Camera Parameters

Overview

The GoPro camera used in the UXO Dataset 2024 was calibrated for four different field of view (FOV) modes. Each mode has distinct intrinsic parameters including the camera matrix and distortion coefficients. All calibration files are stored in /calibration/camera_parameters/ and follow OpenCV’s camera calibration model.

GoPro Field of View Modes

The GoPro supports multiple FOV modes that affect the lens distortion and field of view:

Linear

Digitally corrected mode with minimal distortion. Best for photogrammetry and measurement applications.

Narrow

Telephoto mode with reduced field of view and less distortion than wide modes.

Wide

Standard wide-angle mode with moderate barrel distortion. Balances FOV and distortion.

SuperView

Maximum field of view with dynamic stretching. Highest distortion levels.

Camera Calibration Parameters

Each FOV mode has calibrated intrinsic parameters stored as NumPy arrays in text format.

Camera Matrix

The camera matrix (K) contains the focal lengths and principal point:

[[fx,  0, cx],
 [ 0, fy, cy],
 [ 0,  0,  1]]

Where:

fx, fy: Focal lengths in pixels (x and y directions)
cx, cy: Principal point coordinates (optical center)

Distortion Coefficients

The distortion vector contains four coefficients for the fisheye distortion model:

[k1, k2, k3, k4]

These coefficients model radial distortion characteristic of wide-angle lenses.

Linear Mode

camera_parameter_linear.txt

calibration

Digitally corrected linear mode with minimal distortion.

camera_parameter_linear.txt

camera_matrix =  [[1.47304513e+03 0.00000000e+00 9.69389055e+02]
 [0.00000000e+00 1.47833421e+03 5.40775107e+02]
 [0.00000000e+00 0.00000000e+00 1.00000000e+00]]
distortion =  [[ 0.90938145]
 [ 0.09319444]
 [ 7.88195247]
 [-3.68132837]]

Parameter Breakdown

fx: 1473.0 pixels
fy: 1478.3 pixels
cx: 969.4 pixels
cy: 540.8 pixels
k1: 0.909 (positive radial distortion)
k2: 0.093
k3: 7.882
k4: -3.681 (negative correction)

Narrow Mode

camera_parameter_narrow.txt

calibration

Telephoto mode with reduced field of view.

camera_parameter_narrow.txt

camera_matrix =  [[1.96032520e+03 0.00000000e+00 9.61545001e+02]
 [0.00000000e+00 1.96508356e+03 5.44228971e+02]
 [0.00000000e+00 0.00000000e+00 1.00000000e+00]]
distortion =  [[  0.86674484]
 [ -0.03704667]
 [  8.587814  ]
 [-18.75784521]]

Parameter Breakdown

fx: 1960.3 pixels (higher focal length = narrower FOV)
fy: 1965.1 pixels
cx: 961.5 pixels
cy: 544.2 pixels
k1: 0.867
k2: -0.037 (slight negative distortion)
k3: 8.588
k4: -18.758 (strong negative correction)

Wide Mode

camera_parameter_wide.txt

calibration

Standard wide-angle mode with moderate distortion.

camera_parameter_wide.txt

camera_matrix =  [[1.31243683e+03 0.00000000e+00 9.80421992e+02]
 [0.00000000e+00 1.31261251e+03 5.31336901e+02]
 [0.00000000e+00 0.00000000e+00 1.00000000e+00]]
distortion =  [[ 0.14790296]
 [ 1.18643565]
 [-3.77146525]
 [ 5.44358806]]

Parameter Breakdown

fx: 1312.4 pixels (lower focal length = wider FOV)
fy: 1312.6 pixels
cx: 980.4 pixels
cy: 531.3 pixels
k1: 0.148
k2: 1.186
k3: -3.771 (negative distortion)
k4: 5.444

SuperView Mode

camera_parameter_superview.txt

calibration

Maximum field of view with dynamic stretching and highest distortion.

camera_parameter_superview.txt

camera_matrix =  [[1.37477315e+03 0.00000000e+00 9.65037288e+02]
 [0.00000000e+00 1.25389393e+03 3.46383440e+02]
 [0.00000000e+00 0.00000000e+00 1.00000000e+00]]
distortion =  [[  0.43139299]
 [  1.46997173]
 [-22.94272641]
 [ 62.08773762]]

Parameter Breakdown

fx: 1374.8 pixels
fy: 1253.9 pixels (asymmetric due to dynamic stretching)
cx: 965.0 pixels
cy: 346.4 pixels (shifted principal point)
k1: 0.431
k2: 1.470
k3: -22.943 (very strong negative distortion)
k4: 62.088 (very strong positive correction)

SuperView mode has significant distortion (k3 = -22.94, k4 = 62.09) and asymmetric focal lengths. Use with caution for measurement applications.

