Standard Camera Calibrations

12min
The Camera calibration format is based on OpenCVs format and this paper. The different camera types supported are: PINHOLE, FISHEYE, KANNALA, PRINCIPALPOINTDIST, and FUSEDCYLINDRICAL. If your calibration model is not supported, you can also provide a Custom Camera Calibrations﻿ where you provide the implementation in the form of a WebAssembly module.
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Common
All camera calibrations have the following attributes
Key
Value
Parameters
rotation_quaternion
A RotationQuaternion object
w, x, y, z
position
A Position object
x, y, z
camera_matrix
A CameraMatrix object
fx, fy, cx, cy
image_width
Integer
NA
image_height
Integer
NA
field_of_view
Float
NA
Pinhole
The PINHOLE camera model expands the common model with:
Key
Value
Parameters
distortion_coefficients
A DistortionCoefficients object
k1, k2, p1, p2, k3
Python
from kognic.io.model.calibration.camera.common import CameraMatrix, DistortionCoefficients
from kognic.io.model.calibration.camera.pinhole_calibration import PinholeCalibration
from kognic.io.model.calibration.common import Position, RotationQuaternion


def unity_pinhole_calibration():
    camera_position = Position(x=0.0, y=0.0, z=0.0)
    camera_rotation = RotationQuaternion(w=1.0, x=0.0, y=0.0, z=0.0)
    camera_camera_matrix = CameraMatrix(fx=3450, fy=3250, cx=622, cy=400)
    camera_distortion_coefficients = DistortionCoefficients(k1=0.0, k2=0.0, p1=0.0, p2=0.0, k3=1.0)
    return PinholeCalibration(
        position=camera_position,
        rotation_quaternion=camera_rotation,
        camera_matrix=camera_camera_matrix,
        distortion_coefficients=camera_distortion_coefficients,
        image_height=1080,
        image_width=1920,
        field_of_view=190.0,
    )
from kognic.io.model.calibration.camera.common import CameraMatrix, DistortionCoefficients
from kognic.io.model.calibration.camera.pinhole_calibration import PinholeCalibration
from kognic.io.model.calibration.common import Position, RotationQuaternion


def unity_pinhole_calibration():
    camera_position = Position(x=0.0, y=0.0, z=0.0)
    camera_rotation = RotationQuaternion(w=1.0, x=0.0, y=0.0, z=0.0)
    camera_camera_matrix = CameraMatrix(fx=3450, fy=3250, cx=622, cy=400)
    camera_distortion_coefficients = DistortionCoefficients(k1=0.0, k2=0.0, p1=0.0, p2=0.0, k3=1.0)
    return PinholeCalibration(
        position=camera_position,
        rotation_quaternion=camera_rotation,
        camera_matrix=camera_camera_matrix,
        distortion_coefficients=camera_distortion_coefficients,
        image_height=1080,
        image_width=1920,
        field_of_view=190.0,
    )
﻿
Fisheye
The Fisheye camera model expands the PINHOLE model with the following
Key
Value
Parameters
xi
Float
NA
Python
from kognic.io.model.calibration.camera.common import CameraMatrix, DistortionCoefficients
from kognic.io.model.calibration.camera.fisheye_calibration import FisheyeCalibration
from kognic.io.model.calibration.common import Position, RotationQuaternion


def unity_fisheye_calibration():
    camera_position = Position(x=0.0, y=0.0, z=0.0)
    camera_rotation = RotationQuaternion(w=1.0, x=0.0, y=0.0, z=0.0)
    camera_camera_matrix = CameraMatrix(fx=3450, fy=3250, cx=622, cy=400)
    camera_distortion_coefficients = DistortionCoefficients(k1=0.0, k2=0.0, p1=0.0, p2=0.0, k3=0.1)
    return FisheyeCalibration(
        position=camera_position,
        rotation_quaternion=camera_rotation,
        camera_matrix=camera_camera_matrix,
        distortion_coefficients=camera_distortion_coefficients,
        image_height=1080,
        image_width=1920,
        xi=123.456,
        field_of_view=190.0,
    )
from kognic.io.model.calibration.camera.common import CameraMatrix, DistortionCoefficients
from kognic.io.model.calibration.camera.fisheye_calibration import FisheyeCalibration
from kognic.io.model.calibration.common import Position, RotationQuaternion


