how do we know that the homography matrix has 8 degrees of freedom? i'm sort of unclear about where we got that number from based on the information on this slide
motoole2
The degrees of freedom represent the number of independent variables which affect the transformation. We can simply count the number of parameters used to express each transform---though we have to be a little careful about how we do this for homographies.
For example, affine transforms depend on 6 independent variables, and therefore it has 6 degree of freedom. For homographies, we work with a 3x3 matrix (9 elements), but there are only 8 independent variables (not 9) due to homography matrices being scale invariant.
how do we know that the homography matrix has 8 degrees of freedom? i'm sort of unclear about where we got that number from based on the information on this slide
The degrees of freedom represent the number of independent variables which affect the transformation. We can simply count the number of parameters used to express each transform---though we have to be a little careful about how we do this for homographies.
For example, affine transforms depend on 6 independent variables, and therefore it has 6 degree of freedom. For homographies, we work with a 3x3 matrix (9 elements), but there are only 8 independent variables (not 9) due to homography matrices being scale invariant.