ¡ Provide smoothing ¡ Reduce distortion, such as excessive thinning or thickening of object boundaries ¡

Periodic Noise Reduction by Frequency Domain Filtering ¡ Bandreject filters l Ideal bandreject filter

l Butterworth bandreject filter of order n l Gaussian bandreject filter

¡ Bandpass filters

¡ Notch filters l Ideal notch reject filter

¡ Butterworth notch reject filter of order n

¡ Gaussian notch reject filter

¡ Notch pass filter

¡ Optimum notch filtering

l Interference noise pattern in the spatial domain l Subtract from portion of estimate of a weighted to obtain an

l l l Minimize the local variance of The detailed steps are listed in Page 251 Result