% POLARTRANS - Transforms image to polar coordinates
% Usage: pim = polartrans(im, nrad, ntheta, cx, cy, linlog, shape)
% Arguments:
% im - image to be transformed.
% nrad - number of radius values.
% ntheta - number of theta values.
% cx, cy - optional specification of origin. If this is not
% specified it defaults to the centre of the image.
% linlog - optional string 'linear' or 'log' to obtain a
% transformation with linear or logarithmic radius
% values. linear is the default.
% shape - optional string 'full' or 'valid'
% 'full' results in the full polar transform being
% returned (the circle that fully encloses the original
% image). This is the default.
% 'valid' returns the polar transform of the largest
% circle that can fit within the image.
% Returns pim - image in polar coordinates with radius increasing
% down the rows and theta along the columns. The size
% of the image is nrad x ntheta. Note that theta is
% +ve clockwise as x is considered +ve along the
% columns and y +ve down the rows.
% When specifying the origin it is assumed that the top left pixel has
% coordinates (1,1).
% Copyright (c) 2002 Peter Kovesi
% School of Computer Science & Software Engineering
% The University of Western Australia
% http://www.csse.uwa.edu.au/
%
% Permission is hereby granted, free of charge, to any person obtaining a copy
% of this software and associated documentation files (the "Software"), to deal
% in the Software without restriction, subject to the following conditions:
%
% The above copyright notice and this permission notice shall be included in
% all copies or substantial portions of the Software.
%
% The Software is provided "as is", without warranty of any kind.
% December 2002
% November 2006 Correction to calculation of maxlogr (thanks to Chang Lei)
function pim = polartrans(im, nrad, ntheta, cx, cy, linlog, shape)
[rows, cols] = size(im);
if nargin==3 % Set origin to centre.
cx = cols/2+.5; % Add 0.5 because indexing starts at 1
cy = rows/2+.5;
end
if nargin < 7, shape = 'full'; end
if nargin < 6, linlog = 'linear'; end
if strcmp(shape,'full') % Find maximum radius value
dx = max([cx-1, cols-cx]);
dy = max([cy-1, rows-cy]);
rmax = sqrt(dx^2+dy^2);
elseif strcmp(shape,'valid') % Find minimum radius value
rmax = min([cx-1, cols-cx, cy-1, rows-cy]);
else
error('Invalid shape specification');
end
% Increments in radius and theta
deltatheta = 2*pi/ntheta;
if strcmp(linlog,'linear')
deltarad = rmax/(nrad-1);
[theta, radius] = meshgrid([0:ntheta-1]*deltatheta, [0:nrad-1]*deltarad);
elseif strcmp(linlog,'log')
maxlogr = log(rmax);
deltalogr = maxlogr/(nrad-1);
[theta, radius] = meshgrid([0:ntheta-1]*deltatheta, exp([0:nrad-1]*deltalogr));
else
error('Invalid radial transformtion (must be linear or log)');
end
xi = radius.*cos(theta) + cx; % Locations in image to interpolate data
yi = radius.*sin(theta) + cy; % from.
[x,y] = meshgrid([1:cols],[1:rows]);
pim = interp2(x, y, double(im), xi, yi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
新的对数极变换的代码
%function [rout,g,b] = LHimlogpolar(image,Nrho,Ntheta,Method,Center,Shape)
function [rout,g,b] = LHimlogpolar(varargin)
%IMLOGPOLAR Compute logarithmic polar transformation of image.
% B = IMLOGPOLAR(A,NRHO,NTHETA,METHOD) computes the logarithmic
% polar transformation of image A, generating a log polar image
% of size NRHO by NTHETA. METHOD describes the interpolation
% method. METHOD is a string that can have one of these values:
%
% 'nearest' (default) nearest neighbor interpolation
%
% 'bilinear' bilinear interpolation
%
% 'bicubic' bicubic interpolation
%
% If you omit the METHOD argument, IMLOGPOLAR uses the default
% method of 'nearest'.
%
% B = IMLOGPOLAR(A,NRHO,NTHETA,METHOD,CTR) assumes that the 2x1
% vector CTR contains the coordinates of the origin in image A.
