This example shows how to align or register two images that differ by a rotation and a scale change. You can use
fitgeotrans to find the rotation angle and scale factor after manually picking corresponding points. You can then transform the distorted image to recover the original image.
Read an image into the workspace.
original = imread('cameraman.tif'); imshow(original); text(size(original,2),size(original,1)+15, ... 'Image courtesy of Massachusetts Institute of Technology', ... 'FontSize',7,'HorizontalAlignment','right');
scale = 0.7; distorted = imresize(original,scale); % Try varying the scale factor. theta = 30; distorted = imrotate(distorted,theta); % Try varying the angle, theta. figure, imshow(distorted)
Use the Control Point Selection Tool to pick at least two pairs of control points.
movingPoints = [151.52 164.79; 131.40 79.04]; fixedPoints = [135.26 200.15; 170.30 79.30];
You can run the rest of the example with these pre-picked points, but try picking your own points to see how the results vary.
Save control points by choosing the File menu, then the Save Points to Workspace option. Save the points, overwriting variables
Fit a nonreflective similarity transformation to your control points.
tform = fitgeotrans(movingPoints,fixedPoints,'nonreflectivesimilarity');
After you have done Steps 5 and 6, repeat Steps 4 through 6 but try using 'affine' instead of 'NonreflectiveSimilarity'. What happens? Are the results as good as they were with 'NonreflectiveSimilarity'?
The geometric transformation,
tform, contains a transformation matrix in
tform.T. Since you know that the transformation includes only rotation and scaling, the math is relatively simple to recover the scale and angle.
Let sc = s*cos(theta)
Let ss = s*sin(theta)
Then, Tinv = invert(tform), and Tinv.T = [sc -ss 0;
ss sc 0;
tx ty 1]
where tx and ty are x and y translations, respectively.
tformInv = invert(tform); Tinv = tformInv.T; ss = Tinv(2,1); sc = Tinv(1,1); scale_recovered = sqrt(ss*ss + sc*sc)
scale_recovered = 0.7000
theta_recovered = atan2(ss,sc)*180/pi
theta_recovered = 29.3741
The recovered values of
theta_recovered should match the values you set in Step 2: Resize and Rotate the Image.
Recover the original image by transforming
distorted, the rotated-and-scaled image, using the geometric transformation
tform and what you know about the spatial referencing of
original. The 'OutputView' Name/Value pair is used to specify the resolution and grid size of the resampled output image.
Roriginal = imref2d(size(original)); recovered = imwarp(distorted,tform,'OutputView',Roriginal);
original by looking at them side-by-side in a montage.
recovered (right) image quality does not match the
original (left) image because of the distortion and recovery process. In particular, the image shrinking causes loss of information. The artifacts around the edges are due to the limited accuracy of the transformation. If you were to pick more points in Step 3: Select Control Points, the transformation would be more accurate.