What is the difference between solvePnP and calibrateCamera in opencv?

Question

calibrateCamera() provides rvec, tvec, distCoeff and cameraMatrix whereas solvePnP() takes cameraMatrix, distCoeff as input and provides rvec, tvec as output. What is the difference between these two functions?

Answer 1

calibrateCamera (doc) estimates intrinsics coefficients (i.e. camera matrix and distortion coefficients) for a given camera. This function requires you to provide as input N sets of 2D-3D correspondences, associated to N images taken with the same camera from varying viewpoints (typically N=30, see this tutorial on this topic). The function returns the camera matrix and distortion coefficients for the considered camera. Although those are usually not used, the extrinsics parameters (i.e. position and orientation) are also estimated, hence the function returns one pair of rvec and tvec for each of the N input images.

solvePnP (doc) estimates extrinsics parameters for a given camera image. This function requires you to provide a set of 2D-3D correspondences, associated to a single image taken with a camera with known intrinsics parameters. The function returns a single pair of rvec and tvec, corresponding to the input image.

Answer 2

cv::calibrateCamera(...)

The function estimates the following parameters of a monocular camera from several views of a calibration pattern. The geometry of this pattern is usually known (i.e. it can be a chessboard):

• The linear intrinsic parameters: the focal lengths in terms of pixels (these are basically scale factors), the principal point which would be ideally in the center of the image, and sometimes a skew coefficient between the x and the y axis (but this is often zero).
• The non-linear intrinsic parameters: the previously mentioned parameters are forming the linear camera matrix, but there are also some non-linear parameters in the tranformation from the 3D camera to the 2D image plane, i.e. the lens distortion.
• The extrinsic parameters: the tranformation matrix between the 3D world and 3D camera coordinate systems.

The estimation of the above mentioned parameters is usually based on 2D-3D correspondences. The algorithm detects some 2D points in the image (i.e. chessboard) for what the corresponding 3D object points are specified (known 3D geometry). It performs the following steps in the simplest case (can vary on the flags of cv::calibrateCamera(..., int flags, ...)):

• Computes the linear intrinsic parameters and considers the non-linear ones to zero.
• Estimates the initial camera pose (extrinsics) in function of the approximated intrinsics. This is done using cv::solvePnP(...).
• Performs the Levenberg-Marquardt optimization algorithm to minimize the re-projection error between the detected 2D image points and 2D projections of the 3D object points. This is done using cv::projectPoints(...).

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cv::solvePnP(...)

At this point, I also answered implicitly the role of cv::solvePnP(...) as this is the part of cv::calibrateCamera(...). Once you have the intrinsics of a camera, you can assume that these will never change (except you change the optics or zooming). On the other hand the extrinsics can be changed, i.e. you can rotate the camera or put it to another location. You should see that the scenario of changing an object's pose to the camera is very similar in this case. And this is what the cv::solvePnP(...) is used for.

The function estimates the object pose given:

• A set of 3D object points in a model coordinate system (can be the 3D world as well),
• Their 2D projections on the image plane,
• The linear and non-linear intrinsic parameters.

The output of cv::solvePnP(...) is given as a rotation vector (rvec) together with a translation vector (tvec) that bring the 3D object points from the model coordinate system to the 3D camera coordinate system.

Answer 3

calibrateCamera() provides rvec, tvec, distCoeff, cameraMatrix ---- distCoeffs are related to distortion of the image and cameraMatrix provides the center of image(Cx and Cy) and focal length (Fx and Fy) (projection center). These are called intrinsic parameters. Unless you change the aperture/focus of the camera they will remain the same. [it also provides rvec and tvec, I don't know yet now what can be any possible use of it. These are the position of the camera in the real world. rvec and tvec are also known as extrinsic parameters]

solvePnP() takes cameraMatrix, distCoeff as input and provides rvec, tvec --- Using the Cx, Cy, Fx, Fy it can estimate the current position of the camera i.e. the extrinsic parameters. In other words, first use calibrateCamera() to obtain the CameraMatrix and distCoeff. Use them in solvePNP() and it will tell you the rotation (rvec) and translation (tvec) of the camera as you move the camera with respect to your real world object (with some marker as you can presume).