Tony Lian's Project 4

PRPJECT 4 PART A: IMAGE WARPING and MOSAICING

Shoot the Pictures (20 pts)

I shoot 10 images from a garden from the same viewing point with different perspectives on my phone, with AE/AF lock that preserves lighting and focus. Some images are too bright and too dark because of this, so I pick and choose from these 10 images.


Recover homographies (20 pts)

I add at least 4 points on pairs of images used by later parts, as an example, I add 4 points to this pair of images.

Then, I turn the projection formula: $$p' = Hp$$ where p' is the objective point and p is the point that we want to warp, into a formula $$A\textbf{h}=b$$ where \(\textbf{h}\) vector includes 8 parameters that are the degrees of freedom in \(H\): $$\textbf{h} = [a, b, c, d, e, f, g, h]^T$$ For each correspondence, I add two equations:

$$a p_1 + b p_2 - g p_1p_1' - hp_2p_1' + c - p_1' = 0$$

$$d p_1 + e p_2 - g p_1p_2' - hp_2p_2' + f - p_2' = 0$$

These are linear equations that can form a system, and to be solved either precisely or with least squares if the number of equations is greater than 8 (the degree of freedom).

Warp the images (20 pts) [produce at least two examples of rectified images]

I then warp two images with rectangle structure into front-facing images.

Before warping:

With warping:

Before warping:

With warping:

The second one has artifacts because the original region is too small.

Blend images into a mosaic (20 pts) [show source images and results for three mosaics.]

Mosaic 1:




Mosaic 2:




Mosaic 3:



Optional Bells and Whistles (up to 20 pts, combined from Parts A and B)

Be creative: Image-in-Image

Original image:

Image in image:





Tell us what you've learned

I finally learned how panorama taken on the phone is synthesized. It's amazing to learn these transformations.