Documentation

Calculates a fundamental matrix from the corresponding points in two images

The minimum number of points required depends on the FundamentalMatMethod.

• FM_7Point: N == 7
• FM_8Point: N >= 8
• FM_Ransac: N >= 15
• FM_Lmeds: N >= 8

With 7 points the FM_7Point method is used, despite the given method.

With more than 7 points the FM_7Point method will be replaced by the FM_8Point method.

Between 7 and 15 points the FM_Ransac method will be replaced by the FM_Lmeds method.

With the FM_7Point method and with 7 points the result can contain up to 3 matrices, resulting in either 3, 6 or 9 rows. This is why the number of resulting rows in tagged as Dynamic. For all other methods the result always contains 3 rows.

OpenCV Sphinx doc

For points in an image of a stereo pair, computes the corresponding epilines in the other image

OpenCV Sphinx doc

Finds an object pose from 3D-2D point correspondences.

Parameters:

objectImageMatches

Correspondences between object coordinate space (3D) and image points (2D).

cameraMatrix

Input camera matrix \[ A = \begin{bmatrix} f_x & 0 & c_x \\ 0 & f_y & c_y \\ 0 & 0 & 1 \end{bmatrix} \]

distCoeffs

Input distortion coefficients \( \left ( k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6 [, s_1, s_2, s_3, s_4[, \tau_x, \tau_y ] ] ] ] \right ) \) of 4, 5, 8, 12 or 14 elements. If not given, the zero distortion coefficients are assumed.

In case of success the algorithm outputs 3 values:

rvec

Output rotation vector that, together with tvec, brings points from the model coordinate system to the camera coordinate system.

tvec

Output translation vector.

cameraMatrix

Output camera matrix. In most cases a copy of the input camera matrix. With the SolvePnP_UPNP method the \(f_x\) and \(f_y\) parameters will be estimated.

The function estimates the object pose given a set of object points, their corresponding image projections, as well as the camera matrix and the distortion coefficients, see the figure below (more precisely, the X-axis of the camera frame is pointing to the right, the Y-axis downward and the Z-axis forward).

Points expressed in the world frame \(\bf{X_w}\) are projected into the image plane \([u,v]\) using the perspective projection model \(\bf{\Pi}\) and the camera intrinsic parameters matrix \(\bf{A}\):

\[ \begin{align*} \begin{bmatrix} u \\ v \\ 1 \end{bmatrix} &= \bf{A} \hspace{0.1em} \Pi \hspace{0.2em} ^{c}\bf{M}_w \begin{bmatrix} X_{w} \\ Y_{w} \\ Z_{w} \\ 1 \end{bmatrix} \\ \begin{bmatrix} u \\ v \\ 1 \end{bmatrix} &= \begin{bmatrix} f_x & 0 & c_x \\ 0 & f_y & c_y \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix} \begin{bmatrix} r_{11} & r_{12} & r_{13} & t_x \\ r_{21} & r_{22} & r_{23} & t_y \\ r_{31} & r_{32} & r_{33} & t_z \\ 0 & 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} X_{w} \\ Y_{w} \\ Z_{w} \\ 1 \end{bmatrix} \end{align*} \]

The estimated pose is thus the rotation (rvec) and the translation (tvec) vectors that allow to transform a 3D point expressed in the world frame into the camera frame:

\[ \begin{align*} \begin{bmatrix} X_c \\ Y_c \\ Z_c \\ 1 \end{bmatrix} &= \hspace{0.2em} ^{c}\bf{M}_w \begin{bmatrix} X_{w} \\ Y_{w} \\ Z_{w} \\ 1 \end{bmatrix} \\ \begin{bmatrix} X_c \\ Y_c \\ Z_c \\ 1 \end{bmatrix} &= \begin{bmatrix} r_{11} & r_{12} & r_{13} & t_x \\ r_{21} & r_{22} & r_{23} & t_y \\ r_{31} & r_{32} & r_{33} & t_z \\ 0 & 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} X_{w} \\ Y_{w} \\ Z_{w} \\ 1 \end{bmatrix} \end{align*} \]