From 5486a69b61d98e47aaf5814cfa505ab0f08029d2 Mon Sep 17 00:00:00 2001 From: Kautenja Date: Tue, 27 Feb 2018 21:44:14 -0600 Subject: [PATCH] cleanup remaining TODO blocks --- tex/review.nlo | 8 ++++++++ tex/review.tex | 46 +++++++++++++++++++++++----------------------- 2 files changed, 31 insertions(+), 23 deletions(-) create mode 100644 tex/review.nlo diff --git a/tex/review.nlo b/tex/review.nlo new file mode 100644 index 0000000..d13cef6 --- /dev/null +++ b/tex/review.nlo @@ -0,0 +1,8 @@ +\nomenclatureentry{P$c$@[{$c$}]\begingroup Speed of light in a vacuum inertial system\nomeqref {0}|nompageref}{1} +\nomenclatureentry{P$h$@[{$h$}]\begingroup Plank Constant\nomeqref {0}|nompageref}{1} +\nomenclatureentry{P$g$@[{$g$}]\begingroup Gravitational Constant\nomeqref {0}|nompageref}{1} +\nomenclatureentry{N$\mathbb{R}$@[{$\mathbb{R}$}]\begingroup Real Numbers\nomeqref {0}|nompageref}{1} +\nomenclatureentry{N$\mathbb{C}$@[{$\mathbb{C}$}]\begingroup Complex Numbers\nomeqref {0}|nompageref}{1} +\nomenclatureentry{N$\mathbb{H}$@[{$\mathbb{H}$}]\begingroup Quaternions\nomeqref {0}|nompageref}{1} +\nomenclatureentry{O$V$@[{$V$}]\begingroup Constant Volume\nomeqref {0}|nompageref}{1} +\nomenclatureentry{O$\rho$@[{$\rho$}]\begingroup Friction Index\nomeqref {0}|nompageref}{1} diff --git a/tex/review.tex b/tex/review.tex index b9dd04d..481423e 100644 --- a/tex/review.tex +++ b/tex/review.tex @@ -22,9 +22,6 @@ \begin{document} \title{Review: A Neural Algorithm of Artistic Style} -%% TODO: notations section? -%% TODO: clarify notations for both content and styl representation (N_l etc.) - \author{ James C. Kauten \\ Department of Software Engineering \\ @@ -59,7 +56,7 @@ \section{Paper Summary} T\"{u}bingen, Germany in the style of Claude Monet's \textit{Houses of Parliament}. -\begin{figure}[htp] +\begin{figure} \centering \caption{Style Transfer from $\textbf{a}$ to $\textbf{p}$ via $\textbf{x}$} \label{basic-example} @@ -98,11 +95,10 @@ \subsection{Content Representation} $\frac{1}{2}$ to simplify the formulation of the analytical gradient in Eq. \ref{eq:content-grad}. -% TODO: note the M_l and N_l variables in the above paragraph \begin{equation} \label{eq:content-loss} \mathcal{L}_{content}(\mathbf{p}, \mathbf{x}, l) = -\frac{1}{2} \sum_{i=1}^{N_l}\sum_{j=1}^{M_l}{(F^l_{ij} - P^l_{ij})^2} +\frac{1}{2} \sum_{i,j}{(F^l_{ij} - P^l_{ij})^2} \end{equation} \begin{equation} @@ -134,7 +130,7 @@ \subsubsection{Content Reconstruction} this looser representation allows the content to blend more smoothly with other images while still preserving the global features of the content. -\begin{figure}[htp] +\begin{figure} \centering \caption{Content Reconstruction of \textit{T\"{u}bingen, Germany}} \label{fig:content-reconstruction} @@ -173,12 +169,16 @@ \subsection{Style Representation} feature responses of particular layers in the \ac{CNN}. However, this representation uses a different feature space. Converting each activation map to a \textit{gram matrix} allows the extraction of just the texture from -a given image. It does so by computing the correlations between different -filters in an arbitrary convolutional layer $l$. Simply put, the gram matrix -$G^l$ for an activation map is the inner product of feature maps: +a given image. It does so by computing the correlations between $N_l$ +different filters in an arbitrary convolutional layer $l$. Simply put, the +gram matrix $G^l$ for an activation map is