So, now we have figured out, the optical center, we have a very simple method estimated, let's look into the focal length, the second element of this camera projection. Our cell phones usually have a very small focal lens, due to the size constraints of your software. Software pretty skinny. In fact, the focal length of your cellphone is on the order of millimeters. On the other hand, a professional camera may usually have a much longer focal lens, and that focal lens can go on to the order of 1,000 millimeters. In this case, go out to 1,700 millimeters, which is about 2 meters long. With such a long camera focal lens magic happens. You can look into a world and take a picture of an object miles down the road and the image will appear to be super magnified. Of course, that can be also done with your cell phone. You just have to walk further down the street a mile closer to the object, take the same picture. So you can think of the telephoto lens camera, what it does for you is magnification and if you don't have that, you have to walk. So the process of changing the focal lens is also called zooming. And here we illustrate a camera that goes through a change of focal lens from 400 millimeter to 17 millimeters. And a change in focal lens, what it does is not only magnify the image for you, but also trace an interesting desk compression effects. So pay attention to the foreign object and the background building in this sequence of images. What we see in the 400 millimeter is the background building appear to be relatively large compared to the foreground object. While we change the zooms, we're now changing, we not only change the focal lens, we see that the relative size of objects in the background to the foreground object is changes. And this creates an interesting visual sensation, as if the background object is being moved closer or further away from you by changing the focal lens. And this is an interesting effect create sensation of moving to a space by simply changing the focal lens. And is a very different effect from just magnify the picture itself. There's reason we have such a sensation is because optical center and focal lens changes occur simultaneously, as illustrated in this figure. As we change the focal lens, it's not just we are increase the distance of the image plane to the camera center. What happened is the camera center itself is moving, and recall the distance of an object is defined as the distance of the object to me, the camera center and it made of two components. One is the components for the object to the image plane. Which remain fixed during a focal lens change. Plus, the focal lens from the image plane to the optical center. And that quantity is changing. The combination of the changing focal lens and center of projection creates an interesting effect. Which we can use to define a sequence of images creating a sensation called a dolly zoom. And dolly zoom is shown here. The top is the first person view, a three dimensional image, how I see the world. On the top you see an overhead view of the setup where you had a two teacup, two cubes and the camera is moving in space, changing the optical center while changing it's focal lens. The focal lens change is illustrated by the field of view changes. At the beginning of the sequence we have a large field of view. Illustrating a short focal lens. At the end of the sequence we have a narrow field of view increase a larger focal lens. And this change of the optical center and focal lens is calculated precisely, so that we create an illusion such as the object. The two cubes each size remain the same size visually, while the two objects in the background appeared to get bigger and bigger. And this a fact that Hitchcock had used in his movie be vertical and create a sensation of moving object in the space. Illusions that is created by moving the camera around rather than moving the objects themself. And here's another dolly zoom sequence that we have created on the campus of the University of Pennsylvania. Three person each stand in front of the images are kept at the same size and the background appears to be larger and larger flying towards the foreground person. This image is created by artificial sequences of computing a three dimensional depth map of the image, and creating this simulation illustrating Dolly zoom. Also a sequence of Dolly zoom examples. In this example, the image here shows overhead view of the situation we have. We have a camera, a first person camera. The world is again defined as origin as me. The X direction is a horizontal direction, Y is the downward direction and Z is pointing forward. We have a field of view in front of us, and the 3 objects. A green cube, a blue cube and a pink pyramid on the right. And in an image we will see a picture like this. You got a green cube on the left, a blue cube in the middle and a pink object on the right. And let's focus on the green object and the blue object. The green object has a sight, on the left side, of a height of 400 pixels in the image. And the blue cube is further out in the distance and appears smaller because its distance is small the further out. It has a height of 120 pixels. The optical center intersected the image right in the middle, (0,0). Next, what we do is pull back the camera, we move into the distance Z equal to -4. The object in the space still stay stationary, nothing had moved. We had changed the focal lens to make it longer and that shows up in this diver as the field of view become narrower. By just taking a step back and changing the focal lens the image in front of us appear changed. The blue object has get bigger and move further to the left. We have designed the move purposely such that we kept the green cube on the side exactly at 400 pixels tall. But, you can see the further step we took in changing focal lens make the distant object blue appear to be larger, rather to the foreground. And this figure shows the side by side. On the top we have the first person camera since center 0,0 origin larger through the view. An object at the distance, the blue object looks fairly small. We took a step back, changed the field of view to be smaller, by increased the focal lens. And this process of changing the optical center moving backwards while magnify the image by changing the field of view, or increase the focal lens. Create a sensation so the green objects are exactly the same height. 400 pixels tall. But now blue object becomes bigger in comparison have become 200 pixel tall. So this process create a sensation of a further object, get bigger and bigger as we move further out. And this is illustrated in this video. Again, objects that stay stationary and the only thing changing is the camera itself has moved back in a Z axis while we continuously increase the focal lens and decrease the full fielder view. And this creates a sensation of a three dimensional movements in a scene what we call the Dolly zoom or the vertical effect.
