diff --git a/thesis/Main.tex b/thesis/Main.tex
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+++ b/thesis/Main.tex
@@ -250,7 +250,13 @@
 
 
 \newchapter{deepsad}{DeepSAD: Semi-Supervised Anomaly Detection}
- Deep Semi-Supervised Anomaly Detection~\cite{deepsad} is a deep-learning based anomaly detection method whose performance in regards to sensor degradation quantification we explore in this thesis. It is a semi-supervised method which allows the introduction of manually labeled samples in addition to the unlabeled training data to improve the algorithm's performance over its unsupervised predecessor Deep One-Class Classification~\cite{deepsvdd}.\todo{phrasing} The working principle of the method is to encode the input data onto a latent space and train the network to cluster normal data close together while anomalies get mapped further away in that latent space. 
+
+  %In this chapter we explore the method \emph{Deep Semi-Supervised Anomaly Detection}~\cite{deepsad} which we employed during our experiments to quanitfy the degradation of lidar scans caused by artifically introduced water vapor from a theater smoke machine. The same approach of modeling a degradation quantification problem as an anomaly detection task was succesfully used in \cite{degradation_quantification_rain} to quantify the degradation caused to lidar scans by bad weather conditions such as rain, fog and snow for autonomous driving tasks. DeepSAD is characterized by it being a deep-learning approach to anomaly detection which enables it to learn more complex anomalous data patterns than more classic statistical approaches and its capability of employing hand-labeled data samples-both normal and anomalous-during its training step to better teach the model to differentiate between know anomalies and normal data than if only an unsupervised approach was used which basically just learns the most common patterns in the implicitely more common normal data and to differentiate anything from that.
+
+In this chapter, we explore the method \emph{Deep Semi-Supervised Anomaly Detection} (DeepSAD)~\cite{deepsad}, which we employed to quantify the degradation of LiDAR scans caused by artificially introduced water vapor from a theater smoke machine. A similar approach—modeling degradation quantification as an anomaly detection task—was successfully applied in \cite{degradation_quantification_rain} to assess the impact of adverse weather conditions (rain, fog, and snow) on LiDAR data for autonomous driving applications. DeepSAD leverages deep learning to capture complex anomalous patterns that classical statistical methods might miss. Furthermore, by incorporating a limited amount of hand-labeled data (both normal and anomalous), it can more effectively differentiate between known anomalies and normal data compared to purely unsupervised methods, which typically learn only the most prevalent patterns in the dataset.
+
+
+ %Deep Semi-Supervised Anomaly Detection~\cite{deepsad} is a deep-learning based anomaly detection method whose performance in regards to sensor degradation quantification we explore in this thesis. It is a semi-supervised method which allows the introduction of manually labeled samples in addition to the unlabeled training data to improve the algorithm's performance over its unsupervised predecessor Deep One-Class Classification~\cite{deepsvdd}. The working principle of the method is to encode the input data onto a latent space and train the network to cluster normal data close together while anomalies get mapped further away in that latent space. 
     %\todo[inline, color=green!40]{DeepSAD is a semi-supervised anomaly detection method proposed in cite, which is based on an unsupervised method (DeepSVDD) and additionally allows for providing some labeled data which is used during the training phase to improve the method's performance}
     \newsection{algorithm_description}{Algorithm Description}
     %\todo[inline]{explain deepsad in detail}
@@ -390,6 +396,8 @@ While the density of these near-sensor returns might be used to estimate data qu
     %END early returns
 
     \newsection{preprocessing}{Preprocessing Steps and Labeling}
+
+    \newsubsubsectionNoTOC{Preprocessing}
     %\todo{describe how 3d lidar data was preprocessed (2d projection), labeling}
     %\todo[inline]{screenshots of 2d projections?}
 
@@ -397,23 +405,41 @@ While the density of these near-sensor returns might be used to estimate data qu
 
     %As described in section~\ref{sec:algorithm_description} the method we want to evaluate is datatype agnostic and can be adjusted to work with any kind of data. The data from~\cite{subter} that we will train on is a point cloud per scan created by the lidar sensor which contains up to 65536 points with \emph{X}, \emph{Y}, and \emph{Z} coordinates (in meters) per point. To adjust the architecture of DeepSAD to work with a specific datatype, we have to define an autoencoder architecture that works for the given datatype. While autoencoders can be created for any datatype, as~\cite{autoencoder_survey} points out over 60\% of research papers pertaining autoencoders in recent years look at image classification and reconstruction, so we have a better understanding of their architectures for two dimensional images than for three dimensional point clouds.
 
