MATLAB: how to transform one image to another image

Question

I am trying to transform one image to another in MATLAB, and in the meantime also get the transformation function T(x,y) from this operation (eg. T(x,y) = (x + a(x,y), y + b(x,y)) ). Let's use the following figures as an example. I want to transform the square in the first figure to the circle in the other figure, and output gives me a transformation function, so whenever I use the function on the square I will get the circle.

Functions I have looked into:

I have looked into imwarp , but it should be only for geometric transformation (scaling, rotating, shearing). I don't think this is useful in transforming a square to a circle, while not providing any transformation matrix beforehand.

I have looked into using imregconfig and imregister from a MATLAB example , but it seems to only work for images with same structure but different intensities. Plus, it doesn't give out any transformation function. Please correct me if I am wrong.

Thank you in advance for any help!

Answer 1

The solution space for valid transformations is infinite. How do we choose the "right" one?

One possible transformation for those inputs is to translate the square -0.5 in x and -0.5 in y . Then scale it to double the size ( x' = 2x , y' = 2y ) and apply a square-to-circle mapping function . (Solution 1)

Another completely valid transformation function could run all the points in the input through the expression

( (x == 0 || x == 1) && (0 <= y <= 1) || ( (y == 0 || y == 1) && (0 <= x <= 1) )

and if all points pass, simply print out "x^2 + y^2 = 1" . (Solution 2)

Solutions (1) and (2) both produce code that seems to satisfy the case you've presented, but clearly (2) is so non-general as to be useless. I think you need to define the problem more precisely before we can start writing a solution in code.