matlabimage-processingoctavehomographyprojective-geometry

Warping an image using control points

I want to convert an image using control points according to this scheme extracted from here:

enter image description here

A and B contains the coordinates of the source an target vertices.

I am computing the transformation matrix as:

A = [51 228;  51 127; 191 127; 191 228];
B = [152 57; 219 191;  62 240;  92 109];
X = imread('rectangle.png');
info = imfinfo('rectangle.png');
T = cp2tform(A,B,'projective');

Up to here it seems to properly work, because (using normalized coordinates) a source vertex produces its target vertex:

H = T.tdata.T;
> [51 228 1]*H
ans =
  -248.2186   -93.0820    -1.6330
> [51 228 1]*H/ -1.6330
ans =
   152.0016    57.0006     1.0000

The problem is that imtransform produces an unexpected result:

Z = imtransform(X,T,'XData',[1 info.Width], 'YData',[1 info.Height]);
imwrite(Z,'projective.png');

Unexpected result

How can I use imtransform to produce this my expected result?:

enter image description here

Is there an alternative way to achieve it?

Solution

  • You have to "adapt" the control points to the size of the image you're working with. The way I did this is by computing an affine transformation between the corners of the control points in A and the corners of the source image (preferrably you want to make the points are in the same clockwise order).

    One thing I should point out is that the order of points in your matrix A does not match the picture you've shown, so I fixed that in the code below...

    Here is the code to estimate the homography (tested in MATLAB):

    % initial control points
A = [51 228;  51 127; 191 127; 191 228];
B = [152 57; 219 191;  62 240;  92 109];
A = circshift(A, [-1 0]);  % fix the order of points to match the picture

% input image
%I = imread('peppers.png');
I = im2uint8(checkerboard(32,5,7));
[h,w,~] = size(I);

% adapt control points to image size
% (basically we estimate an affine transform from 3 corner points)
aff = cp2tform(A(1:3,:), [1 1; w 1; w h], 'affine');
A = tformfwd(aff, A);
B = tformfwd(aff, B);

% estimate homography between A and B
T = cp2tform(B, A, 'projective');
T = fliptform(T);
H = T.tdata.Tinv

    I get:

    >> H
H =
   -0.3268    0.6419   -0.0015
   -0.4871    0.4667    0.0009
  324.0851 -221.0565    1.0000

    Now let's visualize the points:

    % check by transforming A points into B
%{
BB = [A ones(size(A,1),1)] * H;        % convert to homogeneous coords
BB = bsxfun(@rdivide, BB, BB(:,end));  % convert from homogeneous coords
%}
BB = tformfwd(T, A(:,1), A(:,2));
fprintf('error = %g\n', norm(B-BB));

% visually check by plotting control points and transformed A
figure(1)
subplot(121)
plot(A([1:end 1],1), A([1:end 1],2), '.-', 'MarkerSize',20, 'LineWidth',2)
line(BB([1:end 1],1), BB([1:end 1],2), 'Color','r', 'Marker','o')
text(A(:,1), A(:,2), num2str((1:4)','a%d'), ...
    'VerticalAlign','top', 'HorizontalAlign','left')
title('A'); legend({'A', 'A*H'}); axis equal ij
subplot(122)
plot(B([1:end 1],1), B([1:end 1],2), '.-', 'MarkerSize',20, 'LineWidth',2)
text(B(:,1), B(:,2), num2str((1:4)','b%d'), ...
    'VerticalAlign','top', 'HorizontalAlign','left')
title('B'); legend('B'); axis equal ij

    control_points

    Finally we can apply the transformation on the source image:

    % transform input image and show result
J = imtransform(I, T);
figure(2)
subplot(121), imshow(I), title('image')
subplot(122), imshow(J), title('warped')

    warped_image