Adding the paper

Paper/Literatur.bib

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+% Encoding: UTF-8
+
+@Misc{jetsonNano,
+  howpublished = {https://developer.nvidia.com/embedded/jetson-nano-developer-kit},
+  note         = {Accessed: 2022-03-24},
+  title        = {{Jetson Nano Developer Kit}},
+}
+
+@Misc{nvidia3070ti,
+  howpublished = {https://www.nvidia.com/en-us/geforce/graphics-cards/30-series/rtx-3070-3070ti/},
+  note         = {Accessed: 2022-03-24},
+  title        = {{GeForce RTX 3070 Familiy - Specs}},
+}
+
+@Misc{jetsonNanoTensorFlow,
+  howpublished = {https://forums.developer.nvidia.com/t/official-tensorflow-for-jetson-nano/71770},
+  note         = {Accessed: 2022-03-24},
+  title        = {{Official TensorFlow for Jetson Nano!}},
+}
+
+@Misc{opencv,
+  howpublished = {https://opencv.org/releases/},
+  note         = {Accessed: 2022-03-24},
+  title        = {{OpenCV - releases}},
+}
+
+@Misc{resnet,
+  author    = {He, Kaiming and Zhang, Xiangyu and Ren, Shaoqing and Sun, Jian},
+  title     = {Deep Residual Learning for Image Recognition},
+  year      = {2015},
+  copyright = {arXiv.org perpetual, non-exclusive license},
+  doi       = {10.48550/ARXIV.1512.03385},
+  keywords  = {Computer Vision and Pattern Recognition (cs.CV), FOS: Computer and information sciences},
+  publisher = {arXiv},
+  url       = {https://arxiv.org/abs/1512.03385},
+}
+
+@InProceedings{vanishingGradients,
+  author    = {Tan, Hong Hui and Lim, King Hann},
+  booktitle = {2019 7th International Conference on Smart Computing Communications (ICSCC)},
+  title     = {Vanishing Gradient Mitigation with Deep Learning Neural Network Optimization},
+  year      = {2019},
+  pages     = {1-4},
+  doi       = {10.1109/ICSCC.2019.8843652},
+}
+
+@Misc{overparameterization,
+  author    = {Allen-Zhu, Zeyuan and Li, Yuanzhi and Liang, Yingyu},
+  title     = {Learning and Generalization in Overparameterized Neural Networks, Going Beyond Two Layers},
+  year      = {2018},
+  copyright = {arXiv.org perpetual, non-exclusive license},
+  doi       = {10.48550/ARXIV.1811.04918},
+  keywords  = {Machine Learning (cs.LG), Data Structures and Algorithms (cs.DS), Neural and Evolutionary Computing (cs.NE), Optimization and Control (math.OC), Machine Learning (stat.ML), FOS: Computer and information sciences, FOS: Mathematics},
+  publisher = {arXiv},
+  url       = {https://arxiv.org/abs/1811.04918},
+}
+
+@Misc{autoencoderImg,
+  howpublished = {https://en.wikipedia.org/wiki/Autoencoder\#/media/File:Autoencoder\_structure.png},
+  note         = {Accessed: 2022-03-24},
+  title        = {{Schematic structure of an autoencoder with 3 fully connected hidden layers. The code (z, or h for reference in the text) is the most internal layer.}},
+}
+
+@Misc{residualConnectionImg,
+  howpublished = {https://i.stack.imgur.com/d9HNk.png},
+  note         = {Accessed: 2022-03-24},
+  title        = {{Figure of a residual connection}},
+}
+
+@Misc{ConvolutionAnimation,
+  howpublished = {https://spinkk.github.io/singlekernel\_nopadding.html},
+  note         = {Accessed: 2022-03-24},
+  title        = {{Animation of a Convolution}},
+}
+
+@Article{colorize,
+  author    = {Zhang, Richard and Isola, Phillip and Efros, Alexei A.},
+  title     = {Colorful Image Colorization},
+  year      = {2016},
+  copyright = {arXiv.org perpetual, non-exclusive license},
+  doi       = {10.48550/ARXIV.1603.08511},
+  keywords  = {Computer Vision and Pattern Recognition (cs.CV), FOS: Computer and information sciences, FOS: Computer and information sciences},
+  publisher = {arXiv},
+  url       = {https://arxiv.org/abs/1603.08511},
+}
+
+@Comment{jabref-meta: databaseType:bibtex;}

Paper/Literatur.bib.bak

@@ -0,0 +1,87 @@
+% Encoding: UTF-8
+
+@Misc{jetsonNano,
+  howpublished = {https://developer.nvidia.com/embedded/jetson-nano-developer-kit},
+  note         = {Accessed: 2022-03-24},
+  title        = {{Jetson Nano Developer Kit}},
+}
+
+@Misc{nvidia3070ti,
+  howpublished = {https://www.nvidia.com/en-us/geforce/graphics-cards/30-series/rtx-3070-3070ti/},
