Intrinsic Parameters

Definition

The intrinsic parameters describe the transformation from film coordinates (the projected image, metric) to pixel coordinates. They depend only on the camera hardware, not on where the camera is.

Intrinsic matrix

$$M_{int}=\left[\begin{array}{cccc}f/s_x& 0& o_x& 0\\ 0& f/s_y& o_y& 0\\ 0& 0& 1& 0\end{array}\right]u=\frac{1}{s_x}f\frac{X}{Z}+o_x,v=\frac{1}{s_y}f\frac{Y}{Z}+o_y$$

Parameter	Meaning
$f$	focal length
$s_x,s_y$	pixel sizes. They can differ, so pixels are not necessarily square. Aspect ratio $s_y/s_x$
$o_x,o_y$	principal point (image center). Moves the origin from the center of the film plane to the corner of the pixel array

Tip

Some conventions flip the axes, which puts a minus sign on $f/s_x$ and $f/s_y$. A flipped or cropped image in your own renderer usually comes from this.

Appears in

• Lecture 2.1, Film to pixel: offsets, flipped axes, scales, intrinsic matrix
• Lecture 2.1, Worked Examples: pixel coordinates and back

Related concepts

• Extrinsic Parameters
• Projection Matrix
• Focal Length