CameraParameters

class CameraParameters(*args, **kwargs)

Bases: pybind11_object

Generic class defining intrinsic camera parameters.

1. Supported camera models

Two camera models are implemented in ViSP.

1.1. Pinhole camera model

In this model [31] , a scene view is formed by projecting 3D points into the image plane using a perspective transformation.

\[\begin{split}\left[ \begin{array}{c} u \\v \\1 \end{array}\right] = \left[ \begin{array}{ccc} p_x & 0 & u_0 \\0 & p_y & v_0 \\0 & 0 & 1 \end{array}\right] \left[ \begin{array}{c} x \\y \\1 \end{array}\right] \end{split}\]

where:

  • \((X_c,Y_c,Z_c)\) are the coordinates of a 3D point in the camera frame

  • \((x,y)\) are the coordinates of the projection of the 3D point in the image plane

  • \((u,v)\) are the coordinates in pixels of the projected 3D point

  • \((u_0,v_0)\) are the coordinates of the principal point (the intersection of the optical axes with the image plane) that is usually near the image center

  • \(p_x\) (resp \(p_y\) ) is the ratio between the focal length of the lens \(f\) in meters and the size of the pixel \(l_x\) in meters: \(p_x=f/l_x\) (resp, \(l_y\) being the height of a pixel, \(p_y=f/l_y\) ).

When \(Z_c \neq 0\) , the previous equation is equivalent to the following:

\[\begin{split}\begin{array}{lcl} x &=& X_c / Z_c \\y &=& Y_c / Z_c \\u &=& u_0 + x \; p_x \\v &=& v_0 + y \; p_y \end{array} \end{split}\]

Real lenses usually have some radial distortion. So, the above model is extended as:

\[\begin{split}\begin{array}{lcl} x &=& X_c / Z_c \\y &=& Y_c / Z_c \\x^{'} &=& x (1 + k_{ud} r^2) \\y^{'} &=& y (1 + k_{ud} r^2) \\r^2 &=& x^2 + y^2 \\u &=& u_0 + x^{'} \; p_x \\v &=& v_0 + y^{'} \; p_y \end{array} \end{split}\]

where \(k_{ud}\) is the first order radial distortion. Higher order distortion coefficients are not considered in ViSP.

Now in ViSP we consider also the inverse transformation, where from pixel coordinates we want to compute their normalized coordinates in the image plane. Previous equations could be written like:

\[\begin{split}\begin{array}{lcl} x &=& (u - u_0) / p_x \\y &=& (v - v_0) / p_y \end{array} \end{split}\]

Considering radial distortion, the above model is extended as:

\[\begin{split}\begin{array}{lcl} (u-u_0)^{'} &=& (u-u_0) (1 + k_{du} r^2) \\(v-v_0)^{'} &=& (v-v_0) (1 + k_{du} r^2) \\r^2 &=& ((u-u_0)/p_x)^2 + ((v-v_0)/p_y)^2 \\x &=& (u - u_0)^{'} / p_x \\y &=& (v - v_0)^{'} / p_y \end{array} \end{split}\]

Finally, in ViSP the main intrinsic camera parameters are \((p_x, p_y)\) the ratio between the focal length and the size of a pixel, and \((u_0, v_0)\) the coordinates of the principal point in pixel. The lens distortion can also be considered by two additional parameters \((k_{ud}, k_{du})\) .

Note

The tutorial-calibration-intrinsic shows how to calibrate a camera to estimate the parameters corresponding to the model implemented in this class.

Note

Note also that tutorial-bridge-opencv gives the correspondence between ViSP and OpenCV camera modelization.

Note

The conversion from pixel coordinates \((u,v)\) in the normalized space \((x,y)\) is implemented in vpPixelMeterConversion , whereas the conversion from normalized coordinates into pixel is implemented in vpMeterPixelConversion .

From a practical point of view, two kinds of camera modelization are implemented in this class:

1.1.1. Camera parameters for a perspective projection without distortion model

In this modelization, only \(u_0,v_0,p_x,p_y\) parameters are considered.

Initialization of such a model can be done using:

  • initPersProjWithoutDistortion() that allows to set \(u_0,v_0,p_x,p_y\) parameters;

  • initFromFov() that computes the parameters from an image size and a camera field of view.

1.1.2. Camera parameters for a perspective projection with distortion model

In this modelization, all the parameters \(u_0,v_0,p_x,p_y,k_{ud},k_{du}\) are considered. Initialization of such a model can be done using:

  • initPersProjWithDistortion() that allows to set \(u_0,v_0,p_x,p_y,k_{ud},k_{du}\) parameters;

The selection of the camera model (without or with distortion) is done during vpCameraParameters initialisation.

