CODEWITHSUNDEEP
matlabimage-processingtransformpolar-coordinates
keyserSoze
keyserSoze

Reputation: 135

Image Transformation - Cartesian to Polar, and back again (MATLAB)

I have been using Peter Kovesi's MatLab functions for machine vision (which are outstanding if you aren't aware of them).
I have been transforming images to polar co-ordinates using the polar transform. The function from Peter Kovesi is named 'PolarTrans' and can be found here - http://www.peterkovesi.com/matlabfns/#syntheticimages

The function beautifully transforms an images into polar co-ordinates. However, I would like the reverse to happen also. Peter Kovesi uses interp2 to transform images, but I can't seem to figure out how to reverse this transform. A requirement of interp2 is that it needs a meshgrid as input.

In short - can you help me reverse the transformation: polar to cartesian. I would like it be accordance with Peter's function - i.e. using the same parameters for coherence.

Dear Swjm, I am posting my reply here because I do not have space in the comments section.
Firstly, thank you very much indeed for your reply. You have shown me how to invert interp2 - something I thought was impossible. This is a huge step forwards. However your code only maps a small segment of the image. Please see the demo code below to understand what I mean.

clc; clear all; close all;

gauss   = fspecial('gauss',64,15);
gauss   = uint8(mat2gray(gauss).*255);
[H,W]   = size(gauss);

pim = polartrans(gauss,64,360);

cim = carttrans(pim,64,64);

subplot(2,2,1);
imagesc(gauss); colormap(jet);
axis off;
title('Image to be Transformed');


subplot(2,2,2);
imagesc(pim); colormap(jet);
axis off;
title('Polar Representation');

subplot(2,2,3);
imagesc(cim);   colormap(jet);
axis off;
title('Back to Cartesian');

subplot(2,2,4);
diff = uint8(gauss) - uint8(cim);
imagesc(diff); colormap(jet);
axis off;
title('Difference Image');

Upvotes: 1

Views: 1612

Answers (1)

swjm
swjm

Reputation: 46

I've had a look at Kovesi's code and this code should perform the reverse transformation. It assumes you used the 'full' shape and 'linear' map parameters in polartrans. Note that polar transforms generally lose resolution at low radial values (and gain resolution at high values), so it won't be lossless even if your polar image has the same dimensions as your original image.

function im = carttrans(pim, nrows, ncols, cx, cy)

[rad, theta] = size(pim);      % Dimensions of polar image.

if nargin==3
    cx = ncols/2 + .5;         % Polar coordinate center, should match 
    cy = nrows/2 + .5;         % polartrans. Defaults to same.
end

[X,Y] = meshgrid(1:ncols, 1:nrows);

[TH,R] = cart2pol(X-cx,Y-cy);  % Polar coordinate arrays.
TH(TH<0) = TH(TH<0)+2*pi;      % Put angles in range [0, 2*pi].

rmax = max(R(:));              % Max radius.

xi = TH * (theta+1) / 2*pi;    % Query array for angles.
yi = R * rad / (rmax-1) + 1;   % Query array for radius.

pim = [pim pim(:,1)];          % Add first col to end of polar image.

[pX,pY] = meshgrid(1:theta+1, 1:rad);
im = interp2(pX, pY, pim, xi, yi);

Upvotes: 1

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