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## Polar To/From Rectangular Transform of Images

version 1.0 (47 KB) by

converts rectangular image to polar and back

4.38889
20 Ratings

Updated

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

V0.1 16 Dec 2007 (Created), Prakash Manandhar pmanandhar@umassd.edu

VinceZhao

### VinceZhao (view profile)

Very good functions. One typo in "PolarToIm" function:
"y = (yi - On)/sx;" should be "y = (yi - On)/sy;"

Biswarup Mukherjee

Yannick Mermet

### Yannick Mermet (view profile)

hi there
I am using the ImtoPolar.m file. how do I display the polar image after the transformation?

Sophia

### Sophia (view profile)

Kristian Moesgaard

### Kristian Moesgaard (view profile)

Here the code is to work with RGB image and independent on image format. Thought somebody might find it useful :)

function imP = FISHCOLOR2(imR)

rMin=0.1;
rMax=1;

reduced_dim = min(size(imR,1),size(imR,2));
imR = imresize(imR,[reduced_dim reduced_dim]);

M=size(imR,1);N=size(imR,2);

CenterX = (M+1)/2; % co-ordinates of the center of the image
CenterY = (N+1)/2;
ScaleX = (M-1)/2; % scale factors
ScaleY = (N-1)/2;

DeltaR = (rMax - rMin)/(M-1);
DeltaTheta = 2*pi/N;

R=rMin:DeltaR:rMin+(M-1)*DeltaR;
Theta=0:DeltaTheta:(N-1)*DeltaTheta;
[R,Theta]=meshgrid(R,Theta);

X=R*cos(Theta);
Y=R*sin(Theta);
LatX = X*ScaleX + CenterX;
LongY = Y*ScaleY + CenterY;

for k=1:3 % colors
imP(:,:,k) = interp2(imR(:,:,k), LatX, LongY); % add k channel
end

imP = imresize(imP,[size(imP,1), size(imP,2)/3]);

imP = imrotate(imP,270);

@Kristian: If your RGB image comes from the imread function, it is an M x N x 3 array. You can then apply ImToPolar or PolarToIm (whichever you're interested in) 3 times, once for each plane (R,G,B) of the image. For instance:

im(:,:,1) = PolarToIm(polar(:,:,1), rMin, rMax, Mr, Nr);
im(:,:,2) = PolarToIm(polar(:,:,2), rMin, rMax, Mr, Nr);
im(:,:,3) = PolarToIm(polar(:,:,3), rMin, rMax, Mr, Nr);

Hope this helps!

Kristian Moesgaard

### Kristian Moesgaard (view profile)

Great and functional work.. Does anybody know a quick way of converting this code so that i can be used on a RGB image?

Killo

ramsha

### ramsha (view profile)

it worked out :) awsm work

ramsha

### ramsha (view profile)

if i want to transform circluar to rectangle ? thn

Yves DELIGNON

### Yves DELIGNON (view profile)

Thank you, very useful

Florian

### Florian (view profile)

Cool! Thanks a lot

Ruth Livingstone

### Ruth Livingstone (view profile)

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;

Ruth Livingstone

### Ruth Livingstone (view profile)

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;

Dhruv Agrawal

### Dhruv Agrawal (view profile)

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.

Fernando Villafañe

### Fernando Villafañe (view profile)

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

Raphael Attie

### Raphael Attie (view profile)

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;

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);

deepak lawrence

Anna Saranti

### Anna Saranti (view profile)

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

shoo chen

Thanks.

Petter

### Petter (view profile)

Lots of for-loops

Saif

### Saif (view profile)

Very nice work !! thanks !

kinsam yen

thank you. i need this function

Eleni Vasilaki

Thanks a lot.

anitha sumathi

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

Danny Luong

Thank you, it works great for me!

MATLAB 7 (R14)