Here an example of camera initialisation, for a model without distortion. A complete example is given in initPersProjWithoutDistortion() .

double px = 600; double py = 600; double u0 = 320; double v0 = 240;

// Create a camera parameter container
vpCameraParameters cam;
// Camera initialization with a perspective projection without distortion
// model
cam.initPersProjWithoutDistortion(px,py,u0,v0);
// It is also possible to print the current camera parameters
std::cout << cam << std::endl;

Here an example of camera initialisation, for a model with distortion. A complete example is given in initPersProjWithDistortion() .

double px = 600; double py = 600;
double u0 = 320; double v0 = 240;
double kud = -0.19; double kdu = 0.20;

// Create a camera parameter container
vpCameraParameters cam;

// Camera initialization with a perspective projection without distortion
model cam.initPersProjWithDistortion(px,py,u0,v0,kud,kdu);

The code below shows how to know the currently used projection model:

vpCameraParameters cam;
...
vpCameraParameters::vpCameraParametersProjType projModel;
projModel = cam.get_projModel(); // Get the projection model type

An XML parser for camera parameters is also provided in vpXmlParserCamera .

1.2. Kannala-Brandt camera model

This model [20] deals with fish-eye lenses designed to cover the whole hemispherical field in front of the camera and the angle of view is very large. In this case, the inherent distortion of a fish-eye lens should not be considered only as a derivation from the pinhole model.

The following projection in the general form is adapted:

\[\begin{array}{lcl} r(\theta) &=& k_1 \theta + k_2 \theta^3 + k_3 \theta^5 + k_4 \theta^7 + k_5 \theta^9 \end{array} \]

where:

  • \(\theta\) is the angle in rad between a point in the real world and the optical axis.

  • \(r\) is the distance between the image point and the principal point.

In ViSP, we only consider radially symmetric distortions (caused by fisheye lenses).

2. JSON serialization

Since ViSP 3.6.0, if ViSP is build with soft_tool_json 3rd-party we introduce JSON serialization capabilities for vpCameraParameters . The following sample code shows how to save camera parameters in a file named cam.json and reload the parameters from this JSON file.

#include <visp3/core/vpCameraParameters.h>

int main()
{
#if defined(VISP_HAVE_NLOHMANN_JSON)
  std::string filename = "cam.json";
  {
    // Save camera parameters in a JSON file
    vpCameraParameters cam(801, 802, 325, 245);
    std::ofstream file(filename);
    const nlohmann::json j = cam;
    file << j;
    file.close();
  }
  {
    // Load camera parameters from a JSON file
    std::ifstream file(filename);
    const nlohmann::json j = nlohmann::json::parse(file);
    vpCameraParameters cam;
    cam = j;
    file.close();
    std::cout << "Read camera parameters from " << filename << ":\n" << cam << std::endl;
  }
#endif
}

If you build and execute the sample code, it will produce the following output:

Read camera parameters from cam.json:
Camera parameters for perspective projection without distortion:
  px = 801   py = 802
  u0 = 325   v0 = 245

The content of the cam.json file is the following:

$ cat cam.json
{"model":"perspectiveWithoutDistortion","px":801.0,"py":802.0,"u0":325.0,"v0":245.0}

Overloaded function.

  1. __init__(self: visp._visp.core.CameraParameters) -> None

Default constructor. By default, a perspective projection without distortion model is set.

Note

See init()

  1. __init__(self: visp._visp.core.CameraParameters, c: visp._visp.core.CameraParameters) -> None

Copy constructor

  1. __init__(self: visp._visp.core.CameraParameters, px: float, py: float, u0: float, v0: float) -> None

Constructor for perspective projection without distortion model

  1. __init__(self: visp._visp.core.CameraParameters, px: float, py: float, u0: float, v0: float, kud: float, kdu: float) -> None

Constructor for perspective projection with distortion model

  1. __init__(self: visp._visp.core.CameraParameters, px: float, py: float, u0: float, v0: float, distortion_coefficients: list[float]) -> None

Constructor for projection with Kannala-Brandt distortion model

Methods

__init__

Overloaded function.

computeFov

Compute angles and normals of the FOV.

getFovNormals

Get the list of the normals corresponding to planes describing the field of view.

getHorizontalFovAngle

Get the horizontal angle in radian of the field of view.

getKannalaBrandtDistortionCoefficients

getVerticalFovAngle

Get the vertical angle in radian of the field of view.

get_K

Return the camera matrix \(K\) given by:

get_K_inverse

Return the inverted camera matrix \(K^{-1}\) given by:

get_kdu

get_kud

get_projModel

get_px

get_px_inverse

get_py

get_py_inverse

get_u0

get_v0

init

Overloaded function.

initFromCalibrationMatrix

Initialise the camera from a calibration matrix.

initFromFov

Initialize the camera model without distortion from the image dimension and the camera field of view.The following sample code shows how to use this function:

initPersProjWithDistortion

Initialization with specific parameters using perspective projection with distortion model.

initPersProjWithoutDistortion

Initialization with specific parameters using perspective projection without distortion model.

initProjWithKannalaBrandtDistortion

Initialization with specific parameters using Kannala-Brandt distortion model

isFovComputed

Specify if the fov has been computed.

printParameters

Print the camera parameters on the standard output.

