Camera Calibration#

Topics#

Fisheye camera model

Detailed Description#

The functions in this section use a so-called pinhole camera model. The view of a scene is obtained by projecting a scene’s 3D point \(P_w\) into the image plane using a perspective transformation which forms the corresponding pixel \(p\). Both \(P_w\) and \(p\) are represented in homogeneous coordinates, i.e. as 3D and 2D homogeneous vector respectively. You will find a brief introduction to projective geometry, homogeneous vectors and homogeneous transformations at the end of this section’s introduction. For more succinct notation, we often drop the ‘homogeneous’ and say vector instead of homogeneous vector.

The distortion-free projective transformation given by a pinhole camera model is shown below.

\[ s \; p = A \begin{bmatrix} R|t \end{bmatrix} P_w, \]

where \(P_w\) is a 3D point expressed with respect to the world coordinate system, \(p\) is a 2D pixel in the image plane, \(A\) is the camera intrinsic matrix, \(R\) and \(t\) are the rotation and translation that describe the change of coordinates from world to camera coordinate systems (or camera frame) and \(s\) is the projective transformation’s arbitrary scaling and not part of the camera model.

The camera intrinsic matrix \(A\) (notation used as in [353] and also generally notated as \(K\)) projects 3D points given in the camera coordinate system to 2D pixel coordinates, i.e.

\[ p = A P_c. \]

The camera intrinsic matrix \(A\) is composed of the focal lengths \(f_x\) and \(f_y\), which are expressed in pixel units, and the principal point \((c_x, c_y)\), that is usually close to the image center:

\[ A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}, \]

and thus

\[ s \vecthree{u}{v}{1} = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1} \vecthree{X_c}{Y_c}{Z_c}. \]

The matrix of intrinsic parameters does not depend on the scene viewed. So, once estimated, it can be re-used as long as the focal length is fixed (in case of a zoom lens). Thus, if an image from the camera is scaled by a factor, all of these parameters need to be scaled (multiplied/divided, respectively) by the same factor.

The joint rotation-translation matrix \([R|t]\) is the matrix product of a projective transformation and a homogeneous transformation. The 3-by-4 projective transformation maps 3D points represented in camera coordinates to 2D points in the image plane and represented in normalized camera coordinates \(x' = X_c / Z_c\) and \(y' = Y_c / Z_c\):

\[\begin{split} Z_c \begin{bmatrix} x' \\ y' \\ 1 \end{bmatrix} = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix} \begin{bmatrix} X_c \\ Y_c \\ Z_c \\ 1 \end{bmatrix}. \end{split}\]

The homogeneous transformation is encoded by the extrinsic parameters \(R\) and \(t\) and represents the change of basis from world coordinate system \(w\) to the camera coordinate sytem \(c\). Thus, given the representation of the point \(P\) in world coordinates, \(P_w\), we obtain \(P\)’s representation in the camera coordinate system, \(P_c\), by

\[\begin{split} P_c = \begin{bmatrix} R & t \\ 0 & 1 \end{bmatrix} P_w, \end{split}\]

This homogeneous transformation is composed out of \(R\), a 3-by-3 rotation matrix, and \(t\), a 3-by-1 translation vector:

\[\begin{split} \begin{bmatrix} R & t \\ 0 & 1 \end{bmatrix} = \begin{bmatrix} r_{11} & r_{12} & r_{13} & t_x \\ r_{21} & r_{22} & r_{23} & t_y \\ r_{31} & r_{32} & r_{33} & t_z \\ 0 & 0 & 0 & 1 \end{bmatrix}, \end{split}\]

and therefore

\[\begin{split} \begin{bmatrix} X_c \\ Y_c \\ Z_c \\ 1 \end{bmatrix} = \begin{bmatrix} r_{11} & r_{12} & r_{13} & t_x \\ r_{21} & r_{22} & r_{23} & t_y \\ r_{31} & r_{32} & r_{33} & t_z \\ 0 & 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} X_w \\ Y_w \\ Z_w \\ 1 \end{bmatrix}. \end{split}\]

