Intrinsics Math

Intrinsics recover the camera matrix $K$ and distortion coefficients so raw frames can be undistorted before classification (and before extrinsic solve, which assumes already-rectified images).

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

Each calibration image contributes:

• Object points: known 3D checkerboard corners in the board frame ($z=0$), spaced by square_m on a (9,6) internal-corner grid.
• Image points: the same corners detected in the photo (findChessboardCorners + cornerSubPix).

OpenCV’s calibrateCamera / calibrateCameraRO estimates $K$, distortion, and a per-image board pose by minimizing reprojection error: after projecting object points with the estimated pose and camera model, how far (in pixels) the predicted corners sit from the detections.

Our scripts seed $K$ from the lens datasheet (focal length and sensor size at 1920×1200) with CALIB_USE_INTRINSIC_GUESS, and typically fix $k_3$ (CALIB_FIX_K3) so the radial model stays $k_1,k_2$ plus tangential terms unless otherwise configured.

Output

seecam_calibration_{l|r}.yaml stores roughly:

• camera_matrix: $K$
• dist_coeffs: distortion vector
• reprojection_error: scalar summary from the solve

At runtime, SeeCamManager loads that YAML, builds undistort maps from getOptimalNewCameraMatrix, and (for the right camera) rotates each frame 180°. Extrinsics must use the same runtime pixel space; see projection math.

Validation

validate_rect_calibration.py re-detects boards on a held-out split, runs solvePnP with the saved $K$/distortion, projects corners, and reports mean / max pixel error. Script target: mean ≤ 1.0 px.

Board poses should span the field of view. Center-only captures leave distortion and principal-point terms weakly constrained even when mean training error is low.

Procedure steps: calibration procedure.