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Fix typos <noupdate>

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Tian Cheng (Riccardo) Xia
2024-06-20 10:48:32 +02:00
parent 892ed09c26
commit 0969f767e9
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9
src/year1/image-processing-and-computer-vision/module2/sections/_architectures.tex
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@ -5,7 +5,7 @@
\begin{description}
\item[Stem layer] \marginnote{Stem layer}
First convolutional layer of a CNN that aims to reduce the spatial size of the activations for memory and computational purposes
First convolutional layer(s) of a CNN that aims to reduce the spatial size of the activations for memory and computational purposes
but also to rapidly increase the receptive field.
\item[Model parallelism] \marginnote{Model parallelism}
@ -299,6 +299,7 @@ The authors constrained the layers to:
On the other hand, two activations are computed and both need to be stored for backpropagation.
\indenttbox
\begin{example}
\phantom{}
\begin{center}
@ -451,7 +452,7 @@ Network that aims to optimize computing resources.
\begin{description}
\item[Stem layers]
Down-sample the image from a shape of 224 to 28.
As in ZFNet, multiple layers are used (5) and the largest convolution is of shape $7 \times 7$ and stride $2$.
As in ZFNet, multiple layers are used (5) and the largest convolution is of shape $7 \times 7$ with stride $2$.
\item[Inception module] \marginnote{Inception module}
Main component of Inception-v1 that computes multiple convolutions on the input.
@ -621,7 +622,7 @@ A larger version of Inception v3 with more complicated stem layers.
\begin{description}
\item[Standard residual block] \marginnote{Standard residual block}
Block that allows to easily learn the identity function through skip connections.
Block that allows to easily learn the identity function through a skip connection.
The output of a residual block with input $x$ and a series of convolutional layers $F$ is:
\[ F(x; \matr{\theta}) + x \]
@ -779,7 +780,7 @@ It has the following properties:
\item The majority of the possible paths have a length of $\sim 30$.
\item The gradient magnitude is significant at the first layers (i.e. in shorter paths).
\end{itemize}
By multiplying values of two points above, results show that the total gradient magnitude is significant only up until paths of length $\sim 20$.
By multiplying the values of the two points above, results show that the total gradient magnitude is significant only up until paths of length $\sim 20$.
\begin{figure}[H]
\centering

10
src/year1/image-processing-and-computer-vision/module2/sections/_classification.tex
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@ -291,7 +291,7 @@ The prediction is obtained as the index of the maximum score.
\begin{figure}[H]
\centering
\includegraphics[width=0.45\linewidth]{./img/data_representation_linear.png}
\includegraphics[width=0.40\linewidth]{./img/data_representation_linear.png}
\caption{
\parbox[t]{0.6\linewidth}{
Example of non-linearly separable data points that become linearly separable in polar coordinates
@ -386,12 +386,12 @@ The prediction is obtained as the index of the maximum score.
\begin{figure}[H]
\centering
\begin{subfigure}{0.55\linewidth}
\begin{subfigure}{0.6\linewidth}
\centering
\includegraphics[width=\linewidth]{./img/relu_separability_1.png}
\end{subfigure}
\begin{subfigure}{0.55\linewidth}
\begin{subfigure}{0.6\linewidth}
\centering
\includegraphics[width=\linewidth]{./img/relu_separability_2.png}
\end{subfigure}
@ -442,7 +442,7 @@ Image filtering can be implemented through:
Given an image of size $H \times W$, a convolution requires:
\begin{itemize}
\item $2$ parameters.
\item $2$ parameters (in the case of edge detection).
\item $3 (H \cdot (W-1)) \approx 3HW$ FLOPs.
\end{itemize}
@ -469,7 +469,7 @@ Image filtering can be implemented through:
\begin{description}
\item[Multi-channel convolution] \marginnote{Multi-channel convolution}
On inputs with multiple channels (i.e. 3D inputs), different 2D convolutions are applied across the different channels.
On inputs with multiple channels (e.g. RGB images), different 2D convolutions are applied across the different channels.
Given a $C_\text{in} \times H_\text{in} \times W_\text{in}$ image $I$, a convolution kernel $K$ will have shape $C_\text{in} \times H_K \times W_K$
and the output activation at each pixel is computed as:

11
src/year1/image-processing-and-computer-vision/module2/sections/_image_formation.tex
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@ -84,7 +84,7 @@ is done in two steps:
\marginnote{Roto-translation}
The conversion from the world reference system to the camera reference system
is done through a roto-translation wrt the optical center.
is done through a roto-translation w.r.t. the optical center.
Given:
\begin{itemize}
@ -111,7 +111,7 @@ the coordinates $\vec{M}_C$ in CRF corresponding to $\vec{M}_W$ are given by:
\]
\begin{remark}
The coordinates $\vec{C}_W$ of the optical center $\vec{C}$ are obtained as:
The coordinates $\vec{C}_W$ of the optical center $\vec{C} = \nullvec$ are obtained as:
\[
\nullvec = \matr{R}\vec{C}_W + \vec{t}
\iff (\nullvec - \vec{t}) = \matr{R}\vec{C}_W
@ -378,7 +378,7 @@ where:
\]
where $p_1$ and $p_2$ are additional intrinsic parameters.
\begin{remark}
This approximation has empirically been shown to work.
This approximation has been empirically shown to work.
\end{remark}
\end{itemize}
@ -620,7 +620,7 @@ Therefore, the complete workflow for image formation becomes the following:
\item[Homographies non-linear refinement]
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 $i$,
the IRF coordinates $\matr{H}_i\vec{w}_j = (\frac{h_{i, 1}^T \tilde{\vec{w}}_j}{h_{i, 3}^T \tilde{\vec{w}}_j}, \frac{h_{i, 2}^T \tilde{\vec{w}}_j}{h_{i, 3}^T \tilde{\vec{w}}_j})$
the IRF coordinates $\matr{H}_i\vec{w}_j = \left( \frac{h_{i, 1}^T \tilde{\vec{w}}_j}{h_{i, 3}^T \tilde{\vec{w}}_j}, \frac{h_{i, 2}^T \tilde{\vec{w}}_j}{h_{i, 3}^T \tilde{\vec{w}}_j} \right)$
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.
\begin{figure}[H]
\centering
@ -896,7 +896,7 @@ The computed input coordinates might be continuous. Possible discretization stra
\subsection{Undistort warping}
Once a camera has been calibrated, the lens distortion parameters can be used to obtain the undistorted image through backward warping.
Once a camera has been calibrated using Zhang's method, the lens distortion parameters can be used to obtain the undistorted image through backward warping.
\[
\begin{split}
w_u &= u_\text{undist} + (k_1 r^2 + k_2 r^4)(u_\text{undist} - u_0) \\
@ -1018,6 +1018,7 @@ Undistorted images enjoy some properties:
Finally, the homography $\matr{A}\matr{R}_\text{pitch}\matr{A}^{-1}$ relates the pitched image to the ideal image.
\indenttbox
\begin{remark}
The same procedure can be done for the yaw.
\end{remark}

2
src/year1/image-processing-and-computer-vision/module2/sections/_training.tex
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@ -297,7 +297,7 @@ Given $C$ classes, labels can be smoothed by assuming a small uniform noise $\va
Dropout and batch normalization show a general pattern for regularization:
\begin{itemize}
\item At train time, some randomness is added.
\item Ad test time, inference is done by averaging or approximating the output of the network.
\item At test time, inference is done by averaging or approximating the output of the network.
\end{itemize}
\end{remark}