Use Correlation as Preprocessing Step in Image Registration

This example shows how to use gradient correlation as a preliminary step for automatic image registration. In this process, first you perform gradient correlation using imregcorr, and then you pass the result of that registration as the initial condition of an optimization-based registration using imregister. Gradient correlation and optimization-based registration are complementary algorithms. Gradient correlation is good for finding gross alignment, even for severely misaligned images. Optimization-based registration is good for finding precise alignment, given a good initial condition.

Get Misaligned Images

Read an image that will be the reference image in the registration.

fixed = imread("cameraman.tif");
imshow(fixed)

Create an unregistered image by deliberately distorting this image using rotation, isotropic scaling, and shearing in the y direction.

theta = 170;
rot = [
    cosd(theta) -sind(theta) 0; ... 
    sind(theta)  cosd(theta) 0; ... 
    0 0 1]; 
sc = 2.3;
scale = [sc 0 0; 0 sc 0; 0 0 1]; 
sh = 0.1;
shear = [1 sh 0; 0 1 0; 0 0 1]; 

tform = affinetform2d(shear*scale*rot);
moving = imwarp(fixed,tform); 

Add noise to the image, and display the result.

moving = imnoise(moving,"gaussian");
imshow(moving)

Find Rough Alignment Using Gradient Correlation

Estimate the registration required to bring these two images into alignment. imregcorr returns a simtform2d object that defines the transformation.

tformEstimate = imregcorr(moving,fixed)

tformEstimate = 
  simtform2d with properties:

    Dimensionality: 2
             Scale: 0.4182
     RotationAngle: -167.1995
       Translation: [245.7549 302.3793]
                 R: [2×2 double]

                 A: [-0.4078    0.0926  245.7549
                     -0.0926   -0.4078  302.3793
                           0         0    1.0000]

Apply the estimated geometric transform to the misaligned image. Specify the OutputView name-value argument to ensure the registered image is the same size as the reference image.

Rfixed = imref2d(size(fixed));
movingReg = imwarp(moving,tformEstimate,OutputView=Rfixed);

Display the original image and the registered image in a montage. You can see that imregcorr has done a good job handling the rotation and scaling differences between the images. The registered image, movingReg, is very close to being aligned with the original image, fixed. However, some misalignment remains. imregcorr can handle rotation and scale distortions well, but not shear distortion.

imshowpair(fixed,movingReg,"montage");

View the aligned image overlaid on the original image, using imshowpair. In this view, imshowpair uses color to highlight areas of misalignment.

imshowpair(fixed,movingReg,"falsecolor");

Refine Alignment Using Optimization-based Registration

Configure the optimizer and the metric values for the optimization-based registration. Specify a monomodal configuration because the two images originate from the same sensor.

[optimizer,metric] = imregconfig("monomodal");

To finish the registration, use imregister, passing the estimated transformation returned by imregcorr as the initial condition. imregister is more effective if the two images are roughly in alignment at the start of the operation. The transformation estimated by imregcorr provides this information for imregister.

movingRegistered = imregister(moving,fixed,"affine", ...
    optimizer,metric,InitialTransformation=tformEstimate);

Display the result of this registration. Note that imregister achieves a very accurate registration, given the good initial condition provided by imregcorr.

imshowpair(fixed,movingRegistered,"falsecolor",Scaling="joint");