CS194-26 Project 4: Part A

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Image Warping and Mosaicing

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Sean Kwan, Fall 2021

Shoot the Pictures

Shown below are the three pairs of projective transform photographs. I tried to get a wide range of photos, including nature, the interior of a room and people.

Recover Homographies

In order to recover the homography transformation H, and to create the function:

I set up the equation:

where p is the correspondence points im1_pts, p' is the correspondence points im2_pts and H is the 3x3 Homography matrix. There are 8 unknowns so I set up a system of linear equations, transforming the p'=Hp into the form Ah=b, where h is the 8 unknown elements to be solved for in the homography matrix.

In practice, although only 8 equations (4 correspondence pair points) are needed I used more than 8 equations as the images turned out better. In order to solve this I used the least squares method.

Warp the Images & Image Rectification

In order to warp the images, I used the homography matrix H computed from the previous part. As I don't want any missed points, I used inverse warping on the image I wanted modified so I had multiply all the coordinate points by the inverse of H in order to compute the perspective transform. Using these new coordinates, I used cv2.remap in order to map the image into the new shape. Below are two examples of image rectification.