Contents
How to calculate transformation between two sets of points?
I want to make assumption that object’s can be treated as 2D so only 2D transformations should be computed. First I want to to it in manually assisted way. The user selects base point on model image and then target point on target image. The number of points should be defined by user (but no less than some minimum 2-3 points).
What should be the minimum number of points for a transformation?
The number of points should be defined by user (but no less than some minimum 2-3 points). When points gives different information, the transformation should be averaged and for example from this the quality of matching can be computed.
How to find the optimal rigid transformation matrix?
R is a 3×3 rotation matrix and t is the translation vector (technically matrix Nx3). Finding the optimal rigid transformation matrix can be broken down into the following steps: Bring both dataset to the origin then find the optimal rotation R
What do you need to know about align to shape?
This includes the shape to align to, which layers are updated, and the tolerance. Since Align To Shape is an interactive tool that requires that you manually trace the shape to align to, it works best for cases where just portions of features need to be adjusted, rather than when you have many features to align.
Is the affine transformation written in a 3 * 3 matrix?
Your transformation is an affine transformation, which can be written in a 3*3 matrix. So your problem is basically to compute the least-mean-square-error affine transformation from one set of points to the others. This problem is quite simply resolved in common computational geometry literature.
How to generalize the problem in a simple affine transformation?
First generalize the problem in a simple affine transformation with a 3×3 affine transformation matrix: i.e. Since we already know that the third row will always be [0 0 1] we can simply disregard it. where xp and yp are the projected coordinates and x and y are the original coordinates.
Which is the optimal transformation in the least square sense?
Putting it all together, this gives you the optimal transform in the least square sense. Your transformation is an affine transformation, which can be written in a 3*3 matrix. So your problem is basically to compute the least-mean-square-error affine transformation from one set of points to the others.