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lensdistort.m
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function I2 = lensdistort(I, k, varargin)
%LENSDISTORT corrects for barrel and pincusion lens abberations
% I = LENSDISTORT(I, k)corrects for radially symmetric distortions, where
% I is the input image and k is the distortion parameter. lens distortion
% can be one of two types: barrel distortion and pincushion distortion.
% In "barrel distortion", image magnification decreases with
% distance from the optical axis. The apparent effect is that of an image
% which has been mapped around a sphere (or barrel). In "pincushion
% distortion", image magnification increases with the distance from the
% optical axis. The visible effect is that lines that do not go through the
% centre of the image are bowed inwards, towards the centre of the image,
% like a pincushion [1].
%
% I = LENSDISTORT(...,PARAM1,VAL1,PARAM2,VAL2,...) creates a new image image,
% specifying parameters and corresponding values that control various aspects
% of the image distortion correction. Parameter names case does not matter.
%
% Parameters include:
%
% 'bordertype' String that controls the treatment of the image
% edges. Valid strings are 'fit' and 'crop'. By
% default, 'bordertype' is set to 'crop'.
%
% 'interpolation' String that specifies the interpolating kernel
% that the separable resampler uses. Valid
% strings are 'cubic', 'linear' and 'nearest'. By
% default, the 'interpolation' is set to 'cubic'
%
% 'padmethod' string that controls how the resampler
% interpolates or assigns values to output elements
% that map close to or outside the edge of the input
% array. Valid strings are 'bound', circular',
% 'fill', 'replicate', and symmetric'. By
% default, the 'padmethod' is set to 'fill'
%
% 'ftype' Integer between 1 and 4 that specifies the
% distortion model to be used. The models
% available are
%
% 'ftype' = 1: s = r.*(1./(1+k.*r));
%
% 'ftype' = 2: s = r.*(1./(1+k.*(r.^2)));
%
% 'ftype' = 3: s = r.*(1+k.*r);
%
% 'ftype' = 4: s = r.*(1+k.*(r.^2));
%
% By default, the 'ftype' is set to 4.
%
% Class Support
% -------------
% An input intensity image can be uint8, int8, uint16, int16, uint32,
% int32, single, double, or logical. An input indexed image can be uint8,
% uint16, single, double, or logical.
%
% Examples
% --------
% % read image
% I = imread('cameraman.tif');
%
% % Distort Image
% I2 = lensdistort(I, 0.1);
%
% % Display both images
% imshow(I), figure, imshow(I2)
%
% References
% --------------
% [1] http://en.wikipedia.org/wiki/Distortion_(optics), August 2012.
%
% [2] Harri Ojanen, "Automatic Correction of Lens Distortion by Using
% Digital Image Processing," July 10, 1999.
%
% [3] G.Vassy and T.Perlaki, "Applying and removing lens distortion in post
% production," year???
%
% [4] http://www.mathworks.com/products/demos/image/...
% create_gallery/tform.html#34594, August 2012.
%
% Created by Jaap de Vries, 8/31/2012
%
%-----------------------------------------------------------------------%
%-------------------------------------------------------------------------
% This part of the codes creates variable input parameters using the input
% parser object
p = inputParser;
% Make input string case independant
p.CaseSensitive = false;
% Specifies the required inputs
addRequired(p,'I',@isnumeric);
addRequired(p,'k',@isnumeric);
% Sets the default values for the optional parameters
defaultFtype = 4;
defaultBorder = 'crop';
defaultInterpolation = 'cubic';
defaultPadmethod = 'fill';
% Specifies valid strings for the optional parameters
validBorder = {'fit','crop'};
validInterpolation = {'cubic','linear', 'nearest'};
validPadmethod = {'bound','circular', 'fill', 'replicate', 'symmetric'};
% Funtion handles to determine wheter a proper input string has been used
checkBorder = @(x) any(validatestring(x,validBorder));
checkInterpolation = @(x) any(validatestring(x,validInterpolation));
checkPadmethod = @(x) any(validatestring(x,validPadmethod));
% Create optional inputs
addParamValue(p,'bordertype',defaultBorder,checkBorder);
addParamValue(p,'interpolation',defaultInterpolation,checkInterpolation);
addParamValue(p,'padmethod',defaultPadmethod,checkPadmethod);
addParamValue(p,'ftype',defaultFtype,@isnumeric);
% Pass all parameters and input to the parse method
parse(p,I,k,varargin{:});
%-------------------------------------------------------------------------
% This determines wether its a color (M,N,3) or gray scale (M,N,1) image
if ndims(I) == 3
for i=1:3
I2(:,:,i) = imdistcorrect(I(:,:,i),k);
end
elseif ismatrix(I)
I2 = imdistcorrect(I,k);
else
error('Unknown image dimensions')
end
%-------------------------------------------------------------------------
% Nested function that perfoms the transformation
function I3 = imdistcorrect(I,k)
% Determine the size of the image to be distorted
[M N]=size(I);
center = [round(N/2) round(M/2)];
% Creates N x M (#pixels) x-y points
[xi,yi] = meshgrid(1:N,1:M);
% Creates converst the mesh into a colum vector of coordiantes relative to
% the center
xt = xi(:) - center(1);
yt = yi(:) - center(2);
% Converts the x-y coordinates to polar coordinates
[theta,r] = cart2pol(xt,yt);
% Calculate the maximum vector (image center to image corner) to be used
% for normalization
R = sqrt(center(1)^2 + center(2)^2);
% Normalize the polar coordinate r to range between 0 and 1
r = r/R;
% Aply the r-based transformation
s = distortfun(r,k,p.Results.ftype);
% un-normalize s
s2 = s * R;
% Find a scaling parameter based on selected border type
brcor = bordercorrect(r,s,k, center, R);
s2 = s2 * brcor;
% Convert back to cartesian coordinates
[ut,vt] = pol2cart(theta,s2);
u = reshape(ut,size(xi)) + center(1);
v = reshape(vt,size(yi)) + center(2);
tmap_B = cat(3,u,v);
resamp = makeresampler(p.Results.interpolation, p.Results.padmethod);
I3 = tformarray(I,[],resamp,[2 1],[1 2],[],tmap_B,255);
end
%-------------------------------------------------------------------------
% Nested function that creates a scaling parameter based on the
% 'bordertype' selected
function x = bordercorrect(r,s,k,center, R)
if k < 0
if strcmp(p.Results.bordertype, 'fit')
x = r(1)/s(1);
end
if strcmp(p.Results.bordertype,'crop')
x = 1/(1 + k*(min(center)/R)^2);
end
elseif k > 0
if strcmp(p.Results.bordertype, 'fit')
x = 1/(1 + k*(min(center)/R)^2);
end
if strcmp(p.Results.bordertype, 'crop')
x = r(1)/s(1);
end
end
end
%-------------------------------------------------------------------------
% Nested function that pics the model type to be used
function s = distortfun(r,k,fcnum)
switch fcnum
case(1)
s = r.*(1./(1+k.*r));
case(2)
s = r.*(1./(1+k.*(r.^2)));
case(3)
s = r.*(1+k.*r);
case(4)
s = r.*(1+k.*(r.^2));
end
end
end