[Matlab] Bilateral Filter

% Bilateral Filter for Matlab/Octave

% Author: Barak Itkin
% Author Website: http://barak-itkin.blogspot.com/
% Created: 2011-09-08

% This work is licensed under a Creative Commons Attribution-ShareAlike
% 3.0 Unported License.
% See http://creativecommons.org/licenses/by-sa/3.0/

% The bilateral filter is a 'Smart Blur' filter that avoids smoothing
% edges. It does so by considering the intensity differences between the
% pixels - if the difference between the 'center pixel' and another
% pixel is too high, then that pixel get's less weight in the weight
% matrix of the blur. In addition to considering the intensity
% difference, we also consider the actual distance (as in a regular
% Gaussian blur).
% The bilateral filter is most commonly used as a noise reduction filter
% due to it's ability to smooth large areas without destroying edges.
% For more information, see http://en.wikipedia.org/wiki/Bilateral_filter
%
% The equation of the bilateral filter is
%
%         (       dx ^ 2       )       (         dI ^2        )
% F = exp (- ----------------- ) * exp (- ------------------- )
%         (  sigma_spatial ^ 2 )       (  sigma_Intensity ^ 2 )
%     ~~~~~~~~~~~~~~~~~~~~~~~~~~
%     This is a guassian filter!
%
% dx - The 'geometric' distance between the 'center pixel' and the pixel
%      to sample
% dI - The difference between the intensity of the 'center pixel' and
%      the pixel to sample
% sigma_spatial and sigma_Intesity are constants. Higher values mean
% that we 'tolerate more' higher value of the distances dx and dI.

% Usage:
%   im         - A GRAY image
%   filterSize - The size of the filter (the lookup area would be
%                filterSize X filterSize). This is a real positive
%                integer. This MUST BE AN ODD (NON EVEN) REAL NUMBER!
%   sSpatial   - The sigma_spatial of the bilateral filter equation.
%                Typically, this is half of the filterSize.
%   SIntensity - The sigma_Intensity of the bilateral filter equation.
%
% Return:
%   ret        - The resulting image.

function [ ret ] = bilateral (im, filterSize, sSpatial, sIntensity)

if (not (nargin == 4))
    error ('Expected exactly 4 arguments!')
end

if (not (ismatrix(im)) || not (ndims (im) == 2))
    error ('Argument 1 (im) must be a GRAY image')
end

if (not (isscalar (filterSize)) || filterSize <= 0 || not (isreal (filterSize)) || not (rem (filterSize, 2) == 1))
    error ('Argument 2 (filterSize) must be a positive real odd integer!')
end

if (not (isscalar (sSpatial)) || not (isreal (sSpatial)))
    error ('Argument 3 (sSpatial) must be a real number!')
end

if (not (isscalar (sIntensity)) || not (isreal (sIntensity)))
    error ('Argument 4 (sIntensity must be a real number!')
end

% Compute the Gaussian filter part of the Bilateral filter
gauss = fspecial ('gaussian', filterSize, sSpatial);

% The radius of the filter
radius = floor (filterSize / 2);

% The original image dimensions
[height,width] = size (im);

% The resulting image
ret = zeros (size (im));

% We will now compute the result by iterating over the result image,
% computing one pixel at a time. For the pixel at (i,j) we want to look
% at:
%
%      im((i - radius):(i + radius), (j - radius):(j + radius))
%
% But, we we must also remember to restrict ourselves to remain inside
% the image boundries
for i=1:height

    % The top part of the lookup area, clamped to the image
    ymin  = max (i - radius, 1);
    % How many rows were outside the image, on the top?
    dymin = ymin - (i - radius);

    % The bottom part of the lookup area, clamped to the image
    ymax  = min (i + radius, height);
    % How many rows were outside the image, on the bottom?
    dymax = (i + radius) - ymax;

    for j=1:width

        % The left part of the lookup area, clamped to the image
        xmin = max (j - radius, 1);
        % How many columns were outside the image, on the left?
        dxmin = xmin - (j - radius);

        % The right part of the lookup area, clamped to the image
        xmax = min (j + radius, width);
        % How many columns were outside the image, on the right?
        dxmax = (j + radius) - xmax;

        % The actual area of the image we will look at
        area = im (ymin:ymax, xmin:xmax);

        % The center pixel
        center = im (i,j);

        % The left expression in the bilateral filter equation
        % We take only the relevant parts of the matrix of the
        % Gaussian weights - we use dxmin, dxmax, dymin, dymax to
        % ignore the parts that are outside the image
        expS = gauss((1+dymin):(filterSize-dymax),(1+dxmin):(filterSize-dxmax));

        % The intensity difference from the center pixel
        dI = area - center;
        % The right expression in the bilateral filter equation
        expI = exp((-dI .* dI) / (sIntensity * sIntensity));

        % The bilater filter (weights matrix)
        F = expI .* expS;
        % Normalized bilateral filter
        Fnormalized = F / sum(F(:));

        % Multiply the area by the filter
        temp = area .* Fnormalized;

        % The resulting pixel is the sum of all the pixels in
        % the area, according to the weights of the filter
        ret(i,j) = sum (temp(:));
    end
end