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Overview

Camera calibration estimates intrinsic parameters (focal length, principal point, distortion coefficients) from multiple views of a calibration pattern. OpenCV supports chessboard and circular grid patterns.

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Core Functions

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calibrateCamera

Finds the camera intrinsic and extrinsic parameters from several views of a calibration pattern. 
double cv::calibrateCamera(
    InputArrayOfArrays objectPoints,
    InputArrayOfArrays imagePoints,
    Size imageSize,
    InputOutputArray cameraMatrix,
    InputOutputArray distCoeffs,
    OutputArrayOfArrays rvecs,
    OutputArrayOfArrays tvecs,
    int flags = 0,
    TermCriteria criteria = TermCriteria(TermCriteria::COUNT + TermCriteria::EPS, 30, DBL_EPSILON)
)
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objectPoints
InputArrayOfArrays
required
Vector of vectors of calibration pattern points in the calibration pattern coordinate space (e.g. std::vector<std::vector<cv::Vec3f>>). The outer vector contains as many elements as pattern views. For planar patterns, Z-coordinate is 0.
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imagePoints
InputArrayOfArrays
required
Vector of vectors of the projections of calibration pattern points (e.g. std::vector<std::vector<cv::Vec2f>>). Must match the size of objectPoints.
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imageSize
Size
required
Size of the image used only to initialize the camera intrinsic matrix.
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cameraMatrix
InputOutputArray
required
Input/output 3x3 floating-point camera intrinsic matrix. If CALIB_USE_INTRINSIC_GUESS is specified, some or all of fx, fy, cx, cy must be initialized before calling.
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distCoeffs
InputOutputArray
required
Input/output vector of distortion coefficients (k1, k2, p1, p2[, k3[, k4, k5, k6[, s1, s2, s3, s4[, τx, τy]]]]).
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rvecs
OutputArrayOfArrays
Output vector of rotation vectors (Rodrigues) estimated for each pattern view. Each rotation vector brings the calibration pattern from object coordinate space to camera coordinate space.
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tvecs
OutputArrayOfArrays
Output vector of translation vectors estimated for each pattern view.
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flags
int
default:"0"
Different flags for calibration behavior (see Calibration Flags below).
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criteria
TermCriteria
default:"TermCriteria(COUNT+EPS, 30, DBL_EPSILON)"
Termination criteria for the iterative optimization algorithm.
Returns: The overall RMS re-projection error.
The algorithm is based on Zhang2000. It performs:
  1. Compute initial intrinsic parameters (for planar patterns) or read from input
  2. Estimate initial camera pose using solvePnP
  3. Run global Levenberg-Marquardt optimization to minimize reprojection error

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Extended Version

double cv::calibrateCamera(
    InputArrayOfArrays objectPoints,
    InputArrayOfArrays imagePoints,
    Size imageSize,
    InputOutputArray cameraMatrix,
    InputOutputArray distCoeffs,
    OutputArrayOfArrays rvecs,
    OutputArrayOfArrays tvecs,
    OutputArray stdDeviationsIntrinsics,
    OutputArray stdDeviationsExtrinsics,
    OutputArray perViewErrors,
    int flags = 0,
    TermCriteria criteria = TermCriteria(TermCriteria::COUNT + TermCriteria::EPS, 30, DBL_EPSILON)
)
Extended version provides additional outputs:
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stdDeviationsIntrinsics
OutputArray
Output vector of standard deviations estimated for intrinsic parameters. Order: (fx, fy, cx, cy, k1, k2, p1, p2, k3, k4, k5, k6, s1, s2, s3, s4, τx, τy)
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stdDeviationsExtrinsics
OutputArray
Output vector of standard deviations estimated for extrinsic parameters. Order: (R0, T0, ..., R_{M-1}, T_{M-1}) where M is the number of pattern views.
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perViewErrors
OutputArray
Output vector of the RMS re-projection error estimated for each pattern view.