def unity_fisheye_calibration():
    camera_position = Position(x=0.0, y=0.0, z=0.0)
    camera_rotation = RotationQuaternion(w=1.0, x=0.0, y=0.0, z=0.0)
    camera_camera_matrix = CameraMatrix(fx=3450, fy=3250, cx=622, cy=400)
    camera_distortion_coefficients = DistortionCoefficients(k1=0.0, k2=0.0, p1=0.0, p2=0.0, k3=0.1)
    return FisheyeCalibration(
        position=camera_position,
        rotation_quaternion=camera_rotation,
        camera_matrix=camera_camera_matrix,
        distortion_coefficients=camera_distortion_coefficients,
        image_height=1080,
        image_width=1920,
        xi=123.456,
        field_of_view=190.0,
    )
﻿
Kannala
The KANNALA camera model changes and expands the PINHOLE with the following
Key
Value
Parameters
distortion_coefficients
A KannalaDistortionCoefficients object. The distortion parameters k3, k4, if available, can be assigned to p1 and p2 respectively. That is p1=k3 and p2=k4.
k1, k2, p1, p2
undistortion_coefficients
A UndistortionCoefficients object.
l1, l2, l3, l4
Python
from kognic.io.model.calibration.camera.common import CameraMatrix
from kognic.io.model.calibration.camera.kannala_calibration import (
    KannalaCalibration,
    KannalaDistortionCoefficients,
    UndistortionCoefficients,
)
from kognic.io.model.calibration.common import Position, RotationQuaternion


def unity_kannala_calibration():
    camera_position = Position(x=0.0, y=0.0, z=0.0)  # similar to Lidar
    camera_rotation = RotationQuaternion(w=1.0, x=0.0, y=0.0, z=0.0)  # similar to Lidar
    camera_camera_matrix = CameraMatrix(fx=3450, fy=3250, cx=622, cy=400)
    camera_distortion_coefficients = KannalaDistortionCoefficients(k1=0.0, k2=0.0, p1=0.0, p2=0.0)
    camera_undistortion_coefficients = UndistortionCoefficients(l1=0.0, l2=0.0, l3=0.0, l4=0.0)
    return KannalaCalibration(
        position=camera_position,
        rotation_quaternion=camera_rotation,
        camera_matrix=camera_camera_matrix,
        distortion_coefficients=camera_distortion_coefficients,
        undistortion_coefficients=camera_undistortion_coefficients,
        image_height=1080,
        image_width=1920,
        field_of_view=180.0,
    )
from kognic.io.model.calibration.camera.common import CameraMatrix
from kognic.io.model.calibration.camera.kannala_calibration import (
    KannalaCalibration,
    KannalaDistortionCoefficients,
    UndistortionCoefficients,
)
from kognic.io.model.calibration.common import Position, RotationQuaternion


def unity_kannala_calibration():
    camera_position = Position(x=0.0, y=0.0, z=0.0)  # similar to Lidar
    camera_rotation = RotationQuaternion(w=1.0, x=0.0, y=0.0, z=0.0)  # similar to Lidar
    camera_camera_matrix = CameraMatrix(fx=3450, fy=3250, cx=622, cy=400)
    camera_distortion_coefficients = KannalaDistortionCoefficients(k1=0.0, k2=0.0, p1=0.0, p2=0.0)
    camera_undistortion_coefficients = UndistortionCoefficients(l1=0.0, l2=0.0, l3=0.0, l4=0.0)
    return KannalaCalibration(
        position=camera_position,
        rotation_quaternion=camera_rotation,
        camera_matrix=camera_camera_matrix,
        distortion_coefficients=camera_distortion_coefficients,
        undistortion_coefficients=camera_undistortion_coefficients,
        image_height=1080,
        image_width=1920,
        field_of_view=180.0,
    )
﻿
Principal point distortion
The principal point distortion model consists of the common attributes plus
Key
Value
Parameters
principal_point_distortion_coefficients
A PrincipalPointDistortionCoefficients object
k1, k2
lens_projection_coefficients (optional. Default to values for model SF806)
A LensProjectionCoefficients object
c1, c2,c3, c4,c5, c6
distortion_center
A DistortionCenter object
x, y
principal_point
A PrincipalPoint object
x, y
Python
from kognic.io.model.calibration.camera.common import CameraMatrix
from kognic.io.model.calibration.camera.principal_point_distortion_calibration import (
    DistortionCenter,
    LensProjectionCoefficients,
    PrincipalPoint,
    PrincipalPointDistortionCalibration,
    PrincipalPointDistortionCoefficients,
)
from kognic.io.model.calibration.common import Position, RotationQuaternion