+  note         = {Accessed: 2022-03-24},
+  title        = {{GeForce RTX 3070 Familiy - Specs}},
+}
+
+@Misc{jetsonNanoTensorFlow,
+  howpublished = {https://forums.developer.nvidia.com/t/official-tensorflow-for-jetson-nano/71770},
+  note         = {Accessed: 2022-03-24},
+  title        = {{Official TensorFlow for Jetson Nano!}},
+}
+
+@Misc{opencv,
+  howpublished = {https://opencv.org/releases/},
+  note         = {Accessed: 2022-03-24},
+  title        = {{OpenCV - releases}},
+}
+
+@Misc{resnet,
+  author    = {He, Kaiming and Zhang, Xiangyu and Ren, Shaoqing and Sun, Jian},
+  title     = {Deep Residual Learning for Image Recognition},
+  year      = {2015},
+  copyright = {arXiv.org perpetual, non-exclusive license},
+  doi       = {10.48550/ARXIV.1512.03385},
+  keywords  = {Computer Vision and Pattern Recognition (cs.CV), FOS: Computer and information sciences},
+  publisher = {arXiv},
+  url       = {https://arxiv.org/abs/1512.03385},
+}
+
+@InProceedings{vanishingGradients,
+  author    = {Tan, Hong Hui and Lim, King Hann},
+  booktitle = {2019 7th International Conference on Smart Computing Communications (ICSCC)},
+  title     = {Vanishing Gradient Mitigation with Deep Learning Neural Network Optimization},
+  year      = {2019},
+  pages     = {1-4},
+  doi       = {10.1109/ICSCC.2019.8843652},
+}
+
+@Misc{overparameterization,
+  author    = {Allen-Zhu, Zeyuan and Li, Yuanzhi and Liang, Yingyu},
+  title     = {Learning and Generalization in Overparameterized Neural Networks, Going Beyond Two Layers},
+  year      = {2018},
+  copyright = {arXiv.org perpetual, non-exclusive license},
+  doi       = {10.48550/ARXIV.1811.04918},
+  keywords  = {Machine Learning (cs.LG), Data Structures and Algorithms (cs.DS), Neural and Evolutionary Computing (cs.NE), Optimization and Control (math.OC), Machine Learning (stat.ML), FOS: Computer and information sciences, FOS: Mathematics},
+  publisher = {arXiv},
+  url       = {https://arxiv.org/abs/1811.04918},
+}
+
+@Misc{autoencoderImg,
+  howpublished = {https://en.wikipedia.org/wiki/Autoencoder\#/media/File:Autoencoder\_structure.png},
+  note         = {Accessed: 2022-03-24},
+  title        = {{Schematic structure of an autoencoder with 3 fully connected hidden layers. The code (z, or h for reference in the text) is the most internal layer.}},
+}
+
+@Misc{residualConnectionImg,
+  howpublished = {https://i.stack.imgur.com/d9HNk.png},
+  note         = {Accessed: 2022-03-24},
+  title        = {{Figure of a residual connection}},
+}
+
+@Misc{ConvolutionAnimation,
+  howpublished = {https://spinkk.github.io/singlekernel\_nopadding.html},
+  note         = {Accessed: 2022-03-24},
+  title        = {{Animation of a Convolution}},
+}
+
+@Article{colorize,
+  author    = {Zhang, Richard and Isola, Phillip and Efros, Alexei A.},
+  title     = {Colorful Image Colorization},
+  year      = {2016},
+  copyright = {arXiv.org perpetual, non-exclusive license},
+  doi       = {10.48550/ARXIV.1603.08511},
+  keywords  = {Computer Vision and Pattern Recognition (cs.CV), FOS: Computer and information sciences, FOS: Computer and information sciences},
+  publisher = {arXiv},
+  url       = {https://arxiv.org/abs/1603.08511},
+}
+
+@Comment{jabref-meta: databaseType:bibtex;}

Paper/Main.aux

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+\bibstyle{ieeetr}
+\bibdata{Literatur}
+\bibcite{jetsonNano}{1}
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+\newlabel{fig:Loss_compareModels}{{9}{8}}
+\@writefile{toc}{\contentsline {section}{\numberline {7}Conclusion}{8}{}\protected@file@percent }
+\bibcite{nvidia3070ti}{2}
+\bibcite{ConvolutionAnimation}{3}
+\bibcite{autoencoderImg}{4}
+\bibcite{jetsonNanoTensorFlow}{5}
+\bibcite{opencv}{6}
+\bibcite{residualConnectionImg}{7}
+\bibcite{vanishingGradients}{8}
+\bibcite{resnet}{9}
+\bibcite{overparameterization}{10}
+\bibcite{colorize}{11}
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Paper/Main.bbl

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+\begin{thebibliography}{10}
+
+\bibitem{jetsonNano}
+``{Jetson Nano Developer Kit}.''