Combining the projective transformation and the homogeneous transformation, we obtain the projective transformation that maps 3D points in world coordinates into 2D points in the image plane and in normalized camera coordinates:

\[\begin{split} Z_c \begin{bmatrix} x' \\ y' \\ 1 \end{bmatrix} = \begin{bmatrix} R|t \end{bmatrix} \begin{bmatrix} X_w \\ Y_w \\ Z_w \\ 1 \end{bmatrix} = \begin{bmatrix} r_{11} & r_{12} & r_{13} & t_x \\ r_{21} & r_{22} & r_{23} & t_y \\ r_{31} & r_{32} & r_{33} & t_z \end{bmatrix} \begin{bmatrix} X_w \\ Y_w \\ Z_w \\ 1 \end{bmatrix}, \end{split}\]

with \(x' = X_c / Z_c\) and \(y' = Y_c / Z_c\). Putting the equations for instrincs and extrinsics together, we can write out \(s \; p = A \begin{bmatrix} R|t \end{bmatrix} P_w\) as

\[\begin{split} s \vecthree{u}{v}{1} = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1} \begin{bmatrix} r_{11} & r_{12} & r_{13} & t_x \\ r_{21} & r_{22} & r_{23} & t_y \\ r_{31} & r_{32} & r_{33} & t_z \end{bmatrix} \begin{bmatrix} X_w \\ Y_w \\ Z_w \\ 1 \end{bmatrix}. \end{split}\]

If \(Z_c \ne 0\), the transformation above is equivalent to the following,

\[\begin{split} \begin{bmatrix} u \\ v \end{bmatrix} = \begin{bmatrix} f_x X_c/Z_c + c_x \\ f_y Y_c/Z_c + c_y \end{bmatrix} \end{split}\]

with

\[\begin{split} \vecthree{X_c}{Y_c}{Z_c} = \begin{bmatrix} R|t \end{bmatrix} \begin{bmatrix} X_w \\ Y_w \\ Z_w \\ 1 \end{bmatrix}. \end{split}\]

The following figure illustrates the pinhole camera model.

Pinhole camera model

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

\[\begin{split} \begin{bmatrix} u \\ v \end{bmatrix} = \begin{bmatrix} f_x x'' + c_x \\ f_y y'' + c_y \end{bmatrix} \end{split}\]

where

\[\begin{split} \begin{bmatrix} x'' \\ y'' \end{bmatrix} = \begin{bmatrix} x' \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6} + 2 p_1 x' y' + p_2(r^2 + 2 x'^2) + s_1 r^2 + s_2 r^4 \\ y' \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6} + p_1 (r^2 + 2 y'^2) + 2 p_2 x' y' + s_3 r^2 + s_4 r^4 \\ \end{bmatrix} \end{split}\]

with

\[ r^2 = x'^2 + y'^2 \]

and

\[\begin{split} \begin{bmatrix} x'\\ y' \end{bmatrix} = \begin{bmatrix} X_c/Z_c \\ Y_c/Z_c \end{bmatrix}, \end{split}\]

if \(Z_c \ne 0\).

The distortion parameters are the radial coefficients \(k_1\), \(k_2\), \(k_3\), \(k_4\), \(k_5\), and \(k_6\) , \(p_1\) and \(p_2\) are the tangential distortion coefficients, and \(s_1\), \(s_2\), \(s_3\), and \(s_4\), are the thin prism distortion coefficients. Higher-order coefficients are not considered in OpenCV.

The next figures show two common types of radial distortion: barrel distortion ( \( 1 + k_1 r^2 + k_2 r^4 + k_3 r^6 \) monotonically decreasing) and pincushion distortion ( \( 1 + k_1 r^2 + k_2 r^4 + k_3 r^6 \) monotonically increasing). Radial distortion is always monotonic for real lenses, and if the estimator produces a non-monotonic result, this should be considered a calibration failure. More generally, radial distortion must be monotonic and the distortion function must be bijective. A failed estimation result may look deceptively good near the image center but will work poorly in e.g. AR/SFM applications. The optimization method used in OpenCV camera calibration does not include these constraints as the framework does not support the required integer programming and polynomial inequalities. See issue #15992 for additional information.

