Pinhole Camera Model


### Single View Geometry
### Principal point
point where principal axis intersects theimage plane
- Principal Axis
> - perpendicular to the image plane
- Normalized coordinate system
> - camera center is at the origin and the principal axis is the z-axis
- f is distance between camera and image plane
- P is principal Point (0, 0, Z)
![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F438bde54-862b-4270-bd7c-6e0f4c0239c1%2FUntitled.png?table=block&id=131b5624-842c-4f8e-926e-d4a49a7f413e&cache=v2)


## Calibration
![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2Faa6222d5-e080-42d8-94c6-85de1ad3fe82%2FUntitled.png?table=block&id=33b243c9-694d-482a-acd3-866fa40f167f&cache=v2)
and then fill decomposed matrix (cameral internal and camera external becuz f is internal to the camera)
![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F71a391ee-da3c-4ce6-9070-36d409edea63%2FUntitled.png?table=block&id=fbe77a96-6f4b-4c6e-a43f-9deef7906bef&cache=v2)
### External Factor
> ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2Ff3e5fa2b-04a8-49c6-b561-aa05e78d82b8%2FUntitled.png?table=block&id=3fad863c-5113-4b25-a20c-73ce69d57ccf&cache=v2)

> ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F0a4b342e-f493-480a-83d0-78ccd1fc2917%2FUntitled.png?table=block&id=7ecf5aac-0c8b-4149-bfb0-876860bf0be5&cache=v2)

### Intrinsic Parameter
![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F524812a7-7f4d-4f4c-b527-5ac087cbcc2a%2FUntitled.png?table=block&id=a9e3d7ab-06f9-43fd-af63-ef7f195f3be2&cache=v2)

1. recover transition matrix
2. recover location
3. recover principle point and image point small x
4. use multiple and recover large X


### Two linearly independent equations
![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2Fd84c3cec-e6e2-446a-954e-9174fc51aee0%2FUntitled.png?table=block&id=865593eb-425e-4dd2-8113-9da716d828fc&cache=v2)
P has 11 degrees of freedom (12 parameters, but scale is arbitrary)
![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2Fe614970a-dd30-4629-a83b-473bc0fcca68%2FUntitled.png?table=block&id=6f13d3e2-8ad6-490c-a965-a316047a9625&cache=v2)
solve the unknown P