+  https://developer.nvidia.com/embedded/jetson-nano-developer-kit.
+\newblock Accessed: 2022-03-24.
+
+\bibitem{nvidia3070ti}
+``{GeForce RTX 3070 Familiy - Specs}.''
+  https://www.nvidia.com/en-us/geforce/graphics-cards/30-series/rtx-3070-3070ti/.
+\newblock Accessed: 2022-03-24.
+
+\bibitem{ConvolutionAnimation}
+``{Animation of a Convolution}.''
+  https://spinkk.github.io/singlekernel\_nopadding.html.
+\newblock Accessed: 2022-03-24.
+
+\bibitem{autoencoderImg}
+``{Schematic structure of an autoencoder with 3 fully connected hidden layers.
+  The code (z, or h for reference in the text) is the most internal layer.}.''
+  https://en.wikipedia.org/wiki/Autoencoder\#/media/File:Autoencoder\_structure.png.
+\newblock Accessed: 2022-03-24.
+
+\bibitem{jetsonNanoTensorFlow}
+``{Official TensorFlow for Jetson Nano!}.''
+  https://forums.developer.nvidia.com/t/official-tensorflow-for-jetson-nano/71770.
+\newblock Accessed: 2022-03-24.
+
+\bibitem{opencv}
+``{OpenCV - releases}.'' https://opencv.org/releases/.
+\newblock Accessed: 2022-03-24.
+
+\bibitem{residualConnectionImg}
+``{Figure of a residual connection}.'' https://i.stack.imgur.com/d9HNk.png.
+\newblock Accessed: 2022-03-24.
+
+\bibitem{vanishingGradients}
+H.~H. Tan and K.~H. Lim, ``Vanishing gradient mitigation with deep learning
+  neural network optimization,'' in {\em 2019 7th International Conference on
+  Smart Computing Communications (ICSCC)}, pp.~1--4, 2019.
+
+\bibitem{resnet}
+K.~He, X.~Zhang, S.~Ren, and J.~Sun, ``Deep residual learning for image
+  recognition,'' 2015.
+
+\bibitem{overparameterization}
+Z.~Allen-Zhu, Y.~Li, and Y.~Liang, ``Learning and generalization in
+  overparameterized neural networks, going beyond two layers,'' 2018.
+
+\bibitem{colorize}
+R.~Zhang, P.~Isola, and A.~A. Efros, ``Colorful image colorization,'' 2016.
+
+\end{thebibliography}

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Paper/Main.lot

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+\documentclass[a4paper,12pt, listof=totoc,toc=sectionentrywithdots]{scrartcl}
+
+\usepackage{graphicx}
+
+\usepackage{color}
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+
+\usepackage{titling}
+\renewcommand\maketitlehooka{\null\mbox{}\vfill}
+\renewcommand\maketitlehookd{\vfill\null}
+
+
+\title{Colorization of Grey Images by applying a Convolutional Autoencoder on the Jetson Nano}
+\date{}
+\author{Tim Niklas Witte and Dennis Konkol}
+
+
+\lstset{
+numbersep=8pt, 
+frame = single, 
+framexleftmargin=15pt,
+framesep=1.5pt, framerule=1.5pt}
+
+\begin{document}
+
+\begin{titlingpage}
+\maketitle
+\end{titlingpage}
+
+
+
+\tableofcontents
+
+\pagenumbering{gobble}
+
+
+\cleardoublepage
+\pagenumbering{arabic}
+
+\section{Introduction}
+Embedded GPUs such as the Jetson Nano provide limited hardware resources than desktop/server GPUs.
