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Camera Calibration Matrix Decomposition

Decompose a $3 \times 3$ upper-triangular camera intrinsic matrix $K$ into its individual parameters.

The intrinsic matrix $K$ has the form:

$K = \begin{pmatrix} f_x & s & c_x \\ 0 & f_y & c_y \\ 0 & 0 & 1 \end{pmatrix}$

where:

$f_x, f_y$ are the focal lengths (in pixels) along the x and y axes
$c_x, c_y$ is the principal point (where the optical axis meets the image plane)
$s$ is the skew coefficient (usually 0 for modern cameras)

Given such a matrix, extract and return these parameters as a dictionary with keys 'fx', 'fy', 'cx', 'cy', and 'skew'.

This decomposition is a fundamental step in camera calibration and is used extensively in 3D reconstruction, augmented reality, and visual SLAM.

Input:

K = [[800.0, 0.0, 320.0],
     [0.0, 800.0, 240.0],
     [0.0, 0.0, 1.0]]

Output:

{'fx': 800.0, 'fy': 800.0, 'cx': 320.0, 'cy': 240.0, 'skew': 0.0}

Reasoning:

The given intrinsic matrix $K$ is a $3 \times 3$ upper-triangular matrix with the form: $K = \begin{pmatrix} f_x & s & c_x \\ 0 & f_y & c_y \\ 0 & 0 & 1 \end{pmatrix}$
We directly extract the values from the input matrix $K$ : $f_x = 800.0$ , $f_y = 800.0$ , $c_x = 320.0$ , $c_y = 240.0$ , and $s = 0.0$ .
These extracted values are then used to create a dictionary with the corresponding keys: 'fx', 'fy', 'cx', 'cy', and 'skew'.
The resulting dictionary is the output, containing the individual parameters of the camera intrinsic matrix: {'fx': 800.0, 'fy': 800.0, 'cx': 320.0, 'cy': 240.0, 'skew': 0.0}.

Editor

Python 3.13.1

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Run code to see test results.