1. Image Restoration II & Morphological Processing
Comp344 Tutorial
Kai Zhang

2. Outline Imgae Degradation Model Inverse Filter Wiener Filter
Morphological Processing

3. 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)

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

5. 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.

6. 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

7. 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

8. Example (noiseless)
Inverse filtering

9. 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');

10. Example (noisy)

11. 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');

12. 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).

13. Dilation

14. 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)

15. Erosion

16. 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);

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

18. 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);

19. Original image; opening; opening followed by closing

20. 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);