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@ -412,11 +412,11 @@ R & t \\ |
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where R is the rotation matrix corresponding to the rotation vector om: R = rodrigues(om); call x, y |
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where R is the rotation matrix corresponding to the rotation vector om: R = rodrigues(om); call x, y |
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and z the 3 coordinates of Xc: |
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and z the 3 coordinates of Xc: |
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\f[x = Xc_1 \\ y = Xc_2 \\ z = Xc_3\f] |
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\f[\begin{array}{l} x = Xc_1 \\ y = Xc_2 \\ z = Xc_3 \end{array} \f] |
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The pinhole projection coordinates of P is [a; b] where |
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The pinhole projection coordinates of P is [a; b] where |
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\f[a = x / z \ and \ b = y / z \\ r^2 = a^2 + b^2 \\ \theta = atan(r)\f] |
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\f[\begin{array}{l} a = x / z \ and \ b = y / z \\ r^2 = a^2 + b^2 \\ \theta = atan(r) \end{array} \f] |
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Fisheye distortion: |
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Fisheye distortion: |
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@ -424,12 +424,12 @@ R & t \\ |
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The distorted point coordinates are [x'; y'] where |
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The distorted point coordinates are [x'; y'] where |
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\f[x' = (\theta_d / r) a \\ y' = (\theta_d / r) b \f] |
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\f[\begin{array}{l} x' = (\theta_d / r) a \\ y' = (\theta_d / r) b \end{array} \f] |
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Finally, conversion into pixel coordinates: The final pixel coordinates vector [u; v] where: |
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Finally, conversion into pixel coordinates: The final pixel coordinates vector [u; v] where: |
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\f[u = f_x (x' + \alpha y') + c_x \\
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\f[\begin{array}{l} u = f_x (x' + \alpha y') + c_x \\
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v = f_y y' + c_y\f] |
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v = f_y y' + c_y \end{array} \f] |
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Summary: |
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Summary: |
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Generic camera model @cite Kannala2006 with perspective projection and without distortion correction |
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Generic camera model @cite Kannala2006 with perspective projection and without distortion correction |
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