In some cases, the image sensor may be tilted in order to focus an oblique plane in front of the camera (Scheimpflug principle). This can be useful for particle image velocimetry (PIV) or triangulation with a laser fan. The tilt causes a perspective distortion of \(x''\) and \(y''\). This distortion can be modeled in the following way, see e.g. [191].

\[\begin{split} \begin{bmatrix} u \\ v \end{bmatrix} = \begin{bmatrix} f_x x''' + c_x \\ f_y y''' + c_y \end{bmatrix}, \end{split}\]

where

\[ s\vecthree{x'''}{y'''}{1} = \vecthreethree{R_{33}(\tau_x, \tau_y)}{0}{-R_{13}(\tau_x, \tau_y)} {0}{R_{33}(\tau_x, \tau_y)}{-R_{23}(\tau_x, \tau_y)} {0}{0}{1} R(\tau_x, \tau_y) \vecthree{x''}{y''}{1} \]

and the matrix \(R(\tau_x, \tau_y)\) is defined by two rotations with angular parameter \(\tau_x\) and \(\tau_y\), respectively,

\[ R(\tau_x, \tau_y) = \vecthreethree{\cos(\tau_y)}{0}{-\sin(\tau_y)}{0}{1}{0}{\sin(\tau_y)}{0}{\cos(\tau_y)} \vecthreethree{1}{0}{0}{0}{\cos(\tau_x)}{\sin(\tau_x)}{0}{-\sin(\tau_x)}{\cos(\tau_x)} = \vecthreethree{\cos(\tau_y)}{\sin(\tau_y)\sin(\tau_x)}{-\sin(\tau_y)\cos(\tau_x)} {0}{\cos(\tau_x)}{\sin(\tau_x)} {\sin(\tau_y)}{-\cos(\tau_y)\sin(\tau_x)}{\cos(\tau_y)\cos(\tau_x)}. \]

In the functions below the coefficients are passed or returned as

\[ (k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6 [, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]]) \]

vector. That is, if the vector contains four elements, it means that \(k_3=0\) . The distortion coefficients do not depend on the scene viewed. Thus, they also belong to the intrinsic camera parameters. And they remain the same regardless of the captured image resolution. If, for example, a camera has been calibrated on images of 320 x 240 resolution, absolutely the same distortion coefficients can be used for 640 x 480 images from the same camera while \(f_x\), \(f_y\), \(c_x\), and \(c_y\) need to be scaled appropriately.

The functions below use the above model to do the following:

Project 3D points to the image plane given intrinsic and extrinsic parameters.
Compute extrinsic parameters given intrinsic parameters, a few 3D points, and their projections.
Estimate intrinsic and extrinsic camera parameters from several views of a known calibration pattern (every view is described by several 3D-2D point correspondences).
Estimate the relative position and orientation of the stereo camera “heads” and compute the rectification* transformation that makes the camera optical axes parallel.

Homogeneous Coordinates

Homogeneous Coordinates are a system of coordinates that are used in projective geometry. Their use allows to represent points at infinity by finite coordinates and simplifies formulas when compared to the cartesian counterparts, e.g. they have the advantage that affine transformations can be expressed as linear homogeneous transformation.

One obtains the homogeneous vector \(P_h\) by appending a 1 along an n-dimensional cartesian vector \(P\) e.g. for a 3D cartesian vector the mapping \(P \rightarrow P_h\) is:

\[\begin{split} \begin{bmatrix} X \\ Y \\ Z \end{bmatrix} \rightarrow \begin{bmatrix} X \\ Y \\ Z \\ 1 \end{bmatrix}. \end{split}\]

For the inverse mapping \(P_h \rightarrow P\), one divides all elements of the homogeneous vector by its last element, e.g. for a 3D homogeneous vector one gets its 2D cartesian counterpart by:

\[\begin{split} \begin{bmatrix} X \\ Y \\ W \end{bmatrix} \rightarrow \begin{bmatrix} X / W \\ Y / W \end{bmatrix}, \end{split}\]

if \(W \ne 0\).

