Image Warping and Mosaicing

Vincent Escueta

Homographies

To warp images, we must first create the homography matrix, H, by recovering 8 unknown entries of the 3x3 matrix. We can find the 8 unknowns, h, by having 4 points to sample from the source image and 4 corresponding points from the warped image. These 4 sets of points are plugged into a matrix A and a set of points, b, to use least-squares to get h. Then having h, we can form H.

Homography Matrix
Ah = b

Warp the Images

To warp the image into a desired warp we do the following:

  1. Given 4 or more correspondences, calculate the homography matrix, H.
  2. Use the corners of the original image to create the bounding box of the warped image by passing the corners through H.
  3. Then use inverse warping to create the warped image

Image Rectification

All the following are pictures with planar surfaces warped so the plane is front-parallel.

Our Lady of Guadalupe
Warped Guadalupe
SF Japanese Tea Garden
Warped Tea Garden
Memorial Stadium
California

Blend the images into a mosaic

For the next part, I combined 2 similar images to create a mosaic panorama. We accomplished this by doing the following:

  1. Plot points on both images where the same objects would correspond to the same points on both images.
  2. calculate the homography matrix, H.
  3. Warp one of the images to match the projection of objects of the other images and shift both images accordingly to fit into a frame and overlap.
  4. Blend (I used both weights and multiresolution blending)

The following are results as I used Yosemite as a clear example of plotting points, warping and overlaying, then blending:

Yosemite points
Lake Tahoe points
More Lake Tahoe points
Yosemite Left
Yosemite Right
Half Dome overlay
Half Dome weights
Half Dome multiresolution blending
Lake Tahoe Left
Lake Tahoe Right
Lake Tahoe weights
Lake Tahoe multiresolution blending
More Lake Tahoe Left
More Lake Tahoe Right
More Lake Tahoe weights
More Lake Tahoe multiresolution blending

What I learned

In this project, I learned how panoramas are created and how simple it is, but also how important it is that the pictures have to be a little similar to each other. Yet, it's easy to recognize that so much still happens in our phones because even when my pictures have very similar lighting, they still seem to have hardlines or noticeable differences where the two pictures overlay. Along with that, with manually picking the points, it becomes likely that human error will make the pictures imperfect and not overlay as well as they could.