+For example, the Jetson Nano has 128 CUDA cores and 4 GB of video memory, compared to the NVIDIA GeForce RTX 3070 Ti which has 6144 CUDA cores and 8 GB of video memory.
+Inference done by massive artificial neural networks (ANN) e.g. over 25.000.000 parameters on the Jetson Nano, becomes slow - about 0.01 forward pass per second.
+An NVIDIA GeForce RTX 3070 Ti does 32 forward passes through the same huge ANN, and this can be achieved within a second.
+This paper presents a convolutional autoencoder for grey image colorization with 300.000 parameters optimized to run on embedded GPUs.
+In order to demonstrate the results during runtime on the Jetson Nano, the live grey camera stream is colorized, as shown in Figure~\ref{fig:OpenCV_window}.  
+
+\begin{figure}[h]
+\centering
+        \includegraphics[totalheight=4cm]{Figures/OpenCV_window.png}
+    \caption{OpenCV window on the Jetson Nano displaying the original, grey, colorized camera stream and corresponding loss between original and colorized image.}
+    \label{fig:OpenCV_window}
+\end{figure}
+
+This paper is organized as follows:
+The concept of a convolutional autoencoder will be covered in section 2.
+Section 3 explains the necessary software and hardware setup on the Jetson Nano.
+The training procedure, including the model architecture, is discussed in section 4.
+Optimization techniques of our model considering running on the Jetson Nano are presented in section 5.
+In section 6, the performance of our model is evaluated by comparing the colorized images generated by our models and by a state-of-the-art ANN for grey image colorization, which has about 25.000.000 parameters.
+Finally, the final results are summed up in section 7.
+
+\section{Convolutional Autoencoder}
+
+\subsection{Convolutions}
+
+Convolutions detect features and extract these from images by applying a filter kernel which is a weight matrix.
+As shown in Figure ~\ref{fig:convolution}, a convolution iterates a filter kernel over the entire image.
+During each iteration, an area with the same size as the kernel is processed by an element-wise multiplication followed by summing each value up, representing the result for the area of this image.
+This area is shifted one step (depending on side size) further to the right in the next step. 
+The same processing step occurs again.
+
+\begin{figure}[h]
+\centering
+        \includegraphics[totalheight=5cm]{Figures/convolution.png}
+    \caption{Concept of a convolution~\cite{ConvolutionAnimation}.}
+    \label{fig:convolution}
+\end{figure}
+
+
+\subsection{Autoencoder}
+
+Autoencoders are artificial neural networks used to learn features of unlabeled data.
+As presented in Figure~\ref{fig:autoencoder}, the encoder part compresses the data by gradually decrease of the layer size.
+The resulting embedding/code is passed to the decoder part responsible for
+reconstructing it.
+In the decoder, the layer size increases per layer.
+Overall, the input \texttt{X} and output \texttt{X'} shall be the same.
+
+\begin{figure}[h]
+\centering
+        \includegraphics[totalheight=5cm]{Figures/Autoencoder.png}
+    \caption{An Autoencoder compresses and decompresses the data~\cite{autoencoderImg}.}
+    \label{fig:autoencoder}
+\end{figure}
+
+Instead of fully connected layers, a convolutional autoencoder applies convolutions in the encoder and transposes convolutions in the decoder.
+
+\section{Setup}
+
+\subsection{Software}
+TensorFlow was installed following the official guide from NVIDIA~\cite{jetsonNanoTensorFlow}.
+Furthermore, it is not recommended to install the current version of OpenCV via pip3 due to compatibility issues with the CSI camera.
+The CSI camera i.e. the \texttt{gstream} can only be accessed with an OpenCV version lower than 3.3.1.
+This version was installed manually by downloading the source code from the official website and compiling it~\cite{opencv}.
+Besides, for speed purposes, the maximal performance mode was enabled by the command \texttt{sudo nvpmodel -m 0}.
