While working with images and computer vision, it is very common that you will require the ability to preprocess an image using known geometric transforms, such as stretching, shrinking, rotation, and warping. The latter is the same as nonuniform resizing. These transforms can be realized through the multiplication of source points with a 2 x 3 matrix and they get the name of affine transformations while turning rectangles in parallelograms. Hence, they have the limitation of requiring the destination to have parallel sides. On the other hand, a 3 x 3 matrix multiplication represents perspective transforms. They offer more flexibility since they can map a 2D quadrilateral to another. The following screenshot shows a very useful application of this concept.

Here, we will find out which is the perspective transform that maps the side of a building in a perspective view to its frontal view:

Note that the input to this problem is the perspective...