Removal of Artifacts
T-61.182, Biomedical Image AnalysisSeminar presentation 19.2.2005
Hannu LaaksonenVibhor Kumar
Overview, part I
Different types of noise Signal dependent noise Stationarity
Simple methods of noise removal Averaging Space-domain filtering Frequency-domain filtering
Matrix representation of images
Introduction
Noise: any part of the image that is of no interest
Removal of noise (artifacts) crucial for image analysis
Artifact removal should not cause distortions in the image
Different types of noise
Random noise Probability density function, PDF Gaussian, uniform, Poisson
Structured noise Physiological interference Other
Signal dependent noise
Noise might not be independent; it may also depend on the signal itself
Poisson noise Film-grain noise Speckle noise
An image with Poisson noise
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Stationarity
Strongly stationary Stationary in the wide sense Nonstationary Quasistationary (block-wise stationary)
Short-time analysis Cyclo-stationary
Synchronized or multiframe averaging If several time instances of the image are available, the noise
can be reduced by averaging Synchronized averaging: frames are acquired in the same
phase Changes (motion, displacement) between frames will cause
distortion
Space-domain filters
Images often nonstationary as a whole, but ma be stationary in small segments
Moving-window filter Sizes, shapes and weights vary Parameters are estimated in the window and
applied to the pixel in center
Examples of space-domain filters Mean filter
Mean of the values in window Median filter
Median of the values in window Nonlinear
Order-statistic filter A large class of nonlinear filters
Frequency-domain filters
In natural images, usually the most important information is located at low frequencies
Frequency-domain filtering: 2D Fourier transform is calculated of the image The transformed image passed through a transfer
function (filter) The image is then transformed back
Matrix representation of image processing Image may be presented as a matrix:f = {f(m,n) : m = 0,1,2,…M-1; n = 0,1,2,…,N-1}
Can be converted into vector by row ordering:f = [f1, f2, …, fM]T
Image properties can be calculated using matrix notation Mean m = E[f] Covariance σ = E[(f - m)(f - m)T] Autocorrelation Φ = E[f fT]