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Polar To/From Rectangular Transform of Images

version 1.0.0.0 (47 KB) by Prakash Manandhar
converts rectangular image to polar and back

33 Downloads

Updated 17 Dec 2007

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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 pmanandhar@umassd.edu

Cite As

Prakash Manandhar (2019). Polar To/From Rectangular Transform of Images (https://www.mathworks.com/matlabcentral/fileexchange/17933-polar-to-from-rectangular-transform-of-images), MATLAB Central File Exchange. Retrieved .

Comments and Ratings (30)

AFSAL CP

GOOD

VinceZhao

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

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

Sophia

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);

Peter Caday

@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:

polar = imread('.../myimage.jpg');
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!

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

it worked out :) awsm work

ramsha

if i want to transform circluar to rectangle ? thn

Thank you, very useful

Florian

Cool! Thanks a lot

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;

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;

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.

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

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);

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

Lots of for-loops

Saif

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!

Updates

1.0.0.0

Added inverse function and examples.

MATLAB Release Compatibility
Created with R14
Compatible with any release
Platform Compatibility
Windows macOS Linux

PolarRectangularConv0.1/