Due to this mapping, all multiples \(k P_h\), for \(k \ne 0\), of a homogeneous point represent the same point \(P_h\). An intuitive understanding of this property is that under a projective transformation, all multiples of \(P_h\) are mapped to the same point. This is the physical observation one does for pinhole cameras, as all points along a ray through the camera’s pinhole are projected to the same image point, e.g. all points along the red ray in the image of the pinhole camera model above would be mapped to the same image coordinate. This property is also the source for the scale ambiguity s in the equation of the pinhole camera model.

As mentioned, by using homogeneous coordinates we can express any change of basis parameterized by \(R\) and \(t\) as a linear transformation, e.g. for the change of basis from coordinate system 0 to coordinate system 1 becomes:

\[\begin{split} P_1 = R P_0 + t \rightarrow P_{h_1} = \begin{bmatrix} R & t \\ 0 & 1 \end{bmatrix} P_{h_0}. \end{split}\]

Homogeneous Transformations, Object frame / Camera frame

Change of basis or computing the 3D coordinates from one frame to another frame can be achieved easily using the following notation:

\[ \mathbf{X}_c = \hspace{0.2em} {}^{c}\mathbf{T}_o \hspace{0.2em} \mathbf{X}_o \]

\[\begin{split} \begin{bmatrix} X_c \\ Y_c \\ Z_c \\ 1 \end{bmatrix} = \begin{bmatrix} {}^{c}\mathbf{R}_o & {}^{c}\mathbf{t}_o \\ 0_{1 \times 3} & 1 \end{bmatrix} \begin{bmatrix} X_o \\ Y_o \\ Z_o \\ 1 \end{bmatrix} \end{split}\]

For a 3D points ( \( \mathbf{X}_o \)) expressed in the object frame, the homogeneous transformation matrix \( {}^{c}\mathbf{T}_o \) allows computing the corresponding coordinate ( \( \mathbf{X}_c \)) in the camera frame. This transformation matrix is composed of a 3x3 rotation matrix \( {}^{c}\mathbf{R}_o \) and a 3x1 translation vector \( {}^{c}\mathbf{t}_o \). The 3x1 translation vector \( {}^{c}\mathbf{t}_o \) is the position of the object frame in the camera frame and the 3x3 rotation matrix \( {}^{c}\mathbf{R}_o \) the orientation of the object frame in the camera frame. With this simple notation, it is easy to chain the transformations. For instance, to compute the 3D coordinates of a point expressed in the object frame in the world frame can be done with:

\[ \mathbf{X}_w = \hspace{0.2em} {}^{w}\mathbf{T}_c \hspace{0.2em} {}^{c}\mathbf{T}_o \hspace{0.2em} \mathbf{X}_o = {}^{w}\mathbf{T}_o \hspace{0.2em} \mathbf{X}_o \]

Similarly, computing the inverse transformation can be done with:

\[ \mathbf{X}_o = \hspace{0.2em} {}^{o}\mathbf{T}_c \hspace{0.2em} \mathbf{X}_c = \left( {}^{c}\mathbf{T}_o \right)^{-1} \hspace{0.2em} \mathbf{X}_c \]

The inverse of an homogeneous transformation matrix is then:

\[\begin{split} {}^{o}\mathbf{T}_c = \left( {}^{c}\mathbf{T}_o \right)^{-1} = \begin{bmatrix} {}^{c}\mathbf{R}^{\top}_o & - \hspace{0.2em} {}^{c}\mathbf{R}^{\top}_o \hspace{0.2em} {}^{c}\mathbf{t}_o \\ 0_{1 \times 3} & 1 \end{bmatrix} \end{split}\]

One can note that the inverse of a 3x3 rotation matrix is directly its matrix transpose. This figure summarizes the whole process. The object pose returned for instance by the solvePnP function or pose from fiducial marker detection is this \( {}^{c}\mathbf{T}_o \) transformation. The camera intrinsic matrix \( \mathbf{K} \) allows projecting the 3D point expressed in the camera frame onto the image plane assuming a perspective projection model (pinhole camera model). Image coordinates extracted from classical image processing functions assume a (u,v) top-left coordinates frame.

