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compare_fisheye_models

compare_fisheye_models

Compare fisheye projection models

Runs calibration with each supported projection model on the same checkerboard frames and reports RMS reprojection error for each.

Models tested

equidistant r = f * theta equisolid r = 2f * sin(theta/2) stereographic r = 2f * tan(theta/2) orthographic r = f * sin(theta)

Usage

python compare_fisheye_models.py --images calibration_frames/frame_.png python compare_fisheye_models.py --images calibration_frames/frame_.png --board-width 7 --board-height 5

project_model 

project_model(pts_3d, rvec, tvec, cx, cy, f, model)

Project 3D points through a named fisheye model.

Source code in calibration\compare_fisheye_models.py 
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def project_model(pts_3d, rvec, tvec, cx, cy, f, model):
    """Project 3D points through a named fisheye model."""
    R = Rotation.from_rotvec(rvec).as_matrix()
    p_cam = (R @ pts_3d.T).T + tvec
    x, y, z = p_cam[:, 0], p_cam[:, 1], p_cam[:, 2]
    norm = np.maximum(np.sqrt(x ** 2 + y ** 2 + z ** 2), 1e-12)
    theta = np.arccos(np.clip(z / norm, -1.0, 1.0))
    phi = np.arctan2(y, x)

    if model == 'equidistant':
        r = f * theta
    elif model == 'equisolid':
        r = 2.0 * f * np.sin(theta / 2.0)
    elif model == 'stereographic':
        r = 2.0 * f * np.tan(theta / 2.0)
    elif model == 'orthographic':
        r = f * np.sin(theta)
    else:
        raise ValueError(f"Unknown model: {model}")

    u = cx + r * np.cos(phi)
    v = cy + r * np.sin(phi)
    return np.column_stack([u, v])

calibrate_model 

calibrate_model(obj_pts_list, img_pts_list, model, initial_cx, initial_cy, initial_f)

Run LM bundle adjustment for a single projection model.

Source code in calibration\compare_fisheye_models.py 
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def calibrate_model(obj_pts_list, img_pts_list, model, initial_cx, initial_cy,
                    initial_f):
    """Run LM bundle adjustment for a single projection model."""
    n = len(obj_pts_list)

    # Initialize extrinsics using equidistant model (good enough for all)
    rvecs, tvecs = [], []
    for obj, img in zip(obj_pts_list, img_pts_list):
        rv, tv = _init_extrinsics_pnp(obj, img, initial_cx, initial_cy,
                                       initial_f)
        rv, tv = _refine_single_frame(obj, img, rv, tv, initial_cx,
                                       initial_cy, initial_f)
        rvecs.append(rv)
        tvecs.append(tv)

    # Pack: [cx, cy, f, rv0, tv0, rv1, tv1, ...]
    p0 = np.zeros(3 + n * 6)
    p0[0], p0[1], p0[2] = initial_cx, initial_cy, initial_f
    for i in range(n):
        p0[3 + i * 6:3 + i * 6 + 3] = rvecs[i]
        p0[3 + i * 6 + 3:3 + i * 6 + 6] = tvecs[i]

    def residuals(params):
        cx, cy, f = params[0], params[1], params[2]
        res = []
        for i in range(n):
            rv = params[3 + i * 6:3 + i * 6 + 3]
            tv = params[3 + i * 6 + 3:3 + i * 6 + 6]
            proj = project_model(obj_pts_list[i], rv, tv, cx, cy, f, model)
            res.append((proj - img_pts_list[i]).ravel())
        return np.concatenate(res)

    result = least_squares(residuals, p0, method='lm',
                           ftol=1e-12, xtol=1e-12, gtol=1e-12,
                           max_nfev=10000, verbose=0)

    cx, cy, f = result.x[0], result.x[1], result.x[2]
    rms = np.sqrt(np.mean(result.fun ** 2))

    # Per-frame RMS
    per_frame = []
    for i in range(n):
        rv = result.x[3 + i * 6:3 + i * 6 + 3]
        tv = result.x[3 + i * 6 + 3:3 + i * 6 + 6]
        proj = project_model(obj_pts_list[i], rv, tv, cx, cy, f, model)
        err = np.sqrt(np.mean((proj - img_pts_list[i]) ** 2))
        per_frame.append(err)

    # Derive FOV
    radius_px = 1750.0
    if model == 'equidistant':
        fov = (2 * radius_px) * 180.0 / (f * np.pi)
    elif model == 'equisolid':
        fov = 4.0 * np.rad2deg(np.arcsin(radius_px / (2.0 * f)))
    elif model == 'stereographic':
        fov = 4.0 * np.rad2deg(np.arctan(radius_px / (2.0 * f)))
    elif model == 'orthographic':
        fov = 2.0 * np.rad2deg(np.arcsin(min(radius_px / f, 1.0)))

    return {
        'model': model,
        'cx': round(float(cx), 4),
        'cy': round(float(cy), 4),
        'focal_length': round(float(f), 4),
        'fov_deg': round(float(fov), 4),
        'rms_error_px': round(float(rms), 6),
        'per_frame_rms': [round(float(e), 4) for e in per_frame],
        'num_frames': n,
        'num_points': sum(len(p) for p in img_pts_list),
    }