Re: Affine Transform


priti wrote:
Hey Everyone,

I have some images that are rotated and translated with respect to each
other and i dont know the rotation or the translational factor and i
need to align them so that each the corresponding pixel at each set of
co-ordinates

You have control points, i.e. points for which you know the coordinates
in both frames?

represent the same structure. From Literature i learnt
that Affine transform is used for rotational and translational
alignment shortly called rigid body transformation/registration.

Rotation combined with translation = rigid body transformation.

Affine allows more, notably scaling. Shear? Not sure. But, yes, rigid
body transformation is an affine transformation.

I m
not very sure as to how to form the affine transform matrix for
implementing the correction. I tried the regular "affine transform"
registration in MATLAB but that doesnt seem to work so well.

If anyone has actually formed an affine transform matrix to perform
this kind of an operation on the images it would be helpful to know as
to how to form that matrix for correcting the rotational and
translational misalignment.


I don't know the MATLAB function to which you refer. Depends on how you
estimated the parameters; unless you have angle and the two
translations (three parameters) from some other source, then you must
estimate them from control points. I can post the formulae, but I have
little soubt that you can find appropriate code on the web --- but I
guess the routine mentioned will work if use properly. Shapiro and
Stockman, Computer Vision, Prentice Hall, 2001 is one book that will
give you the formulae.

Strictly, you need just two control points which yield four equations
in three unknowns. Normally, however, when there are measurement
errors, more than two control points are needed --- leading to
overdetermined system of equations and requiring use of a
pseudo-inverse of a matrix.

Best regards,

Jon C.

.

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