Recover Homographies

For homography, the following equation is setup. $p'$ is the destination correspondence point while $p$ is the associated input correspondence point.

This equation expanded out looks like the below:

In order to get the homography matrix, corresponding points are used to solve the following linear system:

Rectified Images

Now we will rectify a few images. First we will look at the chess board:

The correspondence points are labeled below.

The destination correspondence points will be a square as expected for a chess board:

Next we will look at a poster frame:

The correspondence points are the corners of the frame:

The destination correspondence points are going to be a rectangle as shown below:

Mosaics

Note that all blending for the mosaics were done using laplacian pyramids from project 2.

First we will observe some picture of my friend Matt at the edge of Willard Park:

These images were a bit too dim so I brightened them and defined the following correspondence points:

The resulting mosaic of these two images is shown below:

Next we will observe the following images:

These images have the following correspondence points:

The resulting mosaic is shown below:

Next we observe the following photos:

The correspondences are shown below:

The resulting mosaic is shown below:

What I learned

I thought that the homography was really cool. Being able to view a chess board from the birds eye view was pretty astonishing!