def unity_principal_point_distortion_calibration():
    camera_position = Position(x=0.0, y=0.0, z=0.0)
    camera_rotation = RotationQuaternion(w=1.0, x=0.0, y=0.0, z=0.0)
    camera_camera_matrix = CameraMatrix(fx=3450, fy=3250, cx=622, cy=400)
    camera_distortion_coefficients = PrincipalPointDistortionCoefficients(k1=0.0, k2=0.0)
    principal_point = PrincipalPoint(x=0.0, y=0.0)
    distortion_center = DistortionCenter(x=0.0, y=0.0)
    lens_projection_coefficients = LensProjectionCoefficients(c1=0.0, c2=0.0, c3=0.0, c4=0.0, c5=0.0, c6=0.0)
    return PrincipalPointDistortionCalibration(
        position=camera_position,
        rotation_quaternion=camera_rotation,
        camera_matrix=camera_camera_matrix,
        principal_point_distortion_coefficients=camera_distortion_coefficients,
        lens_projection_coefficients=lens_projection_coefficients,
        principal_point=principal_point,
        distortion_center=distortion_center,
        image_height=1080,
        image_width=1920,
        field_of_view=180.0,
    )
from kognic.io.model.calibration.camera.common import CameraMatrix
from kognic.io.model.calibration.camera.principal_point_distortion_calibration import (
    DistortionCenter,
    LensProjectionCoefficients,
    PrincipalPoint,
    PrincipalPointDistortionCalibration,
    PrincipalPointDistortionCoefficients,
)
from kognic.io.model.calibration.common import Position, RotationQuaternion


def unity_principal_point_distortion_calibration():
    camera_position = Position(x=0.0, y=0.0, z=0.0)
    camera_rotation = RotationQuaternion(w=1.0, x=0.0, y=0.0, z=0.0)
    camera_camera_matrix = CameraMatrix(fx=3450, fy=3250, cx=622, cy=400)
    camera_distortion_coefficients = PrincipalPointDistortionCoefficients(k1=0.0, k2=0.0)
    principal_point = PrincipalPoint(x=0.0, y=0.0)
    distortion_center = DistortionCenter(x=0.0, y=0.0)
    lens_projection_coefficients = LensProjectionCoefficients(c1=0.0, c2=0.0, c3=0.0, c4=0.0, c5=0.0, c6=0.0)
    return PrincipalPointDistortionCalibration(
        position=camera_position,
        rotation_quaternion=camera_rotation,
        camera_matrix=camera_camera_matrix,
        principal_point_distortion_coefficients=camera_distortion_coefficients,
        lens_projection_coefficients=lens_projection_coefficients,
        principal_point=principal_point,
        distortion_center=distortion_center,
        image_height=1080,
        image_width=1920,
        field_of_view=180.0,
    )
﻿
Fused cylindrical
The fused cylindrical model consists of the common attributes plus
Key
Value
Parameters
cut_angles_degree
A CutAngles object. Note these angles should be expressed in degrees.
upper, lower
vertical_fov_degree  (optional. Default 72.5 degrees)
Float. Note this angle should be expressed in degrees.
NA
horizontal_fov_degree (optional. Default 93 degrees)
Float. Note this angle should be expressed in degrees.
NA
max_altitude_angle_degree (optional. Default 90 degrees)
Float. Note this angle should be expressed in degrees.
NA
Python
from kognic.io.model.calibration.camera.common import CameraMatrix
from kognic.io.model.calibration.camera.fused_cylindrical_calibration import CutAngles, FusedCylindricalCalibration
from kognic.io.model.calibration.common import Position, RotationQuaternion