% If CTR is not supplied, the default is CTR = [(m+1)/2,(n+1)/2],
% where A has n rows and m columns.
%
% B = IMLOGPOLAR(A,NRHO,NTHETA,METHOD,CTR,SHAPE) where SHAPE is a
% string that can have one of these values:
%
% 'full' - returns log polar transformation containing ALL
% pixels from image A (the circumscribed circle
% centered at CTR)
%
% 'valid' - returns log polar transformation containing only
% pixels from the largest inscribed circle in image A
% centered at CTR.
%
% If you omit the SHAPE argument, IMLOGPOLAR uses the default shape
% of 'valid'. If you specify the shape 'full', invalid values on the
% periphery of B are set to NaN.
%
% Class Support
% -------------
% The input image can be of class uint8 or double. The output
% image is of the same class as the input image.
%
% Example
% -------
% I = imread('ic.tif');
% J = imlogpolar(I,64,64,'bilinear');
% imshow(I), figure, imshow(J)
%
% See also IMCROP, IMRESIZE, IMROTATE.
% Nathan D. Cahill 8-16-01, modified from:
% Clay M. Thompson 8-4-92
% Copyright 1993-1998 The MathWorks, Inc. All Rights Reserved.
% $Revision: 5.10 $ $Date: 1997/11/24 15:35:33 $
% Grandfathered:
% Without output arguments, IMLOGPOLAR(...) displays the transformed
% image in the current axis.
% Outputs: A the input image
% Nrho the desired number of rows of transformed image
% Ntheta the desired number of columns of transformed image
% Method interpolation method (nearest,bilinear,bicubic)
% Center origin of input image
% Shape output size (full,valid)
% Class storage class of A
[Image,rows,cols,Nrho,Ntheta,Method,Center,Shape,ClassIn] = LHparse_inputs(varargin{:});
threeD = (ndims(Image)==3); % Determine if input includes a 3-D array
if threeD,
[r,g,b] = LHtransformImage(Image,rows,cols,Nrho,Ntheta,Method,Center,Shape);
if nargout==0,
imshow(r,g,b);
return;
elseif nargout==1,
if strcmp(ClassIn,'uint8');
rout = repmat(uint8(0),[size(r),3]);
rout(:,:,1) = uint8(round(r*255));
rout(:,:,2) = uint8(round(g*255));
rout(:,:,3) = uint8(round(b*255));
else
rout = zeros([size(r),3]);
rout(:,:,1) = r;
rout(:,:,2) = g;
rout(:,:,3) = b;
end
else % nargout==3
if strcmp(ClassIn,'uint8')
rout = uint8(round(r*255));
g = uint8(round(g*255));
b = uint8(round(b*255));
else
rout = r; % g,b are already defined correctly above
end
end
else
r = LHtransformImage(Image,rows,cols,Nrho,Ntheta,Method,Center,Shape);
if nargout==0,
imshow(r);
return;
end
if strcmp(ClassIn,'uint8')
if islogical(image)
r = im2uint8(logical(round(r)));
else
r = im2uint8(r);
end
end
rout = r;
end
function [A,Ar,Ac,Nrho,Ntheta,Method,Center,Shape,Class] = LHparse_inputs(varargin)
% Outputs: A the input image
% Nrho the desired number of rows of transformed image
% Ntheta the desired number of columns of transformed image
% Method interpolation method (nearest,bilinear,bicubic)
% Center origin of input image
% Shape output size (full,valid)
% Class storage class of A
error(nargchk(3,6,nargin));
A = varargin{1};
Ar = size(A,1); % Ar = number of rows of the input image
Ac = size(A,2); % Ac = number of columns of the input image
Nrho = varargin{2};
Ntheta = varargin{3};
Class = class(A);
if nargin < 4
Method = '';
else
Method = varargin{4};
end
if isempty(Method)
Method = 'nearest';
end
Method = lower(Method);