Inherited Methods

Operators

__doc__

__eq__

True if the two objects are absolutely identical.

__hash__

__init__

Overloaded function.

__module__

__ne__

False if the two objects are absolutely identical.

__repr__

Attributes

ProjWithKannalaBrandtDistortion

__annotations__

__hash__

perspectiveProjWithDistortion

perspectiveProjWithoutDistortion

class CameraParametersProjType(self, value: int)

Bases: pybind11_object

Values:

  • perspectiveProjWithoutDistortion: Perspective projection without distortion model.

  • perspectiveProjWithDistortion: Perspective projection with distortion model.

  • ProjWithKannalaBrandtDistortion: Projection with Kannala-Brandt distortion model.

__and__(self, other: object) → object
__eq__(self, other: object) → bool
__ge__(self, other: object) → bool
__getstate__(self) → int
__gt__(self, other: object) → bool
__hash__(self) → int
__index__(self) → int
__init__(self, value: int)
__int__(self) → int
__invert__(self) → object
__le__(self, other: object) → bool
__lt__(self, other: object) → bool
__ne__(self, other: object) → bool
__or__(self, other: object) → object
__rand__(self, other: object) → object
__ror__(self, other: object) → object
__rxor__(self, other: object) → object
__setstate__(self, state: int) → None
__xor__(self, other: object) → object
property name : str
__eq__(self, c: visp._visp.core.CameraParameters) → bool

True if the two objects are absolutely identical.

__init__(*args, **kwargs)

Overloaded function.

  1. __init__(self: visp._visp.core.CameraParameters) -> None

Default constructor. By default, a perspective projection without distortion model is set.

Note

See init()

  1. __init__(self: visp._visp.core.CameraParameters, c: visp._visp.core.CameraParameters) -> None

Copy constructor

  1. __init__(self: visp._visp.core.CameraParameters, px: float, py: float, u0: float, v0: float) -> None

Constructor for perspective projection without distortion model

  1. __init__(self: visp._visp.core.CameraParameters, px: float, py: float, u0: float, v0: float, kud: float, kdu: float) -> None

Constructor for perspective projection with distortion model

  1. __init__(self: visp._visp.core.CameraParameters, px: float, py: float, u0: float, v0: float, distortion_coefficients: list[float]) -> None

Constructor for projection with Kannala-Brandt distortion model

__ne__(self, c: visp._visp.core.CameraParameters) → bool

False if the two objects are absolutely identical.

computeFov(self, w: int, h: int) → None

Compute angles and normals of the FOV.

Parameters:
w: int

Width of the image

h: int

Height of the image.

getFovNormals(self) → list[visp._visp.core.ColVector]

Get the list of the normals corresponding to planes describing the field of view.

  • vector[0] : Left Normal.

  • vector[1] : Right Normal.

  • vector[2] : Up Normal.

  • vector[3] : Down Normal.

Returns:

List of the normals.

getHorizontalFovAngle(self) → float

Get the horizontal angle in radian of the field of view.

Note

See computeFov() , getVerticalFovAngle()

Returns:

FOV horizontal angle computed with px and width.

getKannalaBrandtDistortionCoefficients(self) → list[float]
getVerticalFovAngle(self) → float

Get the vertical angle in radian of the field of view.

Note

See computeFov() , getHorizontalFovAngle()

Returns:

FOV vertical angle computed with py and height.

get_K(self) → visp._visp.core.Matrix

Return the camera matrix \(K\) given by:

\(K = \left[\begin{array}{ccc} p_x & 0 & u_0 \\0 & p_y & v_0 \\0 & 0 & 1 \end{array} \right]\)

Note

See get_K_inverse()

get_K_inverse(self) → visp._visp.core.Matrix

Return the inverted camera matrix \(K^{-1}\) given by:

\(K^{-1} = \left[\begin{array}{ccc} 1/p_x & 0 & -u_0/p_x \\0 & 1/p_y & -v_0/p_y \\0 & 0 & 1 \end{array} \right]\)

Note

See get_K()

get_kdu(self) → float
get_kud(self) → float
get_projModel(self) → visp._visp.core.CameraParameters.CameraParametersProjType
get_px(self) → float
get_px_inverse(self) → float
get_py(self) → float
get_py_inverse(self) → float
get_u0(self) → float
get_v0(self) → float
init(*args, **kwargs)

Overloaded function.

