In this assignment we warp images into mosaics to generate panoramas. There are two main parts: 1. Image Rectification, the core utility to image stitching, and 2. Blending to create mosaics.

I. Image Rectification

In order to align the images we have take into account that the camera looks at the same scene from different perspectives, in essence taking a project transform of the scene. A Homography is a projective mapping between two planes with the same center of projection, the camera axis. A projective transform allows mapping between any pairs of quadrilaterals. It does not preserve parallel lines but does straight lines. The projective matrix His below.

We have 8 unknowns. Now it becomes clear why we needed 4 pairs of points in order to solve for h or H. We then plug A and b into a leasr squares solver to recover an H that best fits the specified points.

Here are the images I will be using to demonstrate rectification.

First I chose the 4 corners of objects I knew the geometry for. Here, I chose the slide and a face of the paper bag. Then I just 4 arbitrary correspnding target points at right angles in the rectified canvas space. Then I image warped using the bilinear interpolation we used back in project 4. These are the results. One thing to note is that the transform will match the four points to the four specified target points, however the rest of the image will be projectively transformed in different directions, almost always verging into the negative axes. In order to account for this in the future, we apply shifts into the positive quadrant so that we are able to view more of the image.