Note

for an online video course on this topic, see for instance:
- “3.3.1. Homogeneous Transformation Matrices”, Modern Robotics, Kevin M. Lynch and Frank C. Park
the 3x3 rotation matrix is composed of 9 values but describes a 3 dof transformation
some additional properties of the 3x3 rotation matrix are:
- \( \mathrm{det} \left( \mathbf{R} \right) = 1 \)
- \( \mathbf{R} \mathbf{R}^{\top} = \mathbf{R}^{\top} \mathbf{R} = \mathrm{I}_{3 \times 3} \)
- interpolating rotation can be done using the Slerp (spherical linear interpolation) method
quick conversions between the different rotation formalisms can be done using this online tool Intrinsic parameters from camera lens specifications

When dealing with industrial cameras, the camera intrinsic matrix or more precisely \( \left(f_x, f_y \right) \) can be deduced, approximated from the camera specifications:

\[ f_x = \frac{f_{\text{mm}}}{\text{pixel_size_in_mm}} = \frac{f_{\text{mm}}}{\text{sensor_size_in_mm} / \text{nb_pixels}} \]

In a same way, the physical focal length can be deduced from the angular field of view:

\[ f_{\text{mm}} = \frac{\text{sensor_size_in_mm}}{2 \times \tan{\frac{\text{fov}}{2}}} \]

This latter conversion can be useful when using a rendering software to mimic a physical camera device.

See also calibrationMatrixValues

Additional references, notes

Note

Many functions in this module take a camera intrinsic matrix as an input parameter. Although all functions assume the same structure of this parameter, they may name it differently. The parameter’s description, however, will be clear in that a camera intrinsic matrix with the structure shown above is required.
A calibration sample for 3 cameras in a horizontal position can be found at opencv_source_code/samples/cpp/3calibration.cpp
A calibration sample based on a sequence of images can be found at opencv_source_code/samples/cpp/calibration.cpp
A calibration sample in order to do 3D reconstruction can be found at opencv_source_code/samples/cpp/build3dmodel.cpp
A calibration example on stereo calibration can be found at opencv_source_code/samples/cpp/stereo_calib.cpp
A calibration example on stereo matching can be found at opencv_source_code/samples/cpp/stereo_match.cpp
(Python) A camera calibration sample can be found at opencv_source_code/samples/python/calibrate.py

Namespaces#

cv::fisheye namespace

Enumerations#

enum cv {
    CALIB_USE_INTRINSIC_GUESS = 0x00001,
    CALIB_FIX_ASPECT_RATIO = 0x00002,
    CALIB_FIX_PRINCIPAL_POINT = 0x00004,
    CALIB_ZERO_TANGENT_DIST = 0x00008,
    CALIB_FIX_FOCAL_LENGTH = 0x00010,
    CALIB_FIX_K1 = 0x00020,
    CALIB_FIX_K2 = 0x00040,
    CALIB_FIX_K3 = 0x00080,
    CALIB_FIX_K4 = 0x00800,
    CALIB_FIX_K5 = 0x01000,
    CALIB_FIX_K6 = 0x02000,
    CALIB_RATIONAL_MODEL = 0x04000,
    CALIB_THIN_PRISM_MODEL = 0x08000,
    CALIB_FIX_S1_S2_S3_S4 = 0x10000,
    CALIB_TILTED_MODEL = 0x40000,
    CALIB_FIX_TAUX_TAUY = 0x80000,
    CALIB_USE_QR = 0x100000,
    CALIB_FIX_TANGENT_DIST = 0x200000,
    CALIB_FIX_INTRINSIC = 0x00100,
    CALIB_SAME_FOCAL_LENGTH = 0x00200,
    CALIB_ZERO_DISPARITY = 0x00400,
    CALIB_USE_LU = (1 << 17),
    CALIB_DISABLE_SCHUR_COMPLEMENT = (1 << 18),
    CALIB_USE_EXTRINSIC_GUESS = (1 << 22),
    CALIB_RECOMPUTE_EXTRINSIC = (1 << 23),
    CALIB_CHECK_COND = (1 << 24),
    CALIB_FIX_SKEW = (1 << 25),
    CALIB_STEREO_REGISTRATION = (1 << 26)
}