+In order to enable the Jetson Clock, the command \texttt{sudo jetson\_clocks} was used.
+
+
+\subsection{Hardware}
+The CSI camera was plugged into the corresponding slot in the Jetson Nano.
+Furthermore, the HDMI display shows the OpenCV window as presented in Figure~\ref{fig:OpenCV_window}.
+
+
+\section{Training}
+
+\begin{wrapfigure}{r}{.4\textwidth}
+
+\centering
+        \includegraphics[totalheight=6cm]{Figures/LossPlot.png}
+    \caption{Train and test loss during training.}
+    \label{fig:trainTestLoss}
+
+\end{wrapfigure}
+At the beginning of training our model, we used the common RGB color space.
+In other words, the input was the grey scaled image, and the output was the RGB image.
+However, we lost too much information in the picture.
+So the general input picture was detectable but with a lot of "compression".
+The reason for this is that for one pixel, all three values of RGB are responsible for the brightness of that pixel.
+So it is possible to get the right color but not the correct brightness. That is why we switched to the CIE LAB color space.
+Here we also have three values for each pixel, the L channel for the
+'brightness' and A and B as the color channel.
+The L channel is like the grayscale image for the model.
+The model's output is two values, the A and B channels.
+So with the combination of the given A, B, and our old L values, we get the colored image. We get an overall correct image because of the kept L channel, even if the colors would not match the original
+image.
+
+The model was trained for 13 epochs (in total: 15 hours) with the ImageNet2012 dataset.
+It contains ca. 1.300.000 training images and 300.000 validation images used for test data.
+As presented in Figure~\ref{fig:trainTestLoss} the model was successfully trained to convergence because, after about ten epochs, the train loss does not change significantly ($< 0.0001$) compared with the loss to the next epoch.
+
+
+\subsection{Model}
+As shown in Listing~\ref{lst:ourModel_summary}, our convolutional autoencoder has about 300.000 parameters.
+The model's memory size is about 1.2 MB ($300000 \cdot 4$ Byte).
+Encoder and decoder parts of the ANN are equally balanced due to having almost the same amount of parameters.
+
+\begin{lstlisting}[language=bash, caption=Parameter amount of our model (output of \texttt{summary()} call)., label={lst:ourModel_summary}, basicstyle=\fontsize{11}{9}\selectfont\ttfamily]
+ Model: "autoencoder"
+_______________________________________________________________
+ Layer (type)                Output Shape            Param #   
+===============================================================
+ encoder (Encoder)           multiple                148155    
+                                                               
+ decoder (Decoder)           multiple                150145    
+                                                                 
+===============================================================
+Total params: 298,302
+Trainable params: 297,210
+Non-trainable params: 1,092
+_______________________________________________________________
+\end{lstlisting}
+
+
+Figure~\ref{fig:EncoderLayer} and~\ref{fig:DecoderLayer} present the structure of the layers contained in the encoder and decoder.
+The encoder receives a 256x256 pixel grey image.
+Due to the grey color, there is only one color channel.
+Convolutions can be seen as feature extractors.
+At the first convolution in the encoder (see \texttt{Conv2D\_0} in Figure~\ref{fig:EncoderLayer}), there are 75 features extracted from this grey image.
+These extracted features are represented as channels (similar to color channels but not colors) called feature maps.
+Literally speaking, a feature map could be seen as a heatmap in which the pixel belonging to the corresponding feature has a high magnitude.
+Due to the stride size of 2, the size of these features maps is halved.
+A convolution operation is followed by a batch normalization layer and an activation layer (the drive is normalized before its goes into the activation function).
+In the encoder this occurs four times.
+With each step, the amount of filters increases.
+
+\begin{figure}[h]
+  \centering
+  \begin{minipage}[b]{0.4\textwidth}
+    \includegraphics[width=\textwidth]{Figures/EncoderLayer.png}
+    \caption{Encoder layers.}
+    \label{fig:EncoderLayer}
+  \end{minipage}
+  \hfill
+  \begin{minipage}[b]{0.4\textwidth}
+    \includegraphics[width=\textwidth]{Figures/DecoderLayer.png}
+    \caption{Decoder layers.}
+    \label{fig:DecoderLayer}
+  \end{minipage}
+\end{figure}
+
+
+The resulting embedding is passed into the decoder.
