This example shows how to automatically align two images that differ by a rotation and a scale change. It closely parallels another example titled Find Image Rotation and Scale. Instead of using a manual approach to register the two images, it utilizes feature-based techniques found in the Computer Vision System Toolbox™ to automate the registration process.
In this example, you will use
vision.GeometricTransformEstimator System object to recover rotation angle and scale factor of a distorted image. You will then transform the distorted image to recover the original image.
Bring 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; J = imresize(original, scale); % Try varying the scale factor. theta = 30; distorted = imrotate(J,theta); % Try varying the angle, theta. figure, imshow(distorted)
You can experiment by varying the scale and rotation of the input image. However, note that there is a limit to the amount you can vary the scale before the feature detector fails to find enough features.
Detect features in both images.
ptsOriginal = detectSURFFeatures(original); ptsDistorted = detectSURFFeatures(distorted);
Extract feature descriptors.
[featuresOriginal, validPtsOriginal] = extractFeatures(original, ptsOriginal); [featuresDistorted, validPtsDistorted] = extractFeatures(distorted, ptsDistorted);
Match features by using their descriptors.
indexPairs = matchFeatures(featuresOriginal, featuresDistorted);
Retrieve locations of corresponding points for each image.
matchedOriginal = validPtsOriginal(indexPairs(:,1)); matchedDistorted = validPtsDistorted(indexPairs(:,2));
Show point matches. Notice the presence of outliers.
figure; showMatchedFeatures(original,distorted,matchedOriginal,matchedDistorted); title('Putatively matched points (including outliers)');
Find a transformation corresponding to the matching point pairs using the statistically robust M-estimator SAmple Consensus (MSAC) algorithm, which is a variant of the RANSAC algorithm. It removes outliers while computing the transformation matrix. You may see varying results of the transformation computation because of the random sampling employed by the MSAC algorithm.
[tform, inlierDistorted, inlierOriginal] = estimateGeometricTransform(... matchedDistorted, matchedOriginal, 'similarity');
Display matching point pairs used in the computation of the transformation matrix.
figure; showMatchedFeatures(original,distorted, inlierOriginal, inlierDistorted); title('Matching points (inliers only)'); legend('ptsOriginal','ptsDistorted');
Use the geometric transform, TFORM, to recover the scale and angle. Since we computed the transformation from the distorted to the original image, we need to compute its inverse to recover the distortion.
Let sc = scale*cos(theta) Let ss = scale*sin(theta)
Then, Tinv = [sc -ss 0; ss sc 0; tx ty 1]
where tx and ty are x and y translations, respectively.
Compute the inverse transformation matrix.
Tinv = tform.invert.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 = 0.7010 theta_recovered = 30.2351
The recovered values should match your scale and angle values selected in Step 2: Resize and Rotate the Image.
Recover the original image by transforming the distorted image.
outputView = imref2d(size(original)); recovered = imwarp(distorted,tform,'OutputView',outputView);
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 detect more points in Step 4: Find Matching Features Between Images, the transformation would be more accurate. For example, we could have used a corner detector,
detectFASTFeatures, to complement the SURF feature detector which finds blobs. Image content and image size also impact the number of detected features.