Image warping and Mosaicing

Raiymbek Akshulakov

We worked before with affine transformations, so let's try to upgrade from affine to homological. Before we had only 6 degrees of freedom, but now we got 8. Our goal for this project would be to turn this images:

into this

Our Goal

Shooting the Pictures

First of all to create this mosaic as above we need a fundamental assumptions for those images taken

All images should be taken from one position in space with different angles

We use this because when you consider Plenoptic function we can project one view to another with homological transformations only when the position of the center is not changed.

Recover homographyies

Over here is how we define the homographies. 8 degrees of freedom, 8 unknown variables. Suppose we have n points from image 1 and corresponding n points from another. That mean the equation has to satisfy the equation above for each point or be very close. If we would write down all the equations from each point, unless we have less or equal than 4 points, we would get a lot more equations than variables. One best way is to form the Least squares problem setting as shown below

Solving the least squares problem would give the best estimation for transformation matrix.

Warping Images - Image Rectification

The image warping is very similar to what we have done in the previous project with interpolation. Using this we can try to get the effect that we rotating our eyes in the image

Initial image || turning right

One good application of it is retrieval of small parts of the image that is hard to get in the initial orientation of the camera but a lot easier to see with other view - like in this images below:

Initial image || rectified

Mosaic

The last part of this project is how to create panorama with several images with different rotation

My first step is to create a huge canvas to fit all the images

We put initial image in the center

Let's take image to the right. We can define some correspondences between our central image and the current one. Using them we can define both the current_to_canvas and canvas_to_current homographies

Using current_to_canvas transformation get the edges of the next projection

Using canvas_to_current transformation and interpolation get the pixel values of each

We can project it on the new canvas with put the previous stuff in there to get two images

Now we can blend them using this mask that is basically the edges of the projection of the second image

Now we can repeat for other images but now we map correspondences for the third image and the second image that is already on the canvas. And final results are below:

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