+Instead of convolutions reducing the feature map size, transpose convolutions increase the feature map size by a factor of 2.
+Like the encoder, a transpose convolution is followed by batch normalization and activation layers.
+In the decoder this occurs four times.
+With each step, the amount of filters decreases.
+Except for the last transpose convolution, which is a bottleneck layer:
+It decreases the amount of filters from 75 to 2 (\textit{a} and \textit{b} channel) and keeps the feature map size constant (stride size = 1).
+
+
+\section{Optimizing the model to run on the Jetson Nano }
+
+
+\begin{wrapfigure}{r}{.4\textwidth}
+
+\centering
+        \includegraphics[totalheight=4cm]{Figures/ResidualConnection.png}
+    \caption{Concept of a residual connection~\cite{residualConnectionImg}.}
+    \label{fig:ResidualConnection}
+
+\end{wrapfigure}
+
+Residual connections also called skip connections in neural networks, face the vanishing gradient problem (tiny weight adjustments~\cite{vanishingGradients}) in the backpropagation algorithm~\cite{resnet}.
+As shown in Figure~\ref{fig:ResidualConnection}, the output \texttt{x} of a layer is added two layers further to the input of the third layer~\cite{resnet}.
+The output \texttt{x} must be saved due to it is used in a later time step.
+Therefore, residual connections need a lot of GPU memory, causing a outsource of a part of other data needed for the model.
+To speed up the FPS, our model does not have residual connections.
+
+As mentioned in the first section, the Jetson~Nano has 128 CUDA cores.
+The amount of filters per layer does not exceed this number of cores.
+This limitation enables TensorFlow simple scheduling of a feature map calculation to a specific core during the output calculation of a layer.
+In other words, there are no cores that must do a second filter map calculation after the first one while other cores are idling.
+The calculation of a previous layer must be finished before starting with the next layer.
+Furthermore, limiting the amount of filer reduces the model size.
+
+In Deep Learning, overparameterization often occurs:
+As a result, the number of trainable parameters is much larger than the number of training examples.
+As a consequence, the model tends to overfit the data~\cite{overparameterization}.
+The opposite applies to our model.
+Literally speaking, our model is "under-parameterized" -
+Due to there being only 300.000 parameters on about 1.3 million training images, our model is forced to generalize as strong as possible during training.
+To archive such generalization the model is trained multiple epochs (iteration over the entire training dataset).
+It is assumed that such generalization results in similar results compared with a model which has considerable amounts of parameters.
+In other words, the higher costs for training a small model compared with a larger model shall result in similar results but the latency to generate the result with the smaller model is lower.
+Besides, the non-existence of skip connections increases the chance of vanishing gradients during training.
+Although, multiple training epochs compensate this problem.
+To clarify, millions of tiny weight changes sum up into an effective weight adjustment.
+
+
+\section{Evaluation: Compare with Colorful Image Colorization}
+
+As demonstrated in Listing~\ref{lst:theirModel_summary}, the Colorful Image Colorization model from Richard Zhang et al. has about 25 million parameters~\cite{colorize}.
+The model presented in this paper is about 80 times smaller. 
+Its input shape is 256x256x1 and the same as our model.
+
+\begin{lstlisting}[language=bash, caption=Parameter amount of the Colorful Image Colorization model (output of \texttt{summary()} call)., label={lst:theirModel_summary}, basicstyle=\fontsize{11}{9}\selectfont\ttfamily]
+Model: "ColorfulImageColorization"
+_______________________________________________________________
+ Layer (type)                Output Shape              Param #   
+===============================================================
+[...]   
+                                                                 
+===============================================================
+Total params: 24,793,081
+Trainable params: 24,788,345
+Non-trainable params: 4,736
+_______________________________________________________________
+\end{lstlisting}
+
+
+Figure~\ref{fig:ColoredImages_compareModels} shows grey images colorized by the Colorful Image Colorization model~\cite{colorize} and by our model. 
+Our model tends to colorize the images with a grey touch and the colors are not saturated compared with the Colorful Image Colorization model.
+
+
+
+\begin{figure}
+\centering
+        \includegraphics[totalheight=13cm]{Figures/ColoredImages_compareModels.png}
+    \caption{Colorized images generated by the Colorful Image Colorization model from Richard Zhang et al. and by our model.}
+    \label{fig:ColoredImages_compareModels}
+\end{figure}
+
+
+Our model does regression by predicting the \textit{ab} values.
