对数极坐标变换MATLAB代码

http://www.vision.ee.ethz.ch/~konrads/code/logpolar.m

function [I_lp,I_nearest,I_bilinear] = logpolar(I,slices)
% 
% [I_lp,I_nearest,I_bilinear] = logpolar(I,slices)
%
% Log-polar resampling of an image, and back-sampling to retinal plane
%
% INPUT:
% I ...          source image
% slices ...     number of radial slices
%
% OUTPUT:
% I_lp ...       the log-polar image
% I_nearest ...  backprojection, nearest-neighbor resampling (shows log-polar pixels)
% I_bilinear ... backprojection, bilinear resampling (smooth image with varying resolution)
%
% Konrad, 22.09.2006

    I = double(I);
    [rows,cols,planes] = size(I);

    %%%%%%%%%%%%%%%%%%%
    % log-polar mapping
    %%%%%%%%%%%%%%%%%%%

    ctr = [rows cols]/2;
    mult = 1+2*pi/slices;

    % make empty log-polar image
    lpcols = slices;
    lprows = floor(log(max(ctr)*sqrt(2))/log(mult));
    I_lp = zeros(lpcols,lprows,planes,'uint8');

    % fill pixels
    for u = 1:lpcols
        for v = 1:lprows
            % find the center of the log-polar bin in the original image
            ang = u/slices*2*pi;
            pt = ctr+mult^v*[cos(ang) sin(ang)];
            pt = round(pt);
            if pt(1)<1 || pt(2)<1 || pt(1)>rows || pt(2)>cols, continue; end

            % integrate over log-polar pixel
            rd = mult^v-mult^(v-1);
            sz = ceil(rd);

            if sz<1
                filt = 1;
                bbximg = [ pt ; pt ];
            else
                filt = fspecial('disk',sz);
                bbximg = [ pt-[sz sz] ; pt+[sz sz] ];
                bbxflt = [ 1 1 ; 2*[sz sz]+[1 1] ];

                if bbximg(1,1)>rows || bbximg(1,2)<1 || bbximg(2,1)>cols || bbximg(2,2)<1
                    continue;
                end

                % correct for pixels overlapping the image boundary
                if bbximg(1,1)<1, bbxflt(1,1) = 2-bbximg(1,1); bbximg(1,1) = 1; end
                if bbximg(1,2)<1, bbxflt(1,2) = 2-bbximg(1,2); bbximg(1,1) = 1; end
                if bbximg(2,1)>rows, bbxflt(2,1) = bbxflt(2,1)-bbximg(2,1)+rows; bbximg(2,1) = rows; end
                if bbximg(2,2)>cols, bbxflt(2,2) = bbxflt(2,2)-bbximg(2,2)+cols; bbximg(2,2) = cols; end
                filt = filt(bbxflt(1,1):bbxflt(2,1),bbxflt(1,2):bbxflt(2,2));
                filt = filt/sum(sum(filt));
            end
            for p = 1:planes
                val = I(bbximg(1,1):bbximg(2,1),bbximg(1,2):bbximg(2,2),p).*filt;
                I_lp(u,v,p) = uint8(sum(val(:)));
            end
        end
    end

    % move 360 degrees to 0
    I_lp = [I_lp(2:end,:,:) ; I_lp(1,:,:)];

    %%%%%%%%%%%%%%%%%%%%%%%%%%%
    % back-projection to retina
    %%%%%%%%%%%%%%%%%%%%%%%%%%%

    % circular extension of log-polar image
    lpcols = lpcols+1;
    I_lpbig = [I_lp;I_lp(1,:,:)];

    % make empty images
    I_nearest = zeros(rows,cols,planes,'uint8');
    I_bilinear = zeros(rows,cols,planes,'uint8');

    % fill pixels
    for u = 1:rows
        for v = 1:cols
            % get log-polar coordinate
            uu = u-ctr(1);
            vv = v-ctr(2);
            rfloat = 0.5*log(max(1,uu^2+vv^2))/log(mult)-1.5;
            afloat = atan2(vv,uu)/(2*pi)*slices-1.5;
            ri = afloat<=1;
            afloat(ri) = slices+afloat(ri);

            % round for nearest neighbor
            rind = round(rfloat);
            aind = round(afloat);

            if afloat<1 || rfloat<1 || afloat>lpcols || rfloat>lprows, continue; end

            % get values
            for p = 1:planes
                I_nearest(u,v,p) = I_lpbig(aind,rind,p);
                af = floor(afloat);
                rf = floor(rfloat);
                I_bilinear(u,v,p) = interp2(I_lpbig(af:af+1,rf:rf+1,p),rfloat-rf+1,afloat-af+1,'*linear');
            end
        end
    end

http://blog.csdn.net/luhuillll/archive/2007/08/08/1732818.aspx

% 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