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[Matlab] Bilateral Filter

LightningIsMyName Sep 8th, 2011 2,554 Never
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  1. % Bilateral Filter for Matlab/Octave
  2.  
  3. % Author: Barak Itkin
  4. % Author Website: http://barak-itkin.blogspot.com/
  5. % Created: 2011-09-08
  6.  
  7. % This work is licensed under a Creative Commons Attribution-ShareAlike
  8. % 3.0 Unported License.
  9. % See http://creativecommons.org/licenses/by-sa/3.0/
  10.  
  11. % The bilateral filter is a 'Smart Blur' filter that avoids smoothing
  12. % edges. It does so by considering the intensity differences between the
  13. % pixels - if the difference between the 'center pixel' and another
  14. % pixel is too high, then that pixel get's less weight in the weight
  15. % matrix of the blur. In addition to considering the intensity
  16. % difference, we also consider the actual distance (as in a regular
  17. % Gaussian blur).
  18. % The bilateral filter is most commonly used as a noise reduction filter
  19. % due to it's ability to smooth large areas without destroying edges.
  20. % For more information, see http://en.wikipedia.org/wiki/Bilateral_filter
  21. %
  22. % The equation of the bilateral filter is
  23. %
  24. %         (       dx ^ 2       )       (         dI ^2        )
  25. % F = exp (- ----------------- ) * exp (- ------------------- )
  26. %         (  sigma_spatial ^ 2 )       (  sigma_Intensity ^ 2 )
  27. %     ~~~~~~~~~~~~~~~~~~~~~~~~~~
  28. %     This is a guassian filter!
  29. %
  30. % dx - The 'geometric' distance between the 'center pixel' and the pixel
  31. %      to sample
  32. % dI - The difference between the intensity of the 'center pixel' and
  33. %      the pixel to sample
  34. % sigma_spatial and sigma_Intesity are constants. Higher values mean
  35. % that we 'tolerate more' higher value of the distances dx and dI.
  36.  
  37. % Usage:
  38. %   im         - A GRAY image
  39. %   filterSize - The size of the filter (the lookup area would be
  40. %                filterSize X filterSize). This is a real positive
  41. %                integer. This MUST BE AN ODD (NON EVEN) REAL NUMBER!
  42. %   sSpatial   - The sigma_spatial of the bilateral filter equation.
  43. %                Typically, this is half of the filterSize.
  44. %   SIntensity - The sigma_Intensity of the bilateral filter equation.
  45. %
  46. % Return:
  47. %   ret        - The resulting image.
  48.  
  49. function [ ret ] = bilateral (im, filterSize, sSpatial, sIntensity)
  50.  
  51. if (not (nargin == 4))
  52.         error ('Expected exactly 4 arguments!')
  53. end
  54.  
  55. if (not (ismatrix(im)) || not (ndims (im) == 2))
  56.         error ('Argument 1 (im) must be a GRAY image')
  57. end
  58.  
  59. if (not (isscalar (filterSize)) || filterSize <= 0 || not (isreal (filterSize)) || not (rem (filterSize, 2) == 1))
  60.         error ('Argument 2 (filterSize) must be a positive real odd integer!')
  61. end
  62.  
  63. if (not (isscalar (sSpatial)) || not (isreal (sSpatial)))
  64.         error ('Argument 3 (sSpatial) must be a real number!')
  65. end
  66.  
  67. if (not (isscalar (sIntensity)) || not (isreal (sIntensity)))
  68.         error ('Argument 4 (sIntensity must be a real number!')
  69. end
  70.  
  71. % Compute the Gaussian filter part of the Bilateral filter
  72. gauss = fspecial ('gaussian', filterSize, sSpatial);
  73.  
  74. % The radius of the filter
  75. radius = floor (filterSize / 2);
  76.  
  77. % The original image dimensions
  78. [height,width] = size (im);
  79.  
  80. % The resulting image
  81. ret = zeros (size (im));
  82.  
  83. % We will now compute the result by iterating over the result image,
  84. % computing one pixel at a time. For the pixel at (i,j) we want to look
  85. % at:
  86. %
  87. %      im((i - radius):(i + radius), (j - radius):(j + radius))
  88. %
  89. % But, we we must also remember to restrict ourselves to remain inside
  90. % the image boundries
  91. for i=1:height
  92.  
  93.         % The top part of the lookup area, clamped to the image
  94.         ymin  = max (i - radius, 1);
  95.         % How many rows were outside the image, on the top?
  96.         dymin = ymin - (i - radius);
  97.        
  98.         % The bottom part of the lookup area, clamped to the image
  99.         ymax  = min (i + radius, height);
  100.         % How many rows were outside the image, on the bottom?
  101.         dymax = (i + radius) - ymax;
  102.        
  103.         for j=1:width
  104.        
  105.                 % The left part of the lookup area, clamped to the image
  106.                 xmin = max (j - radius, 1);
  107.                 % How many columns were outside the image, on the left?
  108.                 dxmin = xmin - (j - radius);
  109.                
  110.                 % The right part of the lookup area, clamped to the image
  111.                 xmax = min (j + radius, width);
  112.                 % How many columns were outside the image, on the right?
  113.                 dxmax = (j + radius) - xmax;
  114.                
  115.                 % The actual area of the image we will look at
  116.                 area = im (ymin:ymax, xmin:xmax);
  117.                
  118.                 % The center pixel
  119.                 center = im (i,j);
  120.  
  121.                 % The left expression in the bilateral filter equation
  122.                 % We take only the relevant parts of the matrix of the
  123.                 % Gaussian weights - we use dxmin, dxmax, dymin, dymax to
  124.                 % ignore the parts that are outside the image
  125.                 expS = gauss((1+dymin):(filterSize-dymax),(1+dxmin):(filterSize-dxmax));
  126.  
  127.                 % The intensity difference from the center pixel
  128.                 dI = area - center;
  129.                 % The right expression in the bilateral filter equation
  130.                 expI = exp((-dI .* dI) / (sIntensity * sIntensity));
  131.                
  132.                 % The bilater filter (weights matrix)
  133.                 F = expI .* expS;
  134.                 % Normalized bilateral filter
  135.                 Fnormalized = F / sum(F(:));
  136.                
  137.                 % Multiply the area by the filter
  138.                 temp = area .* Fnormalized;
  139.                
  140.                 % The resulting pixel is the sum of all the pixels in
  141.                 % the area, according to the weights of the filter
  142.                 ret(i,j) = sum (temp(:));
  143.         end
  144. end
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