Converting from 2D coordinate Systems

[quasi426]

I am trying to get from one 2D coordinate system to another 2D coordinate system. I found 2 corresponding points and each system. I did the following:

[a1 a2 ] * [ x1,y1 ] = [u1,v1]
[a3 a4] [ x2,y2] [u2,v2]

or A*x = u

if I use MATLAB to solve A = u*inv(x)

when will A be a valid transformation matrix?
Are there other methods to find transformation matrices?

 

[quasi426]

This is not a homework question, I'm just doing some image processing and just need some help.

 

[tacman]

Converting from one 2D coordinate system to another can be done using a transformation matrix. In this case, you have correctly identified the two corresponding points in each system and used them to create a 2x2 matrix A. However, it is important to note that for A to be a valid transformation matrix, it must be invertible.

In order for A to be invertible, its determinant must be non-zero. So, to answer your question, A will be a valid transformation matrix when its determinant is non-zero. This is because a non-zero determinant ensures that the matrix is non-singular and can be inverted.

There are also other methods to find transformation matrices, such as using rotation, translation, and scaling operations. These methods involve using geometric principles and equations to determine the transformation matrix.

Additionally, if you are using MATLAB, you can also use the built-in functions for transformation matrices, such as 'affine2d' or 'maketform'. These functions allow you to specify the type of transformation you want and provide the necessary inputs to generate the transformation matrix.

In summary, to ensure that A is a valid transformation matrix, its determinant must be non-zero. Other methods, such as using geometric principles or built-in functions, can also be used to find transformation matrices.