Image Restoration II & Morphological Processing Comp344 Tutorial Kai Zhang

Outline Imgae Degradation Model Inverse Filter Wiener Filter Morphological Processing

Degradation Model Spatial domain Frequency domain Problem Definition Observe the degraded image g(x,y) H function and N (noise) are either known or need to be estimated Goal: restore the original image f(x,y)

H can be obtained by Observing the image (say, blurred) Modeling, example: atmospheric turbulence: Motion blur:

Inverse Filtering Simple (noiseless) case: Then original image can be obtained by Note: H(u,v) may have many small entries (close to 0) that spoil the result. Restrict the area to low frequency part or use Gaussian weighting to solve this problem.

Wiener Filtering Noise can be handled explicitly In case there is no noise, this is inverse filtering When noise is difficult to estimate, simply replace the power spectrum ratio between image and noise with a constant K

Functions Matlab builtin functions PSF = fspecial(‘type’, paras); All kinds of spatial filters. Type includes ‘average’, ‘disk’, ‘gaussian’,’motion’… Paras are corresponding parameters PSF is the spatial domain filter created Type help fspecial for more fr = deconvwnr(g, PSF, NSPR); Wiener filrering. G is corrupted image, fr is restored one PSF is the filter that degrades the image NSPR: noise to signal power ratio Type help deconvwnr for more

Example (noiseless) Inverse filtering

Codes f = checkerboard(20); figure, imshow(f,[]); xlabel('original image') PSF = fspecial('motion',7,45); gb = imfilter(f,PSF,'circular'); figure, imshow(gb,[]); xlabel('motion blurred') fr = deconvwnr(gb,PSF); figure, imshow(fr,[]);xlabel('restored');

Example (noisy)

Codes f = checkerboard(8); PSF = fspecial('motion',7,45); gb = imfilter(f,PSF,'circular'); noise = normrnd(0,0.001^0.5,size(f)); gb = gb + noise; figure,subplot(1,3,1);imshow(gb,[]); xlabel('noisy image'); fr1 = deconvwnr(gb, PSF); subplot(1,3,2),imshow(fr1,[]); xlabel('inverse filtering'); Sn = abs(fft2(noise)).^2; %noise power spectrum nA = mean(Sn(:)); % noise average power; Sf = abs(fft2(f)).^2; %image power spectrum fA = mean(Sf(:)); %image average spectrum R = nA/fA; fr2 = deconvwnr(gb,PSF,R); subplot(1,3,3); imshow(fr2,[]);xlabel('Wiener filtering');

Image dilation and Erosion, opening and closing For binary images, after specifying a structuring element: Dilation: grows or thickens the object Erosion: shrinks or thins object Opening of A by B, is simply erosion of A by B, followed by dilation of the result by B. Closing of A by B, is dilation followed by erosion (opposite to opening).

Dilation

Codes A = imread('broken-text.tif'); B = [0 1 0; 1 1 1; 0 1 0]; A2 = imdilate(A,B); imshow(A) figure,imshow(A)

Erosion

Codes A = imread('mask.tif'); figure,imshow(A); se = strel('disk',10); A2 = imerode(A, se); figure,imshow(A2); se = strel('disk',5); A3 = imerode(A, se); figure,imshow(A3); se = strel('disk',20); A4 = imerode(A, se); figure,imshow(A4);

Opening and Closing Original image; opening Closing; closing of top right image

f = imread('shapes.tif'); figure,imshow(f); se = strel('square', 20); fo = imopen(f, se); figure,imshow(fo); fc = imclose(f, se); figure,imshow(fc) foc = imclose(fo,se); figure,imshow(foc);

Original image; opening; opening followed by closing

Codes f = imread('noisy-fingerprint.tif'); figure,imshow(f); se = strel('square', 3); fo = imopen(f,se); figure,imshow(fo); foc = imclose(fo,se); figure,imshow(foc);