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| <div class="tex2jax_ignore mathjax_ignore section" id="intrinsic-calibration-models"> | ||
| <h1>Intrinsic calibration models<a class="headerlink" href="#intrinsic-calibration-models" title="Permalink to this headline"></a></h1> | ||
| <p>Every camera is individually calibrated in production. We use two different models depending on the field of view of the camera.</p> | ||
| <div class="section" id="fisheye-model"> | ||
| <h2>Fisheye model<a class="headerlink" href="#fisheye-model" title="Permalink to this headline"></a></h2> | ||
| <p>This applies to the wide opening angle (O3R225) cameras. For these cameras, we use the fisheye distortion model as described below.</p> | ||
| <div class="section" id="for-unprojection"> | ||
| <h3>For unprojection<a class="headerlink" href="#for-unprojection" title="Permalink to this headline"></a></h3> | ||
| <p>This model is used for converting pixel positions to 3D vectors. It corresponds to <code class="docutils literal notranslate"><span class="pre">modelID=2</span></code>. The following formulas show how to apply the model:</p> | ||
| <p><img alt="Fish eye model for unprojection" src="../../../_images/fisheye_unprojection.png" /></p> | ||
| <p>Where</p> | ||
| <ul class="simple"> | ||
| <li><p>$\left(\begin{array}{c}i_x \ i_y\end{array}\right)$ are the input coordinates as integer numbers, in pixels,</p></li> | ||
| <li><p>$v = \left(\begin{array}{c}v_x\ v_y\ v_z\end{array}\right)$ is the resulting 3D direction vector in the optical coordinate system,</p></li> | ||
| <li><p>$f_x, f_y, m_x, m_y, \alpha, k_1, k_2, k_3, k_4, \theta^*_{max}$ are the model parameters obtained from the <code class="docutils literal notranslate"><span class="pre">modelParameters</span></code> array.</p></li> | ||
| </ul> | ||
| </div> | ||
| <div class="section" id="for-projection"> | ||
| <h3>For projection<a class="headerlink" href="#for-projection" title="Permalink to this headline"></a></h3> | ||
| <p>This model is used for converting directions given as 3D vectors to pixel position. This corresponds to <code class="docutils literal notranslate"><span class="pre">modelID=3</span></code>. The following formulas show how to apply the model:</p> | ||
| <p><img alt="Fish eye model for projection" src="../../../_images/fisheye_projection.png" /></p> | ||
| <p>Where</p> | ||
| <ul class="simple"> | ||
| <li><p>$v = \left(\begin{array}{c}v_x\ v_y\ v_z\end{array}\right)$ is the input direction vector in the optical coordinate system,</p></li> | ||
| <li><p>$\left(\begin{array}{c}i_x \ i_y\end{array}\right)$ are the resulting image coordinates (the upper left pixel has coordinates $(0, 0)$),</p></li> | ||
| <li><p>$f_x, f_y, m_x, m_y, \alpha, k_1, k_2, k_3, k_4, \theta_{max}$ are the model parameters obtained from the <code class="docutils literal notranslate"><span class="pre">modelParameters</span></code> array.</p></li> | ||
| </ul> | ||
| </div> | ||
| </div> | ||
| <div class="section" id="bouguet-model"> | ||
| <h2>Bouguet model<a class="headerlink" href="#bouguet-model" title="Permalink to this headline"></a></h2> | ||
| <div class="section" id="id1"> | ||
| <h3>For unprojection<a class="headerlink" href="#id1" title="Permalink to this headline"></a></h3> | ||
| <p><img alt="Bouguet model for unprojection" src="../../../_images/bouguet_unprojection.png" /></p> | ||
| <p>Where</p> | ||
| <ul class="simple"> | ||
| <li><p>$\left(\begin{array}{c}i_x \ i_y\end{array}\right)$ are the input coordinates are integer numbers, in pixels,</p></li> | ||
| <li><p>$v = \left(\begin{array}{c}v_x\ v_y\ v_z\end{array}\right)$ is the resulting 3D direction vector in the optical coordinate system,</p></li> | ||
| <li><p>$f_x, f_y, m_x, m_y, \alpha, k_1, k_2, k_3, k_4, k_5$ are the model parameters obtained from the <code class="docutils literal notranslate"><span class="pre">modelParameters</span></code> array.</p></li> | ||
| </ul> | ||
| </div> | ||
| <div class="section" id="id2"> | ||
| <h3>For projection<a class="headerlink" href="#id2" title="Permalink to this headline"></a></h3> | ||
| <p><img alt="Bouguet model for projection" src="../../../_images/bouguet_projection.png" /></p> | ||
| <p>Where</p> | ||
| <ul class="simple"> | ||
| <li><p>$v = \left(\begin{array}{c}v_x\ v_y\ v_z\end{array}\right)$ is the input direction vector in the optical coordinate system,</p></li> | ||
| <li><p>$\left(\begin{array}{c}i_x \ i_y\end{array}\right)$ are the resulting image coordinates (the upper left pixel has coordinates $(0, 0)$),</p></li> | ||
| <li><p>$f_x, f_y, m_x, m_y, \alpha, k_1, k_2, k_3, k_4, k_5$ are the model parameters obtained from the <code class="docutils literal notranslate"><span class="pre">modelParameters</span></code> array.</p></li> | ||
| </ul> | ||
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