This project involved the concept of homographies, which are essentially matrices that help map points on one picture to corresponding points on a second picture, in the form p'=Hp, where p' are the source points, p are the target points, and H is the homography matrix. In this project, we use the inverse of H to warp images from the source points to the target points both of which are taken from the same center of perspective. This allows us to do 2 things: rectifying images and stitching images to create a panorama / mosaic.

We can rectify an image by creating a homography that lets us transform 4 source points in an image, which make a generic quadrilaterial, to 4 targer points that create a rectangle / square. I took images of objects that are actually rectangular but look skewed due to perspective. After defining the 4 points as the corners of the object in question, I used simple math to transform generate 4 target points that created a rectangle. I first defined the left, top, right, bottom values of the rectangle as the following: left was the x-average of the 2 left points, top was the y-average of the 2 top points, and so on. I then defined the (x,y) corners as (left, top), (right, top), (left, bottom), (right, bottom).

This part also uses ideas of homography to allow us to "stitch" many photos together in a panoramic essence. Essentially, we have three pictures: left, center, and right. We want to warp points on the left and right photos to points on the center photo using the homographic matrices. When selecting the corresponding points, I had two different sets of points (manually selected) for the left + center images vs. the right + center images, simply because if I tried to share the points across all images, that would mean every point I defined in the left image would also have to be in the right image. This made the homographic matrix more susceptible to overfitting and errors. Once I warped the left and right images onto the center image, I concatenated the results together. To make the stitching smoother, I added a gradient to transition the end of one image to the beginning of the next. Below are the results: