How to calculate the inverse of two dimensional transformation

Hi Recipient,

I am working on two dimensional image registration. I have a transformation \phi which has two components stored into two separate matrices. The standard way to represent the action of \phi on image 'I' is \phi.I=I(\phi^{-1}(x)). I want to know how to calculate \phi^{-1}. Suppose x1 and x2 are two components of \phi. If I use A=interp2(x1,x2,I,y1,y2) then its mean that I am calculating I(\phi(x)) but I want to calculate I(\phi^{-1}(x)). Could anyone help me in this regard.

Answer 1

[Matt J]

Suppose x1 and x2 are two components of \phi. If I use A=interp2(x1,x2,I,y1,y2) then its mean that I am calculating I(\phi(x))

No, you would be calculating I(phi(x)) if the y_i are given by y=phi(x).

If you want I(phi^-1(x)) you would generate the y data instead according to y=phi^-1(x).

If you have the Image Processing Toolbox, you might be able do this more compactly using tforminv() and imtransform().