Using Camera Parameters

Loading Parameters in Python

import numpy as np
import re

def load_camera_params(filename):
    """Load camera matrix and distortion from calibration file."""
    with open(filename, 'r') as f:
        content = f.read()
    
    # Extract camera matrix
    camera_match = re.search(r'camera_matrix = \s*\[(.*?)\]', content, re.DOTALL)
    camera_str = camera_match.group(1).replace('[', '').replace(']', '')
    camera_matrix = np.fromstring(camera_str, sep=' ').reshape(3, 3)
    
    # Extract distortion
    dist_match = re.search(r'distortion = \s*\[(.*?)\]', content, re.DOTALL)
    dist_str = dist_match.group(1).replace('[', '').replace(']', '')
    distortion = np.fromstring(dist_str, sep=' ')
    
    return camera_matrix, distortion

# Load calibration for wide mode
K, D = load_camera_params('calibration/camera_parameters/camera_parameter_wide.txt')

Undistorting Images with OpenCV

import cv2
import numpy as np

# Load calibration
K, D = load_camera_params('calibration/camera_parameters/camera_parameter_wide.txt')

# Load image
img = cv2.imread('gopro_image.jpg')
h, w = img.shape[:2]

# Compute optimal camera matrix
balance = 0.0  # 0.0 = all pixels valid, 1.0 = all source pixels visible
new_K = cv2.fisheye.estimateNewCameraMatrixForUndistortRectify(
    K, D, (w, h), np.eye(3), balance=balance)

# Undistort image
map1, map2 = cv2.fisheye.initUndistortRectifyMap(
    K, D, np.eye(3), new_K, (w, h), cv2.CV_16SC2)
undistorted = cv2.remap(img, map1, map2, cv2.INTER_LINEAR)

Projecting 3D Points to Image

import cv2
import numpy as np

# 3D point in camera frame (meters)
point_3d = np.array([[0.5, 0.3, 2.0]])  # X, Y, Z

# Load calibration
K, D = load_camera_params('calibration/camera_parameters/camera_parameter_wide.txt')

# Project to image using fisheye model
rvec = np.zeros(3)  # No rotation (already in camera frame)
tvec = np.zeros(3)  # No translation

image_points, _ = cv2.fisheye.projectPoints(
    point_3d.reshape(-1, 1, 3), rvec, tvec, K, D)

print(f"Image coordinates: {image_points[0][0]}")

FOV Mode Comparison

Focal Length
Distortion
Principal Point

Mode	fx (pixels)	fy (pixels)	FOV
Narrow	1960.3	1965.1	Narrowest
Linear	1473.0	1478.3	Medium-narrow
SuperView	1374.8	1253.9	Medium-wide
Wide	1312.4	1312.6	Widest

Lower focal length = wider field of view.

Mode	k1	k2	k3	k4	Severity
Wide	0.15	1.19	-3.77	5.44	Low
Linear	0.91	0.09	7.88	-3.68	Low
Narrow	0.87	-0.04	8.59	-18.76	Medium
SuperView	0.43	1.47	-22.94	62.09	High

SuperView has extreme distortion coefficients requiring careful correction.

Mode	cx (pixels)	cy (pixels)	Offset
Linear	969.4	540.8	Centered
Narrow	961.5	544.2	Centered
Wide	980.4	531.3	Centered
SuperView	965.0	346.4	Shifted up

SuperView has a significantly shifted principal point (cy = 346 vs ~540 for others).

Calibration Model

The parameters use OpenCV’s fisheye camera model, which is specifically designed for wide-angle and fisheye lenses:

# Fisheye distortion formula
r = sqrt(x² + y²)
θ = atan(r)
θ_d = θ(1 + k1*θ² + k2*θ⁴ + k3*θ⁶ + k4*θ⁸)
x' = (θ_d / r) * x
y' = (θ_d / r) * y

This is different from the standard pinhole distortion model. Use cv2.fisheye.* functions in OpenCV, not the regular cv2.undistort().

File Locations

All camera parameter files are located in:

/calibration/camera_parameters/
├── camera_parameter_linear.txt
├── camera_parameter_narrow.txt
├── camera_parameter_wide.txt
└── camera_parameter_superview.txt

Recommendations

For Computer Vision Tasks

Use Linear or Wide mode:

Linear: Best for undistorted viewing and measurement
Wide: Good balance of FOV and manageable distortion

For Maximum Coverage

Use Wide mode rather than SuperView:

SuperView’s extreme distortion can cause artifacts
Wide mode provides excellent coverage with moderate distortion

For Long-Range Imaging

Use Narrow mode:

Higher focal length provides better resolution at distance
Lower distortion than wide modes

Overview

Getting Started

Dataset Structure

Processing Pipeline

Calibration

Overview

GoPro Field of View Modes

Linear

Narrow

Wide

SuperView

Camera Calibration Parameters

Camera Matrix

Distortion Coefficients

Linear Mode

Narrow Mode

Wide Mode

SuperView Mode

Using Camera Parameters

Loading Parameters in Python

Undistorting Images with OpenCV

Projecting 3D Points to Image

FOV Mode Comparison

Calibration Model

File Locations

Recommendations

Build docs developers (and LLMs) love

Overview

Getting Started

Dataset Structure

Processing Pipeline

Calibration

Documentation Index

​Overview

​GoPro Field of View Modes

Linear

Narrow

Wide

SuperView

​Camera Calibration Parameters

​Camera Matrix

​Distortion Coefficients

​Linear Mode

​Narrow Mode

​Wide Mode

​SuperView Mode

​Using Camera Parameters

​Loading Parameters in Python

​Undistorting Images with OpenCV

​Projecting 3D Points to Image

​FOV Mode Comparison

​Calibration Model

​File Locations

​Recommendations

Build docs developers (and LLMs) love

Overview

GoPro Field of View Modes

Camera Calibration Parameters

Camera Matrix

Distortion Coefficients

Linear Mode

Narrow Mode

Wide Mode

SuperView Mode

Using Camera Parameters

Loading Parameters in Python

Undistorting Images with OpenCV

Projecting 3D Points to Image

FOV Mode Comparison

Calibration Model

File Locations

Recommendations