if ~any(strcmp(Method,{'nearest','bilinear','bicubic'}))
error('Method must be one of ''nearest'', ''bilinear'', or ''bicubic''.');
end
if nargin < 5
Center = [];
else
Center = varargin{5};
end
if isempty(Center)
Center = [(Ac+1)/2 (Ar+1)/2];
end
if length(Center(:))~=2
error('Center should be 1x2 array.');
end
if any(Center(:)>[Ac;Ar] | Center(:)<1)
% THIS LINE USED TO READ 'ifany(Center(:)>[Ar;Ac] | Center(:)<1)' but Ar and Ac should be swapped round -- look at line 40 for whty this should be. A.I.Wilmer,12th Oct 2002
num2str(['Center is',num2str(Center(1)),',',num2str(Center(2)),'with size of image =',num2str(Ar),'x',num2str(Ac),' (rows,columns)']);
warning('Center supplied is not within image boundaries.');
end
if nargin < 6
Shape = '';
else
Shape = varargin{6};
end
if isempty(Shape)
Shape = 'valid';
end
Shape = lower(Shape);
if ~any(strcmp(Shape,{'full','valid'}))
error('Shape must be one of ''full'' or ''valid''.');
end
if isa(A, 'uint8'), % Convert A to Double grayscale for interpolation
if islogical(A)
A = double(A);
else
A = double(A)/255;
end
end
function [r,g,b] = LHtransformImage(A,Ar,Ac,Nrho,Ntheta,Method,Center,Shape)
% Inputs: A the input image
% Nrho the desired number of rows of transformed image
% Ntheta the desired number of columns of transformed image
% Method interpolation method (nearest,bilinear,bicubic)
% Center origin of input image
% Shape output size (full,valid)
% Class storage class of A
global rho;
theta = linspace(0,2*pi,Ntheta+1); theta(end) = [];
switch Shape
case 'full'
corners = [1 1;Ar 1;Ar Ac;1 Ac];
d = max(sqrt(sum((repmat(Center(:)',4,1)-corners).^2,2)));
case 'valid'
d = min([Ac-Center(1) Center(1)-1 Ar-Center(2) Center(2)-1]);
end
minScale = 1;
rho = logspace(log10(minScale),log10(d),Nrho)'; % default 'base 10' logspace - play with d to change the scale of the log axis
% convert polar coordinates to cartesian coordinates and center
xx = rho*cos(theta+pi) + Center(1);
yy = rho*sin(theta+pi) + Center(2);
if nargout==3
if strcmp(Method,'nearest'), % Nearest neighbor interpolation
[xi,yi] = meshgrid(-3:.1:3,-3:.1:3)
r=interp2(A(:,:,1),xx,yy,'nearest');
g=interp2(A(:,:,2),xx,yy,'nearest');
b=interp2(A(:,:,3),xx,yy,'nearest');
elseif strcmp(Method,'bilinear'), % Linear interpolation
r=interp2(A(:,:,1),xx,yy,'linear');
g=interp2(A(:,:,2),xx,yy,'linear');
b=interp2(A(:,:,3),xx,yy,'linear');
elseif strcmp(Method,'bicubic'), % Cubic interpolation
r=interp2(A(:,:,1),xx,yy,'cubic');
g=interp2(A(:,:,2),xx,yy,'cubic');
b=interp2(A(:,:,3),xx,yy,'cubic');
else
error(['Unknown interpolation method: ',method]);
end
% any pixels outside , pad with black
mask= (xx>Ac) | (xx<1) | (yy>Ar) | (yy<1);
r(mask)=NaN;
g(mask)=NaN;
b(mask)=NaN;
else
if strcmp(Method,'nearest'), % Nearest neighbor interpolation
r=interp2(A,xx,yy,'nearest');
%r=interp2(A,xx,yy,'nearest');
elseif strcmp(Method,'bilinear'), % Linear interpolation
size(A)
r=interp2(A,xx,yy,'linear');
%r=interp2(A,xx,yy,'linear');
elseif strcmp(Method,'bicubic'), % Cubic interpolation
r=interp2(A,xx,yy,'cubic');
%r=interp2(A,xx,yy,'cubic');
else
error(['Unknown interpolation method: ',method]);
end
% any pixels outside warp, pad with black
mask= (xx>Ac) | (xx<1) | (yy>Ar) | (yy<1);
r(mask)=NaN;
end
(Peter Kovesi) |
