image warping and mosaicing

Nadia Hyder

OVERVIEW

In this project, I explored different aspects of image warping, namely image mosaicking. I performed image warping by taking at least 2 photographs, registering, projective warping, resampling, and compositing them. A key step in performing mosaicing was computing homographies and using them to warp the images.

PART 1

RECOVERING HOMOGRAPHIES

Before warping images into alignment, I had to recover the parameters of transformation between pairs of images. This transformation is a homography, which relates the transformation between two planes (images are only related by a homography if they are viewing the same plane from a different angle). The homography matrix H is a 3x3 matrix with 8 degrees of freedom.

Given a point (x,y) in image 1, and its corresponding (x’, y’) point in image 2, we can find H using the following equation (attaining H using least squares):

WARPING AND RECTIFICATION

Warping an image with H transforms the image into the desired perspective, as the homography matrix maps the source points to the desired points. I used inverse warping with linear interpolation to avoid aliasing during resampling. Finally, I was able to rectify images. I chose two sample images with planar surfaces (one square and one rectangular) to warp so the plane is frontal parallel. I used ginput to select 4 points in each image, and defined the corresponding (x’,y’) corners by hand to be square and rectangular, respectively.

Here are the results of rectification:

original	rectified

BLENDING INTO A MOSAIC

We now have the capabilities to take 2 images, warp them, and blend them to create an image mosaic. Where the two images overlap, I used weighted averaging. Here are the results:

Left image	Right image

Warped left image	Warped right image	Composite

Unfortunately the warping created slight edges so I would hope to improve the warping soon. Learning how to rectify images was my favorite part of this assignment because I’ve always wondered how it was performed in photo editors and document scanning apps like Scannable.