the inner product of feature maps. +Eq. \ref{eq:gram-matrix} shows a formulation of the gram matrix. Note that +$F$ is flattened about the height and width dimension. This reduces the two +dimensions to a new dimension of length $M_l = height * width$. \begin{equation} -G_{i j}^l = \sum_{k}^{M_l} F_{i k}^l F_{j k}^l +\label{eq:gram-matrix} +G_{i j}^l = \sum_{k}^{N_l} F_{i k}^l F_{j k}^l \end{equation} With a new feature space representation of raw texture, @@ -188,13 +188,12 @@ \subsection{Style Representation} for $\textbf{a}$ and $\textbf{x}$ are transformed to their respective gram matrices $A^l$, and $G^l$. Then, much like the content loss, we define the style loss for a given layer as the squared euclidean distance between the -gram matrices $A^l$, and $G^l$: +gram matrices $A^l$, and $G^l$. Eq. \ref{eq:style-loss-single-layer} shows the +formulation of the style loss for a single layer $l$. \begin{equation} -E_l = -\frac{1}{4 N_l^2 M_l^2} -\sum_{i=1}^{N_l}\sum_{j=1}^{M_l} -(G^l_{ij} - A^l_{ij})^2 +\label{eq:style-loss-single-layer} +E_l = \frac{1}{4 N_l^2 M_l^2} \sum_{i,j} (G^l_{ij} - A^l_{ij})^2 \end{equation} \cite{2015arXiv150806576G} incorporate multiple layers in the style loss using @@ -241,7 +240,7 @@ \subsubsection{Style Reconstruction} $\textbf{a}$. As more layers contribute to the loss, the details of the texture spread and smoothen across the noise image $\textbf{x}$. -\begin{figure}[htp] +\begin{figure} \centering \caption{Style Reconstruction of Vincent Van Gogh's \textit{A Starry Night}} \label{fig:style-reconstruction} @@ -399,7 +398,7 @@ \section{Questions \& Answers} layers in the style loss. We see that the additional layers do in fact help transfer more of the style. -\begin{figure}[htp] +\begin{figure} \centering \caption{Samford Hall Styled as Pablo Picasso's \textit{Seated Nude} Using Different Style Loss Layer Sets} @@ -442,7 +441,7 @@ \section{Questions \& Answers} somewhere between these. That said, "optimal" depends on the viewers' taste in images. -\begin{figure}[htp] +\begin{figure} \centering \caption{Samford Hall Styled as Pablo Picasso's \textit{Seated Nude} Using Different Content Loss Layers} @@ -485,7 +484,7 @@ \section{Questions \& Answers} portrays how the algorithm can use a photo of New York at night to style a photo of Atlanta at day, resulting in a new image of Atlanta at dusk. -\begin{figure}[htp] +\begin{figure} \centering \caption{Photo-realistic Style Transfer} \label{fig:photo-realistic-style-transfer} @@ -513,7 +512,7 @@ \section{Questions \& Answers} from VGG19, the AlexNet results hardly resembles either image, let alone a transfer of style from one to another. -\begin{figure}[htp] +\begin{figure} \centering \caption{Style Transfer Using AlexNet} \label{fig:alex-net-transfer} @@ -536,7 +535,7 @@ \section{Questions \& Answers} \ref{fig:deep-dream} shows Vincent Van Gogh's \textit{The Starry Night} styled in a "deep dream". -\begin{figure}[htp] +\begin{figure} \centering \caption{\textit{Deep Dream}: Style Transfer Using Inception Net} \label{fig:deep-dream} @@ -625,6 +624,7 @@ \section{Questions \& Answers} % MARK: bibliography %% print the bibliography using the custom NIPS bib style +\clearpage \bibliographystyle{my-unsrtnat} \bibliography{references} @@ -633,7 +633,7 @@ \section{Questions \& Answers} % MARK: appendix % \appendix -\begin{figure}[htp] +\begin{figure} \centering \caption{Style Transfer} \label{fig:style-transfer}