Rank Filters for Image Processing
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This numerical tour explores non-linear local filters that proceeds by ordering the pixels in a neighboorhood and selecting
a given ranked entry.
Contents
Installing toolboxes and setting up the path.
You need to download the following files: signal toolbox and general toolbox.
You need to unzip these toolboxes in your working directory, so that you have toolbox_signal and toolbox_general in your directory.
For Scilab user: you must replace the Matlab comment '%' by its Scilab counterpart '//'.
Recommandation: You should create a text file named for instance numericaltour.sce (in Scilab) or numericaltour.m (in Matlab) to write all the Scilab/Matlab command you want to execute. Then, simply run exec('numericaltour.sce'); (in Scilab) or numericaltour; (in Matlab) to run the commands.
Execute this line only if you are using Matlab.
getd = @(p)path(p,path);
Then you can add the toolboxes to the path.
getd('toolbox_signal/');
getd('toolbox_general/');
Local Image Processing
Image size.
n = 256;
Load an image.
name = 'hibiscus';
f = load_image(name, n);
f = rescale(crop( sum(f,3) ,n));
We proceed first by computing a set of index to extract all the patches in an image.
Neighboorhod size.
w = 3;
w1 = 2*w+1;
[dY,dX] = meshgrid(-w:w,-w:w);
dX = repmat( reshape(dX(:), [1 1 w1*w1]), [n n 1] );
dY = repmat( reshape(dY(:), [1 1 w1*w1]), [n n 1] );
[Y,X] = meshgrid(1:n,1:n);
X = repmat(X,[1 1 w1*w1]);
Y = repmat(Y,[1 1 w1*w1]);
X = mod(X+dX-1,n)+1;
Y = mod(Y+dY-1,n)+1;
I = X + (Y-1)*n;
Extract the set of patches.
P = f(I);
Compute the mean of each patch, which corresponds to a box filter.
clf;
imageplot(mean(P,3));
Opening and Closing Rank Filters
A generic rank filter is obtained by selecting a given rank from the ordered pixel in the neighborhood of size w.
Shortcut for the rank filter.
subsample = @(x,s)x(:,:,s);
rankfilter = @(f,r)subsample(sort(f(I), 3), r);
Exercice 1: (the solution is exo1.m) Compute the rank filter for several rank r.
exo1;
Min filter: closing.
closing = @(f)rankfilter(f,1);
clf;
imageplot(closing(f));
Max filter: opening.
opening = @(f)rankfilter(f,w1*w1);
clf;
imageplot(opening(f));
Exercice 2: (the solution is exo2.m) Compute a closing followed by an opening.
exo2;
Exercice 3: (the solution is exo3.m) Compute an opening followed by a closing.
exo3;
Exercice 4: (the solution is exo4.m) Perform iterated opening and closing.
exo4;
Median Filter
The median filter corresponds to computing the average point of the local histogram.
medfilt = @(f)rankfilter(f,(w1*w1-1)/2);
clf;
imageplot(medfilt(f));
Exercice 5: (the solution is exo5.m) Perform iterated median. Store the final result after 6 iterations in f1.
exo5;
Display.
clf;
imageplot(f1);
