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Merge pull request opencv#25877 from Kumataro:fix25875
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calib3d: doc: enable line breaks in formulas
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asmorkalov authored Jul 8, 2024
2 parents d7a237a + 0b5b401 commit a54de7d
Showing 1 changed file with 5 additions and 5 deletions.
10 changes: 5 additions & 5 deletions modules/calib3d/include/opencv2/calib3d.hpp
Original file line number Diff line number Diff line change
Expand Up @@ -412,24 +412,24 @@ R & t \\
where R is the rotation matrix corresponding to the rotation vector om: R = rodrigues(om); call x, y
and z the 3 coordinates of Xc:
\f[x = Xc_1 \\ y = Xc_2 \\ z = Xc_3\f]
\f[\begin{array}{l} x = Xc_1 \\ y = Xc_2 \\ z = Xc_3 \end{array} \f]
The pinhole projection coordinates of P is [a; b] where
\f[a = x / z \ and \ b = y / z \\ r^2 = a^2 + b^2 \\ \theta = atan(r)\f]
\f[\begin{array}{l} a = x / z \ and \ b = y / z \\ r^2 = a^2 + b^2 \\ \theta = atan(r) \end{array} \f]
Fisheye distortion:
\f[\theta_d = \theta (1 + k_1 \theta^2 + k_2 \theta^4 + k_3 \theta^6 + k_4 \theta^8)\f]
The distorted point coordinates are [x'; y'] where
\f[x' = (\theta_d / r) a \\ y' = (\theta_d / r) b \f]
\f[\begin{array}{l} x' = (\theta_d / r) a \\ y' = (\theta_d / r) b \end{array} \f]
Finally, conversion into pixel coordinates: The final pixel coordinates vector [u; v] where:
\f[u = f_x (x' + \alpha y') + c_x \\
v = f_y y' + c_y\f]
\f[\begin{array}{l} u = f_x (x' + \alpha y') + c_x \\
v = f_y y' + c_y \end{array} \f]
Summary:
Generic camera model @cite Kannala2006 with perspective projection and without distortion correction
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