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Calibration Flags

Flags control which parameters are estimated or fixed during calibration:
FlagValueDescription
CALIB_USE_INTRINSIC_GUESS0x00001cameraMatrix contains valid initial values that are optimized further
CALIB_FIX_PRINCIPAL_POINT0x00004Principal point is not changed during optimization
CALIB_FIX_ASPECT_RATIO0x00002Only fy is estimated, ratio fx/fy stays same as input
CALIB_ZERO_TANGENT_DIST0x00008Tangential distortion coefficients (p1, p2) are set to zero
CALIB_FIX_FOCAL_LENGTH0x00010Focal length is not changed (requires CALIB_USE_INTRINSIC_GUESS)
CALIB_FIX_K10x00020k1 distortion coefficient is not changed
CALIB_FIX_K20x00040k2 distortion coefficient is not changed
CALIB_FIX_K30x00080k3 distortion coefficient is not changed
CALIB_FIX_K40x00800k4 distortion coefficient is not changed
CALIB_FIX_K50x01000k5 distortion coefficient is not changed
CALIB_FIX_K60x02000k6 distortion coefficient is not changed
CALIB_RATIONAL_MODEL0x04000Enable k4, k5, k6 coefficients (8+ coefficients)
CALIB_THIN_PRISM_MODEL0x08000Enable s1, s2, s3, s4 coefficients (12+ coefficients)
CALIB_FIX_S1_S2_S3_S40x10000Thin prism distortion coefficients are not changed
CALIB_TILTED_MODEL0x40000Enable tauX and tauY coefficients (14 coefficients)
CALIB_FIX_TAUX_TAUY0x80000Tilted sensor model coefficients are not changed
CALIB_USE_QR0x100000Use QR instead of SVD decomposition (faster but less precise)
CALIB_FIX_TANGENT_DIST0x200000Fix tangential distortion coefficients
CALIB_USE_LU1 << 17Use LU instead of SVD decomposition (much faster but less precise)

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Pattern Detection

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findChessboardCorners

Finds the positions of internal corners of the chessboard. 
bool cv::findChessboardCorners(
    InputArray image,
    Size patternSize,
    OutputArray corners,
    int flags = CALIB_CB_ADAPTIVE_THRESH + CALIB_CB_NORMALIZE_IMAGE
)
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image
InputArray
required
Source chessboard view. Must be an 8-bit grayscale or color image.
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patternSize
Size
required
Number of inner corners per chessboard row and column: Size(points_per_row, points_per_column) = Size(columns, rows). For an 8x8 chessboard, use Size(7, 7).
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corners
OutputArray
required
Output array of detected corners.
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flags
int
Operation flags:
  • CALIB_CB_ADAPTIVE_THRESH (1): Use adaptive thresholding
  • CALIB_CB_NORMALIZE_IMAGE (2): Normalize image gamma with equalizeHist
  • CALIB_CB_FILTER_QUADS (4): Use additional criteria to filter false quads
  • CALIB_CB_FAST_CHECK (8): Run fast check for chessboard corners
  • CALIB_CB_PLAIN (256): Take image as-is without processing
Returns: Non-zero if all corners are found and placed in order (row by row, left to right), otherwise 0.
The function requires white space (like a square-thick border) around the board to make detection more robust. Without borders, the outer black squares cannot be segmented properly.
Example: 
Size patternsize(8, 6); // interior number of corners
Mat gray = ...; // source image
vector<Point2f> corners;

bool patternfound = findChessboardCorners(gray, patternsize, corners,
    CALIB_CB_ADAPTIVE_THRESH + CALIB_CB_NORMALIZE_IMAGE + CALIB_CB_FAST_CHECK);

if(patternfound)
  cornerSubPix(gray, corners, Size(11, 11), Size(-1, -1),
    TermCriteria(CV_TERMCRIT_EPS + CV_TERMCRIT_ITER, 30, 0.1));

drawChessboardCorners(img, patternsize, Mat(corners), patternfound);

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findChessboardCornersSB

Finds chessboard corners using a sector-based approach (more accurate and robust). 
bool cv::findChessboardCornersSB(
    InputArray image,
    Size patternSize,
    OutputArray corners,
    int flags = 0
)
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flags
int
default:"0"
Operation flags:
  • CALIB_CB_NORMALIZE_IMAGE (2): Normalize image gamma
  • CALIB_CB_EXHAUSTIVE (16): Run exhaustive search to improve detection rate
  • CALIB_CB_ACCURACY (32): Upsample input image for better sub-pixel accuracy
  • CALIB_CB_LARGER (64): Allow detected pattern to be larger than patternSize
  • CALIB_CB_MARKER (128): Pattern must have a marker (for consistent coordinate system)
This method uses a localized Radon transformation and is:
  • More robust to noise
  • Faster on larger images
  • Returns more accurate sub-pixel positions than cornerSubPix
Based on the paper “Accurate Detection and Localization of Checkerboard Corners for Calibration” (Duda 2018).

