Image Restoration

Comp344 Tutorial

Kai Zhang

Outline

DIPUM Tool box Noise models Periodical noise and removal Noise parameter estimation Spatiral noise removal

The DIPUM Tool box

M-functions from the book Digital Image Processing Using MATLAB

http://www.imageprocessingplace.com/DIPUM_Toolbox_1/dipum_toolbox_main_page.htm

Freedownload No original m-functions But can still used for demo

Noise models

Given a random number generator, how to generate random numbers with a pre-specified CDF? Suppose the random number w is in [0,1] We want to generate a Rayleigh distributed sample set

To find z solve the following equation

azeaz

baz

zF

,1,0

/2)(

)(

)1ln(

1/2)(

wbaz

webaz

Functions

Function r = imnoise(f, type, parameters) Corrupt image f with noise specified in type

and parameters Results returned in r Type include: uniform, gaussian, salt &

pepper, lognormal, rayleigh, exponential Function r = imnoise2(type, M,N,a,b);

Generates arrar r of size M-by-N, Entries are of the specified distribution type A and b are parameters

Examples

Codes

Code1 f = imread('lenna.jpg'); g = imnoise(f, 'gaussian', 0, 0.01); figure, imshow(g); g = imnoise(f, 'salt & pepper', 0.01); figure, imshow(g);

Code2 r = imnoise2('gaussian',10000,1,0,1); p = hist(r,50); bar(p);

Periodical spatial noise

Model Using 2-d sinusoid functions

M, N: image size A: magnitude of noise U0, v0: frequency along the two directions Bx, By: phase displacement

Observation: when x goes through 0,1,2,…,M, the left term will repeat u0 times. So the horizontal frequency is u0. Similar for v0.

NByvMBxuAyxr yx /)(2/)(2sin),( 00

Function: [r, R, S] = imnoise3(M,N, C, A, B); Generate a sinusoide noise pattern r Of size M by N With Fourier transform R And spectrum S C is a K-by-2 matrix, each row being coordinate (u,v)

of an impulse A 1-by-K contains the amplitude of each impulse B is K-by-2 matrix each row being the phase

replacement

Periodic noise examples

Codes

C = [0 64; 0 128; 32 32; 64 0; 128 0; -32 32]; [r, R, S] = imnoise3(256,256,C); figure,imshow(S,[]); figure,imshow(r,[]);

Noise estimation

How to determine type and parameters of noise given an image f corrupted by noise? Step 1. Manually choosing a region as featureless as

possible, so that variability is primarily due to noise. [B,c,r] = roipoly(f); Step2. compute the histogram of the selected image

patch [p, npix] = histroi(f, c, r); Step3. determine the noise type through observation Step4. estimating the central moments [v, unv] = statmoments(p, 2);

Illustrations

Functions

Function: [B,c,r] = roipoly(f); F is the image C and r are sequential column and row

coordinates of the polygon / can also be specified by the mouse

B is the region selected (of value 1), and all the rest part of the image is 0

Function [p, npix] = histroi(f, c,r); Generating histogram p of the region of

interest(ROI) specified in c and r (vertex coordinates)

codes

f = imread(‘lenna.jpg’); noisy_f = imnoise(f,'gaussian',0,0.01); figure,imshow(noisy_f,[]); [B, c, r] = roipoly(noisy_f); %needs mouse interations

figure,plot(B); [p,npix] = histroi(f,c,r); figure,bar(p,1); [v, unv] = statmoments(p,2); X = imnoise2('gaussian',

npix,1,unv(1),unv(2)^0.5); figure, hist(X,100);

Spatial noise removal

Function f = spfilter(g, type, m, n, parameter); Performs spatial filtering Type include: amean, gmean, hmean,

chmean, median, max, min, midpoint, artimmed

Codes

Creating a salt noise image f = imread('lenna.jpg'); R = imnoise2('salt & pepper', M, N, 0.1, 0); c = find(R == 0); gp = f; gp(c) = 0; figure, imshow(gp);

Filtering fp = spfilt(gp, 'chmean', 3, 3, 1.5); fpmax = spfilt(gp, 'max',3,3); figure,imshow(fp); figure,imshow(fpmax);

Examples of filtering