I\'m trying to search a specific object in input images by matching SIFT descriptors and finding the transformation matrix by RANSAC. The object can only be modified in scene by
You can use find an affine transformation between the point sets using opencv, this is slightly more general than the case you are describing (known as a similarity transform) as it describes shearing transformations of the shapes as well.
It can be performed using the function getAffineTransform(InputArray src, InputArray dst)
. This takes 2 sets of three points and calculates an affine transform between them.