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drawChessboardCorners

Renders the detected chessboard corners. 
void cv::drawChessboardCorners(
    InputOutputArray image,
    Size patternSize,
    InputArray corners,
    bool patternWasFound
)
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image
InputOutputArray
required
Destination image. Must be an 8-bit color image.
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patternSize
Size
required
Number of inner corners per chessboard row and column.
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corners
InputArray
required
Array of detected corners from findChessboardCorners.
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patternWasFound
bool
required
Parameter indicating whether the complete board was found. Pass the return value of findChessboardCorners.
Draws individual corners as red circles (if board not found) or as colored corners connected with lines (if board found).

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Helper Functions

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initCameraMatrix2D

Finds an initial camera intrinsic matrix from 3D-2D point correspondences. 
Mat cv::initCameraMatrix2D(
    InputArrayOfArrays objectPoints,
    InputArrayOfArrays imagePoints,
    Size imageSize,
    double aspectRatio = 1.0
)
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aspectRatio
double
default:"1.0"
If zero or negative, both fx and fy are estimated independently. Otherwise, fx = fy * aspectRatio.
Returns: Initial camera intrinsic matrix for calibration process.
Currently only supports planar calibration patterns (Z-coordinate = 0).

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calibrationMatrixValues

Computes useful camera characteristics from the camera intrinsic matrix. 
void cv::calibrationMatrixValues(
    InputArray cameraMatrix,
    Size imageSize,
    double apertureWidth,
    double apertureHeight,
    CV_OUT double& fovx,
    CV_OUT double& fovy,
    CV_OUT double& focalLength,
    CV_OUT Point2d& principalPoint,
    CV_OUT double& aspectRatio
)
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apertureWidth
double
required
Physical width of the sensor in mm.
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apertureHeight
double
required
Physical height of the sensor in mm.
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fovx
double&
Output field of view in degrees along horizontal sensor axis.
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fovy
double&
Output field of view in degrees along vertical sensor axis.
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focalLength
double&
Focal length of the lens in mm.
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principalPoint
Point2d&
Principal point in mm.
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aspectRatio
double&
fy/fx ratio.

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Advanced Calibration

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calibrateCameraRO

Calibrates camera using the releasing object method for improved precision. 
double cv::calibrateCameraRO(
    InputArrayOfArrays objectPoints,
    InputArrayOfArrays imagePoints,
    Size imageSize,
    int iFixedPoint,
    InputOutputArray cameraMatrix,
    InputOutputArray distCoeffs,
    OutputArrayOfArrays rvecs,
    OutputArrayOfArrays tvecs,
    OutputArray newObjPoints,
    int flags = 0,
    TermCriteria criteria = TermCriteria(TermCriteria::COUNT + TermCriteria::EPS, 30, DBL_EPSILON)
)
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iFixedPoint
int
required
Index of the 3D object point in objectPoints[0] to be fixed. Range [1, objectPoints[0].size()-2] enables object-releasing method. Values outside this range use standard calibration.
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newObjPoints
OutputArray
Updated output vector of calibration pattern points with potentially scaled coordinates.
This method can dramatically improve precision for inaccurate, unmeasured, roughly planar targets. Requires identical calibration board fully visible in all views.
Calibration time may be much longer with this method. Use CALIB_USE_QR or CALIB_USE_LU for faster calibration.

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See Also

  • Pose Estimation - solvePnP, solvePnPRansac for estimating camera pose
  • Stereo Calibration - stereoCalibrate for calibrating stereo camera systems
  • OpenCV samples: calibration.cpp, 3calibration.cpp

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