def example_fused_cylindrical_calibration():
    camera_position = Position(x=0.0, y=0.0, z=0.0)
    camera_rotation = RotationQuaternion(w=1.0, x=0.0, y=0.0, z=0.0)
    camera_camera_matrix = CameraMatrix(fx=400, fy=400, cx=600, cy=450)
    cut_angles_degree = CutAngles(upper=-40.0, lower=30.0)
    return FusedCylindricalCalibration(
        position=camera_position,
        rotation_quaternion=camera_rotation,
        camera_matrix=camera_camera_matrix,
        image_height=1080,
        image_width=1920,
        cut_angles_degree=cut_angles_degree,
        vertical_fov_degree=70,
        horizontal_fov_degree=90.0,
        max_altitude_angle_degree=90.0,
    )
from kognic.io.model.calibration.camera.common import CameraMatrix
from kognic.io.model.calibration.camera.fused_cylindrical_calibration import CutAngles, FusedCylindricalCalibration
from kognic.io.model.calibration.common import Position, RotationQuaternion


def example_fused_cylindrical_calibration():
    camera_position = Position(x=0.0, y=0.0, z=0.0)
    camera_rotation = RotationQuaternion(w=1.0, x=0.0, y=0.0, z=0.0)
    camera_camera_matrix = CameraMatrix(fx=400, fy=400, cx=600, cy=450)
    cut_angles_degree = CutAngles(upper=-40.0, lower=30.0)
    return FusedCylindricalCalibration(
        position=camera_position,
        rotation_quaternion=camera_rotation,
        camera_matrix=camera_camera_matrix,
        image_height=1080,
        image_width=1920,
        cut_angles_degree=cut_angles_degree,
        vertical_fov_degree=70,
        horizontal_fov_degree=90.0,
        max_altitude_angle_degree=90.0,
    )
﻿
Cylindrical
The cylindrical model consists only of the common attributes. There are no extra attributes to set for this model.
Python
from kognic.io.model.calibration.camera.common import CameraMatrix
from kognic.io.model.calibration.camera.cylindrical_calibration import CylindricalCalibration
from kognic.io.model.calibration.common import Position, RotationQuaternion


def example_cylindrical_calibration():
    camera_position = Position(x=0.0, y=0.0, z=0.0)
    camera_rotation = RotationQuaternion(w=1.0, x=0.0, y=0.0, z=0.0)
    camera_camera_matrix = CameraMatrix(fx=400, fy=400, cx=600, cy=450)
    return CylindricalCalibration(
        position=camera_position,
        rotation_quaternion=camera_rotation,
        camera_matrix=camera_camera_matrix,
        image_height=1080,
        image_width=1920,
    )
from kognic.io.model.calibration.camera.common import CameraMatrix
from kognic.io.model.calibration.camera.cylindrical_calibration import CylindricalCalibration
from kognic.io.model.calibration.common import Position, RotationQuaternion


def example_cylindrical_calibration():
    camera_position = Position(x=0.0, y=0.0, z=0.0)
    camera_rotation = RotationQuaternion(w=1.0, x=0.0, y=0.0, z=0.0)
    camera_camera_matrix = CameraMatrix(fx=400, fy=400, cx=600, cy=450)
    return CylindricalCalibration(
        position=camera_position,
        rotation_quaternion=camera_rotation,
        camera_matrix=camera_camera_matrix,
        image_height=1080,
        image_width=1920,
    )
﻿
Principal point fisheye
The principal point fisheye model consists of the common attributes plus
Key
Value
Parameters
principal_point_fisheye_coefficients
A PrincipalPointFisheyeCoefficients object
alpha_l, alpha_r, beta_u, beta_l
Python
from kognic.io.model.calibration.camera.common import CameraMatrix
from kognic.io.model.calibration.camera.principal_point_fisheye_calibration import (
    PrincipalPointFisheyeCalibration,
    PrincipalPointFisheyeCoefficients,
)
from kognic.io.model.calibration.common import Position, RotationQuaternion


