Step 1: Read 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")

Step 2: Resize and Rotate the Image

Create a distorted version of the image by resizing and rotating the image. Note that imrotate rotates images in a counterclockwise direction when you specify a positive angle of rotation.

scaleFactor = 0.7;
distorted = imresize(original,scaleFactor);

theta = 30;
distorted = imrotate(distorted,theta);
imshow(distorted)

Step 3: Select Control Points

This example specifies three pairs of control points.

movingPoints = [128.6 75.4; 151.9 163.9; 192.1 118.6];
fixedPoints = [169.1 73.6; 135.6 199.9; 217.1 171.9];

If you want to pick the control points yourself, then you can use the Control Point Selection Tool. Open this tool by using the cpselect function.

[movingPoints,fixedPoints] = cpselect(distorted,original,"Wait",true);

Step 4: Estimate Affine Transformation

Fit a geometric transformation to your control points using the fitgeotform2d function. This example fits a similarity transformation because the distortion consists only of rotation and isotropic scaling.

tform = fitgeotform2d(movingPoints,fixedPoints,"similarity");

Step 5: Recover Scale Factor and Rotation Angle

The geometric transformation, tform, represents how to transform the moving image to the fixed image. If you want to determine the scale factor and rotation angle that you applied to the fixed image to create the moving image, then use the inverse of the geometric transformation.

tformInv = invert(tform)

tformInv = 
  simtform2d with properties:

    Dimensionality: 2
             Scale: 0.7014
     RotationAngle: -29.6202
       Translation: [0.0051 89.0695]
                 R: [2×2 double]
                 A: [3×3 double]

The values of the Scale property should match the value of scaleFactor that you set in Step 2: Resize and Rotate the Image.

The value of the RotationAngle property should have the same magnitude as the angle theta that you set in Step 2: Resize and Rotate the Image. However, the angle in RotationAngle has the opposite sign as theta. The sign is opposite because the simtform2d object stores the rotation angle as the amount of rotation from the positive x-axis to the positive y-axis in intrinsic coordinates. For images, the positive x direction points to the right and the positive y axis points downward, therefore a positive rotation angle is in the clockwise direction. A positive rotation angle in the clockwise direction corresponds to a negative rotation angle in the counterclockwise direction, and vice versa.

Step 6: Recover Original 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 argument is used to specify the resolution and grid size of the resampled output image.

Roriginal = imref2d(size(original));
recovered = imwarp(distorted,tform,OutputView=Roriginal);

Compare recovered to original by looking at them side-by-side in a montage.

montage({original,recovered})

The recovered (right) image quality does not match the original (left) image because of the distortion and recovery process. In particular, the image shrinking causes information loss. 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.