View details

enum cv::CameraModel {
    cv::CALIB_MODEL_PINHOLE = 0,
    cv::CALIB_MODEL_FISHEYE = 1
}

View details

enum cv::HandEyeCalibrationMethod {
    cv::CALIB_HAND_EYE_TSAI = 0,
    cv::CALIB_HAND_EYE_PARK = 1,
    cv::CALIB_HAND_EYE_HORAUD = 2,
    cv::CALIB_HAND_EYE_ANDREFF = 3,
    cv::CALIB_HAND_EYE_DANIILIDIS = 4
}

View details

enum cv::RobotWorldHandEyeCalibrationMethod {
    cv::CALIB_ROBOT_WORLD_HAND_EYE_SHAH = 0,
    cv::CALIB_ROBOT_WORLD_HAND_EYE_LI = 1
}

`CALIB_USE_INTRINSIC_GUESS`	Use user provided intrinsics as initial point for optimization.
`CALIB_FIX_ASPECT_RATIO`	Use with CALIB_USE_INTRINSIC_GUESS. The ratio fx/fy stays the same as in the input cameraMatrix.
`CALIB_FIX_PRINCIPAL_POINT`	The principal point (cx, cy) stays the same as in the input camera matrix. Image center is used as principal point, if CALIB_USE_INTRINSIC_GUESS is not set.
`CALIB_ZERO_TANGENT_DIST`	For pinhole model only. Tangential distortion coefficients \((p_1, p_2)\) are set to zeros and stay zero.
`CALIB_FIX_FOCAL_LENGTH`	Use with CALIB_USE_INTRINSIC_GUESS. The focal length (fx, fy) stays the same as in the input cameraMatrix.
`CALIB_FIX_K1`	The corresponding distortion coefficient is not changed during the optimization. 0 value is used, if CALIB_USE_INTRINSIC_GUESS is not set.
`CALIB_FIX_K2`	The corresponding distortion coefficient is not changed during the optimization. 0 value is used, if CALIB_USE_INTRINSIC_GUESS is not set.
`CALIB_FIX_K3`	The corresponding distortion coefficient is not changed during the optimization. 0 value is used, if CALIB_USE_INTRINSIC_GUESS is not set.
`CALIB_FIX_K4`	The corresponding distortion coefficient is not changed during the optimization. 0 value is used, if CALIB_USE_INTRINSIC_GUESS is not set.
`CALIB_FIX_K5`	For pinhole model only. The corresponding distortion coefficient is not changed during the optimization. 0 value is used, if CALIB_USE_INTRINSIC_GUESS is not set.
`CALIB_FIX_K6`	For pinhole model only. The corresponding distortion coefficient is not changed during the optimization. 0 value is used, if CALIB_USE_INTRINSIC_GUESS is not set.
`CALIB_RATIONAL_MODEL`	For pinhole model only. Use rational distortion model with coefficients k4..k6.
`CALIB_THIN_PRISM_MODEL`	For pinhole model only. Use thin prism distortion model with coefficients s1..s4.
`CALIB_FIX_S1_S2_S3_S4`	For pinhole model only. The thin prism distortion coefficients are not changed during the optimization. 0 value is used, if CALIB_USE_INTRINSIC_GUESS is not set.
`CALIB_TILTED_MODEL`	For pinhole model only. Coefficients tauX and tauY are enabled in camera matrix.
`CALIB_FIX_TAUX_TAUY`	For pinhole model only. The tauX and tauY coefficients are not changed during the optimization. 0 value is used, if CALIB_USE_INTRINSIC_GUESS is not set.
`CALIB_USE_QR`	Use QR instead of SVD decomposition for solving. Faster but potentially less precise.
`CALIB_FIX_TANGENT_DIST`	For pinhole model only. Tangential distortion coefficients (p1,p2) are set to zeros and stay zero.
`CALIB_FIX_INTRINSIC`	For stereo and milti-camera calibration only. Do not optimize cameras intrinsics.
`CALIB_SAME_FOCAL_LENGTH`	For stereo calibration only. Use the same focal length for cameras in pair.
`CALIB_ZERO_DISPARITY`	Deprecated synonim of STEREO_ZERO_DISPARITY. See stereoRectify.
`CALIB_USE_LU`	use LU instead of SVD decomposition for solving. much faster but potentially less precise
`CALIB_DISABLE_SCHUR_COMPLEMENT`	disable Schur complement (use Bouguet calibration engine)
`CALIB_USE_EXTRINSIC_GUESS`	For stereo and multi-view calibration. Use user provided extrinsics (R, T) as initial point for optimization.
`CALIB_RECOMPUTE_EXTRINSIC`	For fisheye model only. Recompute board position on each calibration iteration.
`CALIB_CHECK_COND`	For fisheye model only. Check SVD decomposition quality for each frame during extrinsics estimation.
`CALIB_FIX_SKEW`	For fisheye model only. Skew coefficient (alpha) is set to zero and stay zero.
`CALIB_STEREO_REGISTRATION`	For multiview calibration only. Use stereo correspondence approach for initial extrinsics guess. Limitation: all cameras should have the same type.

