Create anaffine2dobject that defines a 30 degree rotation in the counterclockwise direction around the origin.

theta = 30; tform = affine2d([...cosd(theta) sind(theta) 0;...-sind(theta) cosd(theta) 0;...0 0 1])

tform = affine2d with properties: T: [3x3 double] Dimensionality: 2

Apply the forward geometric transformation to a point (10,0).

[x,y] = transformPointsForward(tform,10,0)

x = 8.6603

y = 5

Validate the transformation by plotting the original point (in blue) and the transformed point (in red).

plot(10,0,'bo',x,y,'ro') axis([0 12 0 12]) axissquare

Read and display an image.

I = imread('kobi.png'); imshow(I)

Create anaffine2dtransformation object that rotates images. TherandomAffine2d随机函数选择一个旋转角从一个有限公司ntinuous uniform distribution within the interval [35, 55] degrees.

tform1 = randomAffine2d('Rotation',[35 55]);

Rotate the image and display the result.

J = imwarp(I,tform1); imshow(J)

The transformation object,tform1, rotates all images by the same amount. To rotate an image by a different randomly selected amount, create a newaffine2dtransformation object.

tform2 = randomAffine2d('Rotation',[-10 10]); J2 = imwarp(I,tform2); imshow(J2)

This example shows how to create a geometric transformation that can be used to align two images.

Create a checkerboard image and rotate it to create a misaligned image.

I = checkerboard(40); J = imrotate(I,30); imshowpair(I,J,'montage')

Define some matching control points on the fixed image (the checkerboard) and moving image (the rotated checkerboard). You can define points interactively using the Control Point Selection tool.

fixedPoints = [41 41; 281 161]; movingPoints = [56 175; 324 160];

Create a geometric transformation that can be used to align the two images, returned as anaffine2dgeometric transformation object.

tform = fitgeotrans(movingPoints,fixedPoints,'NonreflectiveSimilarity')

tform = affine2d with properties: T: [3x3 double] Dimensionality: 2

Use thetformestimate to resample the rotated image to register it with the fixed image. The regions of color (green and magenta) in the false color overlay image indicate error in the registration. This error comes from a lack of precise correspondence in the control points.

Jregistered = imwarp(J,tform,'OutputView',imref2d(size(I))); figure imshowpair(I,Jregistered)

Recover angle and scale of the transformation by checking how a unit vector parallel to the x-axis is rotated and stretched.

u = [0 1]; v = [0 0]; [x, y] = transformPointsForward(tform, u, v); dx = x(2) - x(1); dy = y(2) - y(1); angle = (180/pi) * atan2(dy, dx)

angle = 29.7686

scale = 1 / sqrt(dx^2 + dy^2)

scale = 1.0003