-    As described in Section~\ref{sec:algorithm_description}, the method under evaluation is data type agnostic and can be adapted to work with any kind of data. In our case, we train on point clouds from~\cite{subter}, where each scan produced by the LiDAR sensor contains up to 65,536 points, with each point represented by its \emph{X}, \emph{Y}, and \emph{Z} coordinates. To tailor the DeepSAD architecture to this specific data type, we must design an autoencoder suitable for processing three-dimensional point clouds. Although autoencoders can be developed for various data types, as noted in~\cite{autoencoder_survey}, over 60\% of recent research on autoencoders focuses on two-dimensional image classification and reconstruction. Consequently, there is a more established understanding of architectures for images compared to those for three-dimensional point clouds.
+    As described in Section~\ref{sec:algorithm_description}, the method under evaluation is data type agnostic and can be adapted to work with any kind of data. In our case, we train on point clouds from~\cite{subter}, where each scan produced by the LiDAR sensor contains up to 65,536 points, with each point represented by its \emph{X}, \emph{Y}, and \emph{Z} coordinates. To tailor the DeepSAD architecture to this specific data type, we would need to design an autoencoder suitable for processing three-dimensional point clouds. Although autoencoders can be developed for various data types, as noted in~\cite{autoencoder_survey}, over 60\% of recent research on autoencoders focuses on two-dimensional image classification and reconstruction. Consequently, there is a more established understanding of architectures for images compared to those for three-dimensional point clouds.
 
     %\todo[inline, color=green!40]{to achieve this transformation we used the helpful measurement index and channel present in each measurement point of the dataset which allowed a perfect reconstruction of the 2d projection without calculating the pixel position in the projection of each measurement via angles which in our experience typically leads to some ambiguity in the projection (multiple measurements mapping to the same pixel due to precision loss/other errors) the measurement index increases even for unavailable measurements (no ray return) so we can simply create the 2d projection by mapping the normalized range (FIXME really normalized) value to the pixel position y = channel, x = measurement index. by initalizing the array to NaN values originally we have a 2d data structure with the range values and NaN on pixel positions where originally no measurement took place (missing measurements in scans due to no ray return)}
 
     %For this reason we decided to preprocess the point clouds by converting them to two dimensional grayscale images using spherical projection. Additionally, \cite{degradation_quantification_rain}-which we modeled our approach after-successfully chose this approach. In the projected image each measurement is encoded to a single pixel, whose grayscale value $v$ is the normalized range of the measurement $v = \sqrt{\emph{X}^2 + \emph{Y}^2 + \emph{Z}^2}$. Due to the settings of the datasets' lidar, this results in images with the resolution of 2048 pixels wide by 32 pixels tall. Missing measurements of the point cloud are mapped to pixels with a brightness of 0. To create the mapping we used the measurements indices and channels which are available since the dataset contains dense point clouds and which can be used since the point indices are ordered from 0 to 65535 horizontally ascending channel by channel. For point clouds without indices which can be directly mapped, as is often the case for sparse ones, it would be necessary to use the pitch and yaw angles to the sensor origin to map each point to a pixel on the projection.
 
-    To simplify further processing, we converted the point clouds into two-dimensional grayscale images using a spherical projection. This approach—also employed successfully in \cite{degradation_quantification_rain}—encodes each LiDAR measurement as a single pixel, where the pixel’s grayscale value is determined by the normalized range, calculated as $v = \sqrt{\emph{X}^2 + \emph{Y}^2 + \emph{Z}^2}$. Given the LiDAR sensor's configuration, the resulting images have a resolution of 2048 pixels in width and 32 pixels in height. Missing measurements in the point cloud are mapped to pixels with a brightness value of 0.
+    For this reason and to simplify the architecture, we converted the point clouds into two-dimensional grayscale images using a spherical projection. This approach—also employed successfully in \cite{degradation_quantification_rain}—encodes each LiDAR measurement as a single pixel, where the pixel’s grayscale value is determined by the normalized range, calculated as $v = \sqrt{\emph{X}^2 + \emph{Y}^2 + \emph{Z}^2}$. Given the LiDAR sensor's configuration, the resulting images have a resolution of 2048 pixels in width and 32 pixels in height. Missing measurements in the point cloud are mapped to pixels with a brightness value of 0.
 
