IR Camera Calibration

The goal of calibration is to estimate the intrinsic and distortion parameters of the IR camera so that each pixel can be mapped to a metric position on the measured surface.

Camera model

A 3D world point \(X_w\) projects to image pixel \((u, v)\) via:

\[ \begin{bmatrix} u \\ v \\ 1 \end{bmatrix} = K \, [R \mid t] \, X_w \]

Intrinsic matrix K

\[ K = \begin{bmatrix} f_x & 0 & c_x \\ 0 & f_y & c_y \\ 0 & 0 & 1 \end{bmatrix} \]

Symbol	Meaning
\(f_x\), \(f_y\)	Focal lengths in pixels
\(c_x\), \(c_y\)	Principal point (optical axis in image coordinates)

Non-square pixels

IR sensors commonly have \(f_x \neq f_y\) because the pixel pitch differs between axes.

Distortion coefficients

\[\mathbf{d} = (k_1,\, k_2,\, p_1,\, p_2,\, k_3)\]

Symbol	Type	Effect
\(k_1\), \(k_2\), \(k_3\)	Radial	Barrel / pincushion distortion
\(p_1\), \(p_2\)	Tangential	Lens tilt / decentering

Spatial resolution

Once K is known, the physical size of one pixel at working distance \(Z\) is:

\[\Delta x = \frac{Z}{f_x}, \qquad \Delta y = \frac{Z}{f_y}\]

This is used to convert the undistorted image from pixels to millimetres before exporting to VTU.

Running calibration

python scripts/calibrate.py path/to/calibration.h5 --output data/ir_calib.npz

The script expects an HDF5 file with a thermogram dataset of shape (N, H, W) — \(N\) frames of a thermal checkerboard target.

Checkerboard parameters (edit in scripts/calibrate.py):

Parameter	Default	Meaning
`pattern_size`	`(7, 4)`	Inner corners (cols × rows)
`square_size`	`5.0` mm	Physical side length of one square

Output `.npz` fields

Key	Shape	Description
`K`	`(3, 3)`	Camera matrix
`dist`	`(5, 1)`	Distortion coefficients
`img_size`	`(2,)`	Image size `[W, H]`
`rms`	scalar	RMS reprojection error (px)

Undistortion

import cv2, numpy as np

calib = np.load("data/ir_calib.npz")
K     = calib["K"]
dist  = calib["dist"].flatten()

h, w  = img.shape
newK, roi = cv2.getOptimalNewCameraMatrix(K, dist, (w, h), alpha=0.0)
undistorted = cv2.undistort(img, K, dist, None, newK)

alpha=0.0 crops to only valid pixels (no black border).
alpha=1.0 keeps all pixels (black border where no source data exists).