  1. init(self: visp._visp.core.CameraParameters) -> None

Basic initialization with the default parameters.

  1. init(self: visp._visp.core.CameraParameters, c: visp._visp.core.CameraParameters) -> None

Initialization from another vpCameraParameters object.

initFromCalibrationMatrix(self, _K: visp._visp.core.Matrix) → None

Initialise the camera from a calibration matrix. Using a calibration matrix leads to a camera without distortion.

The K matrix in parameters must be like:

\(K = \left(\begin{array}{ccc} p_x & 0 & u_0 \\0 & p_y & v_0 \\0 & 0 & 1 \end{array} \right)\)

initFromFov(self, w: int, h: int, hfov: float, vfov: float) → None

Initialize the camera model without distortion from the image dimension and the camera field of view.The following sample code shows how to use this function:

#include <visp3/core/vpCameraParameters.h>
#include <visp3/core/vpImage.h>

int main()
{
  vpImage<unsigned char> I(480, 640);
  vpCameraParameters cam;
  double hfov = vpMath::rad(56);
  double vfov = vpMath::rad(43);
  cam.initFromFov(I.getWidth(), I.getHeight(), hfov, vfov);

  std::cout << cam << std::endl;
  std::cout << "Field of view (horizontal: " << vpMath::deg(cam.getHorizontalFovAngle())
            << " and vertical: " << vpMath::deg(cam.getVerticalFovAngle()) << " degrees)" << std::endl;
}

It produces the following output:

Camera parameters for perspective projection without distortion:
  px = 601.832   py = 609.275
  u0 = 320   v0 = 240

Field of view (horizontal: 56 and vertical: 43 degrees)
Parameters:
w: int

Image width.

h: int

Image height.

hfov: float

Camera horizontal field of view angle expressed in radians.

vfov: float

Camera vertical field of view angle expressed in radians.

initPersProjWithDistortion(self, px: float, py: float, u0: float, v0: float, kud: float, kdu: float) → None

Initialization with specific parameters using perspective projection with distortion model.

The following sample code shows how to use this function:

#include <visp3/core/vpCameraParameters.h>
#include <visp3/core/vpImage.h>

int main()
{
  vpImage<unsigned char> I(480, 640);
  double u0 = I.getWidth()  / 2.;
  double v0 = I.getHeight() / 2.;
  double px = 600;
  double py = 600;
  double kud = -0.19;
  double kdu = 0.20;
  vpCameraParameters cam;
  cam.initPersProjWithDistortion(px, py, u0, v0, kud, kdu);
  cam.computeFov(I.getWidth(), I.getHeight());
  std::cout << cam << std::endl;
  std::cout << "Field of view (horizontal: " << vpMath::deg(cam.getHorizontalFovAngle())
            << " and vertical: " << vpMath::deg(cam.getVerticalFovAngle())
            << " degrees)" << std::endl;
}

It produces the following output:

Camera parameters for perspective projection with distortion:
  px = 600   py = 600
  u0 = 320   v0 = 240
  kud = -0.19
  kdu = 0.2

Field of view (horizontal: 56.14497387 and vertical: 43.60281897 degrees)
initPersProjWithoutDistortion(self, px: float, py: float, u0: float, v0: float) → None

Initialization with specific parameters using perspective projection without distortion model.

The following sample code shows how to use this function:

#include <visp3/core/vpCameraParameters.h>
#include <visp3/core/vpImage.h>

int main()
{
  vpImage<unsigned char> I(480, 640);
  double u0 = I.getWidth()  / 2.;
  double v0 = I.getHeight() / 2.;
  double px = 600;
  double py = 600;
  vpCameraParameters cam;
  cam.initPersProjWithoutDistortion(px, py, u0, v0);
  cam.computeFov(I.getWidth(), I.getHeight());
  std::cout << cam << std::endl;
  std::cout << "Field of view (horizontal: " << vpMath::deg(cam.getHorizontalFovAngle())
            << " and vertical: " << vpMath::deg(cam.getVerticalFovAngle())
            << " degrees)" << std::endl;
}

It produces the following output:

Camera parameters for perspective projection without distortion:
  px = 600   py = 600
  u0 = 320   v0 = 240

Field of view (horizontal: 56.145 and vertical: 43.6028 degrees)
initProjWithKannalaBrandtDistortion(self, px: float, py: float, u0: float, v0: float, distortion_coefficients: list[float]) → None

Initialization with specific parameters using Kannala-Brandt distortion model

isFovComputed(self) → bool

Specify if the fov has been computed.

Returns:

True if the fov has been computed, False otherwise.

printParameters(self) → None

Print the camera parameters on the standard output.

Note

See operator<<(std::ostream &, const vpCameraParameters &)

__hash__ = None