Polar To/From Rectangular Transform of Images

converts rectangular image to polar and back

Description

Conversion from Rectangular to Polar Image and back from Polar to Rectangular.

Image Processing Toolbox required only for loading and displaying images

V0.1 16 Dec 2007 (Created), Prakash Manandhar [e-mail]

• Required Products: Image Processing Toolbox
• MATLAB release: MATLAB 7 (R14)

[Danny Luong]

Thank you, it works great for me!

[anitha sumathi]

requiring matlab codes for image normalization in iris recognition in image processing.

[Eleni Vasilaki]

Thanks a lot.

[kinsam yen]

thank you. i need this function

[Saif]

Very nice work !! thanks !

[Petter]

Lots of for-loops

[shoo chen]

Thanks.

[Anna Saranti]

Nice work! In PolarToIm.m at line 31 is it perhaps : y = (yi - On)/sy; instead of : y = (yi - On)/sx ?

[deepak lawrence]

 

[Raphael Attie]

im2polar : this update will save you 1 order of magnitude of processing time, by vectorizing the code, and using interp2 (can even do better with mex file ba_interp in file exchange) :
Watch out, this might be the transpose of the original output.

rMin=0;
rMax=1;

[Mr Nr] = size(imR); % size of rectangular image
xRc = (Mr+1)/2; % co-ordinates of the center of the image
yRc = (Nr+1)/2;
sx = (Mr-1)/2; % scale factors
sy = (Nr-1)/2;

imP = zeros(M, N);

dr = (rMax - rMin)/(M-1);
dth = 2*pi/N;

% loop in radius and
r=rMin:dr:rMin+(M-1)*dr;
th=(0:dth:(N-1)*dth)';
[r,th]=meshgrid(r,th);
x=r.*cos(th);
y=r.*sin(th);
xR = x*sx + xRc;
yR = y*sy + yRc;
imP = interp2(imR, xR, yR); %interpolate (imR, xR, yR);

[Fernando Villafañe]

For what serving the matrix (A) and how is obtained?.

function v = interpolate (imR, xR, yR)
    xf = floor(xR);
    xc = ceil(xR);
    yf = floor(yR);
    yc = ceil(yR);
    if xf == xc & yc == yf
        v = imR (xc, yc);
    elseif xf == xc
        v = imR (xf, yf) + (yR - yf)*(imR (xf, yc) - imR (xf, yf));
    elseif yf == yc
        v = imR (xf, yf) + (xR - xf)*(imR (xc, yf) - imR (xf, yf));
    else
       A = [ xf yf xf*yf 1
             xf yc xf*yc 1
             xc yf xc*yf 1
             xc yc xc*yc 1 ];
       r = [ imR(xf, yf)
             imR(xf, yc)
             imR(xc, yf)
             imR(xc, yc) ];
       a = A\double(r);
       w = [xR yR xR*yR 1];
       v = w*a;
    end

[Dhruv Agrawal]

Is it correct to use different scaling factors for different axes? A circle in an image should transpose as a rectangle in polar image, but this makes it an ellipse. Could take the min of the scaling factors (sx,sy) for both, though, you might end leaving some portion of the image.

[Ruth Livingstone]

Hi

Thank you, this code is great, but takes a little too long for my application. After reading the thread I wrote similar code which works ~12 times faster for the PolarToIm section. It doesn't have quite the same functionality but I thought I would share it here in case others are having the same problem

function imC = Polar2Im(imP,W,method)
%Polar2Im turns a polar image (imP) into a cartesian image (imC) of width W
%method can be: '*linear', '*cubic', '*spline', or '*nearest'.
imP(isnan(imP))=0;
w = round(W/2); [M N P]= size(imP);
xy = (1:W-w); [x y] = meshgrid(xy,xy);
n = round(N/4); rr = linspace(1,w,M);
W1 = w:-1:1; PM = [2 1 3;1 2 3;2 1 3;1 2 3];
W2 = w+1:2*w; nn = [1:n; n+1:2*n; 2*n+1:3*n; 3*n+1:N;];
w1 = [W1;W2;W2;W1]; aa = linspace(0,90*pi/180,n);
w2 = [W2;W2;W1;W1]; r = sqrt(x.^2 + y.^2);
a = atan2(y,x); imC= zeros(W,W,P);
for i=1:4 %turn each quarter into a cartesian image
    imC(w1(i,:),w2(i,:),:) = permute(interp2(rr,aa,imP(:,nn(i,:))',r,a,method),PM(i,:));
end
imC(isnan(imC))=0;

[Ruth Livingstone]

Sorry, That looks a little unclear. Here it is again

function imC = Polar2Im(imP,W,method)
%Polar2Im turns a polar image (imP) into a cartesian image (imC) of width W
%method can be: '*linear', '*cubic', '*spline', or '*nearest'.
imP(isnan(imP))=0;
w = round(W/2);
xy = (1:W-w);
[M N P]= size(imP);
[x y] = meshgrid(xy,xy);
n = round(N/4);
rr = linspace(1,w,M);
W1 = w:-1:1;
PM = [2 1 3;1 2 3;2 1 3;1 2 3];
W2 = w+1:2*w;
nn = [1:n; n+1:2*n; 2*n+1:3*n; 3*n+1:N;];
w1 = [W1;W2;W2;W1];
w2 = [W2;W2;W1;W1];
aa = linspace(0,90*pi/180,n);
r = sqrt(x.^2 + y.^2);
a = atan2(y,x);
imC= zeros(W,W,P);
for i=1:4 %turn each quarter into a cartesian image
  imC(w1(i,:),w2(i,:),:)=permute(interp2(rr,aa,imP(:,nn(i,:))',r,a,method),PM(i,:));
end
imC(isnan(imC))=0;