To create a successful mosaic, we needed to take a set of pictures that aligned with each other, along the same focal point. Here are some pictures that could be used to create a mosaic.
The main goal of recovering homographies is find all of the constraints of the H matrix described below.
Solving for the H matrix in this case is possible, but would require extraneous computations. With some algebra, we can create a version of the operation that is more easily vectorizable.
Which leads to:
The results can then be converted to a matrix form similar to the following, which can be solved trivially.
We can then easily use a built in linear equation solver to solve this system of equations.
The main idea of image rectification is to straighten out lines that are not originally perpendicular to the standard (x,y) axes, and force them to fit the two axes. The end result would be if one were to capture the target to be rectified straight on. Here is one example of a successful rectification: