1. Neighborhood Processing
Digital Image Processing

2. Introduction Mask moving (or convolution)
A rectangle (usually with sides of odd length) or other shape over the given image

3. Mask & Overlapping Pixel Values
a 3X5 mask
corresponding pixel values

4. Spatial Filtering Position mask over current pixel
Form all products of filter elements with the corresponding elements of the neighborhood
Add all the product
Repeat for every pixel in image

5. Spatial Convolution Similar to spatial filtering, except ..
The filter must be rotated by 180° before multiplying and adding
Or, equivalently,
The rationale of “convolution” will become apparent in view of Fourier Transform

6. Mean Filter Example
Given a 3×3 mask, take the average of all nine values within the mask
The result of filtering x with 3×3 averaging filter

7. Mask Notation
It is convenient to describe a linear filter simply in terms of the coefficients of all the gray values of pixels within the mask
The averaging filter
The other filter example
Ch5-p.91-92

8. Mask on the Edge
What happens at the edge of the image, where the mask partly falls outside the image?
There are a number of different approaches to dealing with this problem
Ignore the edges
(like the example shown previously)
Pad with zeros
Mirroring

9. Filtering in MATLAB imfilter(image,filter,options..)
filter2(filter, image, shape)
The result is a matrix of data type “double”
shape is optional; it describes the method for dealing with the edges
‘same’ – pad with zeros
‘valid’ – ignore the edges
‘full’ – pad with zeros and applying the filter at all places on and around the image where the mask intersects the image matrix
imfilter(image,filter,options..)
More advanced image filtering function

10. Filtering Examples in MATLAB (1/2)
>> x = uint8(10*magic(5))
>> a = ones(3,3)/9
>> filter2(a,x,'same')
>> filter2(a,x,'valid')

11. Filtering Examples in MATLAB (2/2)
>> filter2(a,x,'full')
filter2 provides no mirroring option
Mirroring can be realized by
>> D = floor(size(a)/2)
>> wr=D(1);wc=D(2); % get half of the mask size
>> m_x=[x(wr:-1:1,:);x;x(end:-1:end-(wr-1),:)] % additional mirrored-rows
>> m_x=[m_x(:,wc:-1:1),m_x,m_x(:,end:-1:end-(wc-1))]; % additional mirrored columns
>> filter2(a,m_x,'valid')

12. Pre-cooked Filtering in MATLAB: fspecial()
I = imread('cameraman.tif');
subplot(2,2,1);imshow(I);title('Original Image');
H = fspecial('motion',20,45);
MotionBlur = imfilter(I,H,'replicate');
subplot(2,2,2);imshow(MotionBlur);title('Motion Blurred Image');
H = fspecial('disk',10);
blurred = imfilter(I,H,'replicate');
subplot(2,2,3);imshow(blurred);title('Blurred Image');
H = fspecial('unsharp');
sharpened = imfilter(I,H,'replicate');
subplot(2,2,4);imshow(sharpened);title('Sharpened Image');

13. Low- and High-Pass Filters (1/2)
Frequencies of an image are a measure of the amount by which gray values change with distance
High-pass filter (left)
Low-pass filter (right)
>> f = fspecial('laplacian')
>> cf = imfilter(c,f);
>> f1 = fspecial('log') % Laplacian of Gaussian
>> cf1 = imfilter(c,f1);
Ch5-p.98

14. Low- and High-Pass Filters (2/2)
Values outside [0,255] range
Make negative value positive
Clip values
0-255 scaling transformation
>> f2 = [1 -2 1; ; ];
>> cf2 = filter2(f2,c);
>> figure, imshow(mat2gray(cf2));
>> % scaling transformation
>> maxcf2 = max(cf2(:));
>> mincf2 = min(cf2(:));
>> cf2g = (cf2-mincf2)/(maxcf2-mincf2);
>> figure, imshow(cf2/60);

15. Gaussian Filters (1/2) Ch5-p.103 >> a=50;s=3;
>> g=fspecial('gaussian',[a a],s);
>> surf(1:a,1:a,g)
>> s = 9;
>> g2 = fspecial('gaussian',[a a],s);
>> figure, surf(1:a,1:a,g2)
Ch5-p.103

16. Gaussian Filters (2/2) g3 g4 g1 g2
>> c = imread('cameraman.tif');
>> g1 = fspecial('gaussian',[5 5]);
>> g2 = fspecial('gaussian',[5 5],2);
>> g3 = fspecial('gaussian',[11 11],1);
>> g4 = fspecial('gaussian',[11 11],5);
>> imshow(filter2(g1,c)/256);
>> figure, imshow(filter2(g2,c)/256);
>> figure, imshow(filter2(g3,c)/256);
>> figure, imshow(filter2(g4,c)/256); g3 g4 g1 g2

17. Scheme for Sharpening Masking
>> c = imread(‘cameraman.tif’);
>> f = fspecial('average');
>> xf = filter2(f,c);
>> xu = double(c)-xf/1.5;
>> imshow(xu/70);
Ch5-p.106

18. Unsharp Masking The unsharp option of fspecial produces such filters
>> p = imread('pelicans.tif');
>> u = fspecial('unsharp',0.5);
>> pu = filter2(u,p);
>> imshow(p), figure, imshow(pu/255);
α = 0.5
Ch5-p.108

19. High-Boost Filtering
Allied to unsharp masking filters are the high-boost filters
where A is an amplification factor
If A = 1, then the high-boost filter becomes an ordinary high-pass filter
>> id = [0 0 0;0 1 0; 0 0 0];
>> f = fspecial('average');
>> hb1 = 3*id-2*f;
>> hb2 = 1.25*id-0.25*f;
>> x1 = filter2(hb1,p);
>> x2 = filter2(hb2,p);
>> figure, imshow(x1/255);
>> figure, imshow(x2/255);

20. Nonlinear Filters Maximum filter Minimum filter
>> cmax = nlfilter(c,[3 3],'max(x(:))');
>> cmin = nlfilter(c,[3 3],'min(x(:))');
>> figure, imshow(cmax);
>> figure, imshow(cmin);
Ch5-p.112

21. Region of Interest Processing
>> ig = imread('iguana.tif');
>> roi = roipoly(ig,[ ],[ ]);
>> figure, imshow(ig);
>> figure, imshow(roi);
>> roi_2 = roipoly(ig); % interactively select ROI
Ch5-p.115

22. Region of Interest Filtering
>> a = fspecial('average',[15 15]);
>> iga = roifilt2(a,ig,roi);
>> imshow(iga);
>> u = fspecial('unsharp');
>> igu = roifilt2(u,ig,roi);
>> figure, imshow(igu);
>> L = fspecial('log');
>> igl = roifilt2(L,ig,roi);
>> figure, imshow(igl);
iga: average filtering
igu: unsharp masking
igl: Laplacian of Gaussian
Ch5-p.116