`CALIB_MODEL_PINHOLE` Python: `cv.CALIB_MODEL_PINHOLE`	Pinhole camera model.
`CALIB_MODEL_FISHEYE` Python: `cv.CALIB_MODEL_FISHEYE`	Fisheye camera model.

`CALIB_HAND_EYE_TSAI` Python: `cv.CALIB_HAND_EYE_TSAI`	A New Technique for Fully Autonomous and Efficient 3D Robotics Hand/Eye Calibration [309].
`CALIB_HAND_EYE_PARK` Python: `cv.CALIB_HAND_EYE_PARK`	Robot Sensor Calibration: Solving AX = XB on the Euclidean Group [237].
`CALIB_HAND_EYE_HORAUD` Python: `cv.CALIB_HAND_EYE_HORAUD`	Hand-eye Calibration [143].
`CALIB_HAND_EYE_ANDREFF` Python: `cv.CALIB_HAND_EYE_ANDREFF`	On-line Hand-Eye Calibration [14].
`CALIB_HAND_EYE_DANIILIDIS` Python: `cv.CALIB_HAND_EYE_DANIILIDIS`	Hand-Eye Calibration Using Dual Quaternions [73].

`CALIB_ROBOT_WORLD_HAND_EYE_SHAH` Python: `cv.CALIB_ROBOT_WORLD_HAND_EYE_SHAH`	Solving the robot-world/hand-eye calibration problem using the kronecker product [270].
`CALIB_ROBOT_WORLD_HAND_EYE_LI` Python: `cv.CALIB_ROBOT_WORLD_HAND_EYE_LI`	Simultaneous robot-world and hand-eye calibration using dual-quaternions and kronecker product [180].

Camera Calibration#

Topics#

Detailed Description#

Namespaces#

Enumerations#

Enumeration Type Documentation#

enum#

CameraModel#

HandEyeCalibrationMethod#

RobotWorldHandEyeCalibrationMethod#

Function Documentation#

calibrateCamera()#

calibrateCamera()#

calibrateCameraRO()#

calibrateCameraRO()#

calibrateHandEye()#

calibrateMultiview()#

calibrateMultiview()#

calibrateRobotWorldHandEye()#

initCameraMatrix2D()#

registerCameras()#

registerCameras()#

stereoCalibrate()#

stereoCalibrate()#

stereoCalibrate()#

Macro Definition Documentation#

CALIB_NINTRINSIC#