Calibration (intrinsic) parameters of a virtual camera with some known information

I need the calibration matrix of my simulated camera, I am trying to fully comprehend and follow the steps from Step by Step Camera Pose Estimation for Visual Tracking and Planar Markers as well as Estimating Plane Pose Without Knowledge of Intrinsic Camera Parameters, but I still don't "get it". Ultimately, I want to use K to find the essential matrix and compute the transformation between two images.

The information available to me are:

• The images.
• Images are planar scenes, camera is perpendicular to the ground. Transformation between them includes rotation (around ground-perpendicular axes), scaling and translation.
• Known distance from image (altitude), FOV, pixel width.

Assuming square pixels and no skew, this is what I am after:

$$K = \left[\begin{matrix} \alpha_u&0&u_0\\0&\alpha_v&v_0\\0&0&1 \end{matrix}\right]$$

• $\alpha_u$ and $\alpha_v$ are the scale factor in the $u$ and $v$ coordinate directions, and are proportional to the focal length $f$ of the camera: $\alpha_u = k_u f$ and $\alpha_v = k_v f$. $k_u$ and $k_v$ are the number of pixels per unit distance in $u$ and $v$ directions.
• $c=[u_0,v_0]^T$ is called the principal point, usually the coordinates of the image center.

Is there an "easy" approach to computing these variables, given the assumptions and the available info about the images?

Going through dsp, I am overwhelmed by the amount of links and information on the matter, usually very technical papers that are hard to follow for beginners in the field, and I am unable to understand what corresponds to my case.

• Do you have any prior information about the visual structure in the image? – Tolga Birdal Sep 21 '15 at 7:13
• I am not sure I follow. I do know and have the (type of) images that completely resemble those that the algorithm will deal with. – user17348 Sep 21 '15 at 7:22
• Is your camera synthetic or real? (Are you simulating or not?) – Tolga Birdal Sep 21 '15 at 7:28
• Synthetic. The camera is simulated. – user17348 Sep 21 '15 at 7:30

alpha_u : image_width = focal_length : sensor_width.