def unity_principal_point_fisheye_calibration():
    camera_position = Position(x=0.0, y=0.0, z=0.0)
    camera_rotation = RotationQuaternion(w=1.0, x=0.0, y=0.0, z=0.0)
    camera_camera_matrix = CameraMatrix(fx=3450, fy=3250, cx=622, cy=400)
    principal_point_fisheye_coefficients = PrincipalPointFisheyeCoefficients(alpha_l=0.0, alpha_r=0.0, beta_u=0.0, beta_l=0.0)
    return PrincipalPointFisheyeCalibration(
        position=camera_position,
        rotation_quaternion=camera_rotation,
        camera_matrix=camera_camera_matrix,
        principal_point_fisheye_coefficients=principal_point_fisheye_coefficients,
        image_height=1080,
        image_width=1920,
        field_of_view=180.0,
    )
from kognic.io.model.calibration.camera.common import CameraMatrix
from kognic.io.model.calibration.camera.principal_point_fisheye_calibration import (
    PrincipalPointFisheyeCalibration,
    PrincipalPointFisheyeCoefficients,
)
from kognic.io.model.calibration.common import Position, RotationQuaternion


def unity_principal_point_fisheye_calibration():
    camera_position = Position(x=0.0, y=0.0, z=0.0)
    camera_rotation = RotationQuaternion(w=1.0, x=0.0, y=0.0, z=0.0)
    camera_camera_matrix = CameraMatrix(fx=3450, fy=3250, cx=622, cy=400)
    principal_point_fisheye_coefficients = PrincipalPointFisheyeCoefficients(alpha_l=0.0, alpha_r=0.0, beta_u=0.0, beta_l=0.0)
    return PrincipalPointFisheyeCalibration(
        position=camera_position,
        rotation_quaternion=camera_rotation,
        camera_matrix=camera_camera_matrix,
        principal_point_fisheye_coefficients=principal_point_fisheye_coefficients,
        image_height=1080,
        image_width=1920,
        field_of_view=180.0,
    )
﻿
﻿
Key	Value	Parameters
rotation_quaternion	A RotationQuaternion object	w, x, y, z
position	A Position object	x, y, z
camera_matrix	A CameraMatrix object	fx, fy, cx, cy
image_width	Integer	NA
image_height	Integer	NA
field_of_view	Float	NA
Key	Value	Parameters
distortion_coefficients	A DistortionCoefficients object	k1, k2, p1, p2, k3
Key	Value	Parameters
xi	Float	NA
Key	Value	Parameters
distortion_coefficients	A KannalaDistortionCoefficients object. The distortion parameters k3, k4, if available, can be assigned to p1 and p2 respectively. That is p1=k3 and p2=k4.	k1, k2, p1, p2
undistortion_coefficients	A UndistortionCoefficients object.	l1, l2, l3, l4
Key	Value	Parameters
principal_point_distortion_coefficients	A PrincipalPointDistortionCoefficients object	k1, k2
lens_projection_coefficients (optional. Default to values for model SF806)	A LensProjectionCoefficients object	c1, c2,c3, c4,c5, c6
distortion_center	A DistortionCenter object	x, y
principal_point	A PrincipalPoint object	x, y
Key	Value	Parameters
cut_angles_degree	A CutAngles object. Note these angles should be expressed in degrees.	upper, lower
vertical_fov_degree (optional. Default 72.5 degrees)	Float. Note this angle should be expressed in degrees.	NA
horizontal_fov_degree (optional. Default 93 degrees)	Float. Note this angle should be expressed in degrees.	NA
max_altitude_angle_degree (optional. Default 90 degrees)	Float. Note this angle should be expressed in degrees.	NA
Key	Value	Parameters
principal_point_fisheye_coefficients	A PrincipalPointFisheyeCoefficients object	alpha_l, alpha_r, beta_u, beta_l
Updated 17 Dec 2024
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Custom Camera Calibrations