Find Image Rotation and Scale - MATLAB & Simulink Example

12/18/13 Find Image Rotation and Scale - MATLAB & Simulink Example

www.mathworks.com/help/images/examples/find-image-rotation-and-scale.html 1/3

Find Image Rotation and Scale

This example show s how to align or register tw o images that differ by a rotation and a scale change. You can use fitgeotrans

to f ind the rotation angle and scale factor after manually picking corresponding points. You can then transform the distorted image

to recover the original image.

Step 1: Read Image

Read an image into the w orkspace.

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

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)



Step 3: Select Control Points

Use the Control Point Selection Tool to pick at least tw o 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 w ith these pre-picked points, but try picking your ow n points to see how the results vary.

cpselect(distorted,original,movingPoints,fixedPoints);

Save control points by choosing the File menu, then the Save Points to Workspace option. Save the points, overw riting

variables movingPoints and fixedPoints.

Step 4: Estimate Transformation

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 'aff ine' instead of 'NonreflectiveSimilarity'. What

happens? Are the results as good as they w ere w ith 'NonreflectiveSimilarity'?

Step 5: Solve for Scale and Angle

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)

theta_recovered = atan2(ss,sc)*180/pi

scale_recovered =

0.7000

theta_recovered =

29.3741

The recovered values of scale_recovered and theta_recovered should match the values you set in Step 2: Resize and

Rotate the Image.

Step 6: Recover Original Image

Recover the original image by transforming distorted, the rotated-and-scaled image, using the geometric transformation tform

and w hat 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);

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

figure, imshowpair(original,recovered,'montage')

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 loss of information. The artifacts around the edges are due to the limited accuracy of the

transformation. If you w ere to pick more points in Step 3: Select Control Points, the transformation w ould be more accurate.

Documents

Find Image Rotation and Scale - MATLAB & Simulink Example