+The model output shape is 256x256x2 (see \texttt{tanh\_3} in Figure~\ref{fig:DecoderLayer}).
+In contrast to the model from Richard Zhang et al., classification is applied here:
+There is a probability distribution for each pixel approximating which color it may be.
+For demonstration purposes, there were 313 colors available.
+As a consequence, the model output shape is 256x256x313~\cite{colorize}.
+Compared to our model, the larger output shape requires a more extensive (ca. 80 times) amount of parameters.
+
+
+
+\begin{figure}[h]
+\centering
+        \includegraphics[totalheight=6cm]{Figures/ColorizedImagesLossPlot_comparedModels.png}
+    \caption{Loss based on colorized images by the 
+    Colorful Image Colorization model from Richard Zhang et al. and by our model.}
+    \label{fig:Loss_compareModels}
+\end{figure}
+
+Considering the loss as shown in Figure~\ref{fig:Loss_compareModels},
+our model outperforms the model from Richard Zhang et al.
+However, the euclidean loss (mean squared error) $L_2(\hat{y}, y)$ for the prediction $y$ and the target (also called ground truth) $\hat{y}$ was applied:
+
+\[ L_2(\hat{y}, y) = \frac{1}{2} \cdot \sum_{h,w} || y_{h,w} - \hat{y}_{h,w} ||^{2} \]
+
+The loss function is ambiguous for the colorization problem.
+Consider the prediction $y$ for a single pixel with a loss of $d$:
+There are two corresponding targets $\hat{y} = y \pm d$ possible instead of a single one.
+Furthermore, consider a set of pixels. For each of these pixels, a corresponding color will be predicted.
+The optimal solution is the mean of all pixels within this set.
+In the case of color prediction, this averaging causes a grey bias and desaturated colors~\cite{colorize}.
+
+
+
+\section{Conclusion}
+
+
+Our model predicts the most possible color by applying regression.
+In contrast to the model proposed by Richard Zhang et al. which classifies the most possible color.
+Due to the one-hot encoding applied for these color classifications, over 80 times more parameters are needed as required for our model, considering the parameter balance between hidden layers and output layers.
+Comparing the colorized images generated by an ANN based on classification and by regression, regression-based ANN tends to colorize images with a grey touch and unsaturated colors because of an ambiguous loss function for the colorization problem.
+However, the results are acceptable considering the difference in the number of parameters between the two models.
+Furthermore, a GPU cannot ultimately accelerate a classification-based model because the last part of the model is a sampling process.
+This process is an argmax operation over 313 possible colors (see model shape) which runs on the CPU.
+Note that transferring data from GPU to CPU could be seen as a performance bottleneck.
+
+Overall, our model archives about 10 FPS on the Jetson Nanos.
+Running the Richard Zhang et al. model will result in less than 0.01 FPS.
+
+
+
+ 
+
+
+
+
+
+
+\bibliographystyle{ieeetr}
+\bibliography{Literatur}
+
+\end{document}
+

Paper/Main.toc

@@ -0,0 +1,14 @@
+\contentsline {section}{\numberline {1}Introduction}{1}{}%
+\contentsline {section}{\numberline {2}Convolutional Autoencoder}{1}{}%
+\contentsline {subsection}{\numberline {2.1}Convolutions}{1}{}%
+\contentsline {subsection}{\numberline {2.2}Autoencoder}{2}{}%
+\contentsline {section}{\numberline {3}Setup}{3}{}%
+\contentsline {subsection}{\numberline {3.1}Software}{3}{}%
+\contentsline {subsection}{\numberline {3.2}Hardware}{3}{}%
+\contentsline {section}{\numberline {4}Training}{3}{}%
+\contentsline {subsection}{\numberline {4.1}Model}{4}{}%
+\contentsline {section}{\numberline {5}Optimizing the model to run on the Jetson Nano}{4}{}%
+\contentsline {section}{\numberline {6}Evaluation: Compare with Colorful Image Colorization}{6}{}%
+\contentsline {section}{\numberline {7}Conclusion}{8}{}%
+\contentsline {section}{References}{9}{}%
+\providecommand \tocbasic@end@toc@file {}\tocbasic@end@toc@file