原文：http://blogs.mathworks.com/steve/2006/02/14/spatial-transformations-maketform-tformfwd-and-tforminv/
Several Image Processing Toolbox functions related to spatial transformations use "tform" structures. A tform structure has data and function handles needed for applying a spatial transformation in the forward or the inverse direction, and sometimes in both directions.
maketform
Function maketform has several syntaxes for constructing different types of tform structures. For example, you can construct an affine transform by providing an A matrix:
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2A = [2 0 0; 0 2 0; 0 0 1]; % Stretch by a factor of 2 in both directions. tform = maketform('affine', A);
tformfwd
Toolbox function tformfwd transforms points from input space to output space. For example, to apply the affine transform above to the point (u,v) = (2,3), do this:
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2uv = [2 3]; xy = tformfwd(tform, uv)
tforminv
Function tforminv transforms points from output space to input space. If we apply the inverse transformation to the point xy computed above, we should get back the original point.
1uvp = tforminv(tform, xy)
Introducing George
The spatial transformation functions imtransform, tformarray, tformfwd, tforminv, etc., were introduced to Image Processing Toolbox version 3 in 2001.
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3% http://blogs.mathworks.com/images/steve/37/george.mat load george plot(x,y), axis ij, axis equal, axis([-1 1 -1 1]), grid on
Scaling example
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11A1 = [2 0 0; 0 2 0; 0 0 1]; tform1 = maketform('affine', A1); uv1 = tformfwd(tform1, [x y]); subplot(1,2,1) plot(x,y), axis ij, axis equal, axis([-2 2 -2 2]), grid on, title('George') subplot(1,2,2) plot(uv1(:,1), uv1(:,2)), axis ij, axis equal, axis([-2 2 -2 2]) grid on title('Scaled by 2')
Rotation example
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12theta = pi/4; A2 = [cos(theta) sin(theta) 0; -sin(theta) cos(theta) 0; 0 0 1]; tform2 = maketform('affine', A2); uv2 = tformfwd(tform2, [x y]); subplot(1,2,1) plot(x,y), axis ij, axis equal, axis([-2 2 -2 2]), grid on, title('George') subplot(1,2,2) plot(uv2(:,1), uv2(:,2)), axis ij, axis equal, axis([-2 2 -2 2]) grid on title('Rotated by 45circ')
Translation example
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11A3 = [1 0 0; 0 1 0; 1 -1 1]; tform3 = maketform('affine', A3); uv3 = tformfwd(tform3, [x y]); subplot(1,2,1) plot(x,y), axis ij, axis equal, axis([-2 2 -2 2]), grid on, title('George') subplot(1,2,2) plot(uv3(:,1), uv3(:,2)), axis ij, axis equal, axis([-2 2 -2 2]) grid on title('Translated')
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