To recover Homographies, we can use a least squares solution to an equation. We are doing p' = Hp. We can do this by solving for the homography matrix, which acts as the transformations from one image to the other. It maps a point p to point p'. To get the rectifications, we have to transform to a rectangle, which I just mapped as the 4 corners of the image. Then we do a warp and have the following examples.
Image Rectification
Rectified
Rectification 2
Rectified
Mosaics
For Mosaics, I use a middle image, and then warp the images to this middle image. I then blend the images to make it better. With Niave blending, we have stitches, however using alpha channel blending, I was able to remove the stitches. The only problem with alpha blending is the obvious darkening of the sides, which is a cause of the gradient. However, this makes the images look a lot better. I aligned only two because I found these to give me the best results. Naive Blend blends by averaging the two where they overlap and taking the respective one where they don't.
Left
Middle
right
Linear blending with alpha channel
Naive Blend with Weight
Left
Middle
right
Linear blending with alpha channel
Naive Blend with Weight
Left
Middle
right
Linear blending with alpha channel
Naive Blend with Weight
Summary
I thought the rectification part was super cool, being able to transform a point into another space and "rectifying" it was something I hadn't seen before. The homography matrix is really cool and I think this class has made me really recognize the power of linear algebra and manipulations with photos. The most challenging part was figuring blending and understanding what it meant, I also think I want to figure out more about how to do cooler blends.
