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Fix typos <noupdate>
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@ -599,7 +599,7 @@ Different modules are used depending on the activation shape.
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\subsection{Inception-v4}
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\subsection{Inception-v4}
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\marginnote{Inception-v4}
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\marginnote{Inception-v4}
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A larger version of Inception v3 with more complicated stem layers.
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A larger version of Inception-v3 with more complicated stem layers.
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@ -660,7 +660,7 @@ It has the following properties:
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\item A stage is composed of residual blocks.
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\item A stage is composed of residual blocks.
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\item A residual block is composed of two $3 \times 3$ convolutions followed by batch normalization.
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\item A residual block is composed of two $3 \times 3$ convolutions followed by batch normalization.
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\item The first residual block of each stage halves the spatial dimension and doubles the number of channels (there is no pooling).
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\item The first residual block of each stage halves the spatial dimension and doubles the number of channels (there is no pooling).
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\item Stem layers are less aggressive than GoogLeNet (\texttt{conv + pool}. Input reduced to $56 \times 56$).
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\item Stem layers are less aggressive than GoogLeNet (\texttt{conv + pool}. Input reduced to a shape of $56 \times 56$).
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\item Global average pooling is used instead of flattening.
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\item Global average pooling is used instead of flattening.
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\end{itemize}
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\end{itemize}
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@ -696,7 +696,7 @@ It has the following properties:
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\end{description}
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\end{description}
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\begin{remark}
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\begin{remark}
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ResNet improves the results of a deeper layer but beyond a certain depth, the gain is negligible.
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ResNet improves the results of a deeper network but, beyond a certain depth, the gain is negligible.
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\begin{figure}[H]
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\begin{figure}[H]
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\centering
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\centering
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\includegraphics[width=0.65\linewidth]{./img/resnet_results.png}
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\includegraphics[width=0.65\linewidth]{./img/resnet_results.png}
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@ -621,7 +621,7 @@ Therefore, the complete workflow for image formation becomes the following:
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\item[Homographies non-linear refinement]
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\item[Homographies non-linear refinement]
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The homographies $\matr{H}_i$ estimated at the previous step are obtained using a linear method and need to be refined as, for each image $i$,
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The homographies $\matr{H}_i$ estimated at the previous step are obtained using a linear method and need to be refined as, for each image $i$,
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the IRF coordinates $\matr{H}_i\vec{w}_j = \left( \frac{h_{i, 1}^T \tilde{\vec{w}}_j}{h_{i, 3}^T \tilde{\vec{w}}_j}, \frac{h_{i, 2}^T \tilde{\vec{w}}_j}{h_{i, 3}^T \tilde{\vec{w}}_j} \right)$
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the IRF coordinates $\matr{H}_i\vec{w}_j = \left( \frac{h_{i, 1}^T \tilde{\vec{w}}_j}{h_{i, 3}^T \tilde{\vec{w}}_j}, \frac{h_{i, 2}^T \tilde{\vec{w}}_j}{h_{i, 3}^T \tilde{\vec{w}}_j} \right)$
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of the world point $\vec{w}_j$ are still not matching the known IRF coordinates $\vec{m}_{i,j}$ of the $j$-corner in the $i$-image.
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of the world point $\vec{w}_j$ are still not matching the known IRF coordinates $\vec{m}_{i,j}$ of the $j$-th corner in the $i$-th image.
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\begin{figure}[H]
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\begin{figure}[H]
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\centering
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\centering
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\includegraphics[width=0.7\linewidth]{./img/_homography_refinement.pdf}
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\includegraphics[width=0.7\linewidth]{./img/_homography_refinement.pdf}
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@ -989,7 +989,7 @@ Undistorted images enjoy some properties:
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\begin{example}[Compensate pitch or yaw]
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\begin{example}[Compensate pitch or yaw]
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In autonomous driving, cameras should be ideally mounted with the optical axis parallel to the road plane and aligned with the direction of motion.
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In autonomous driving, cameras should be ideally mounted with the optical axis parallel to the road plane and aligned with the direction of motion.
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It is usually very difficult to obtain perfect alignment physically
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It is usually very difficult to physically obtain perfect alignment
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but a calibrated camera can help to compensate pitch (i.e. rotation around the $x$-axis)
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but a calibrated camera can help to compensate pitch (i.e. rotation around the $x$-axis)
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and yaw (i.e. rotation around the $y$-axis) by estimating the vanishing point of the lane lines.
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and yaw (i.e. rotation around the $y$-axis) by estimating the vanishing point of the lane lines.
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