Notable Homographic Transformations

It is possible to provide a brief list of the transformations in computer vision that can be represented by a homography.

Given knowledge of the camera orientation and intrinsic parameters, the transformations described in this section make it possible to derive matrix $\mathbf{H}$, which determines the transformation; conversely, by obtaining the homography matrix through point correspondences between the two images, it is possible to derive some parameters relating the views. It is important to point out that, for all transformations involving a homography (change of viewpoint, perspective projection, IPM, and rectification), whenever knowledge of the parameters required to generate the transformation is needed, the representative matrices can nevertheless be recovered implicitly by knowing how at least 4 image points are transformed (see Section 9.5.1 for details). The parameters obtained by decomposing the homography matrix result from an algebraic minimization. The maximum-likelihood solution requires nonlinear minimization, but uses the result obtained in this stage as its starting point.