 To create this mapping, we leveraged the available measurement indices and channel information inherent in the dense point clouds, which are ordered from 0 to 65,535 in a horizontally ascending, channel-by-channel manner. For sparser point clouds without such indices, one would need to rely on the pitch and yaw angles relative to the sensor's origin to correctly map each point to its corresponding pixel.
 
-    \todo[inline, color=green!40]{add two projections one with one without smoke to  }
+%In figure~\ref{fig:data_projections} we see two projections of lidar point clouds from the experiments, which are visually different from the preprocessed data for better understanding of the reader. While the point clouds were converted to grayscale images with a resolution of 2048 by 32 pixels, these projections can be hard to interpret for humans. For this reason the projections are depicted using the viridis colormap and vertically stretched, so single measurements are multiple pixels tall, since otherwise the image is only 32 pixels tall and hard to decipher. The top projection was created from a lidar scan where no artifical smoke and therefore appreciable degradation was present, whereas the lower projection is from an experiment with artifical smoke and a lot of degradation. 
 
+Figure~\ref{fig:data_projections} displays two examples of LiDAR point cloud projections to aid in the reader’s understanding. Although the original point clouds were converted into grayscale images with a resolution of 2048×32 pixels, these raw images can be challenging to interpret. To enhance human readability, we applied the viridis colormap and vertically stretched the images so that each measurement occupies multiple pixels in height. The top projection is derived from a scan without artificial smoke—and therefore minimal degradation—while the lower projection comes from an experiment where artificial smoke introduced significant degradation.
 
-    \todo[inline, color=green!40]{another important preprocessing step is labeling of the lidar frames as normal/anormal. this is one hand used during training (experiments with zero labeled up to most of the data being labeled) and on the other hand is important for evaluation of the method performance. originally we do not have any labels on the data regarding degradation and no analog values from another sensor which measures current smoke particles in the air. our simple approach was to label all frames from experiments which included artifical degradation by fog machine smoke as anomalous and all frames from experiments without artifical degradation as normal.}
-    \todo[inline, color=green!40]{this simple labeling method is quite flawed since we do not label based on the actual degradation of the scan (not by some kind of threshold of analog measurement threshold, statistical info about scan) since (TODO FIXME) this would result in training which only learns this given metric (example missing measurement points) which would make this methodology useless since we could simply use that same measurement as an more simple way to quantify the scan's degradation. }
-    \todo[inline]{TODO maybe evaluate based on different thresholds? missing datapoints, number of detected outliers, number of particles in phantom circle around sensor?}
+    \todo[inline, color=green!40]{add same projections as they are used in training}
 
+    \fig{data_projections}{figures/data_2d_projections.png}{Two-dimensional projections of two pointclouds, one from an experiment without degradation and one from an experiment with artifical smoke as degradation}
+
+    \newsubsubsectionNoTOC{Labeling}
+
+    %\todo[inline, color=green!40]{another important preprocessing step is labeling of the lidar frames as normal/anormal. this is one hand used during training (experiments with zero labeled up to most of the data being labeled) and on the other hand is important for evaluation of the method performance. originally we do not have any labels on the data regarding degradation and no analog values from another sensor which measures current smoke particles in the air. our simple approach was to label all frames from experiments which included artifical degradation by fog machine smoke as anomalous and all frames from experiments without artifical degradation as normal.}
+
+    %We discussed the requirements to data labels in section~\ref{sec:data}, where we mentioned the challenges but also importance of correctly labeled data, especially for evaluation. Since to our knowledege no public dataset with objective labels regarding dataset degradation of lidar data in subterranean environments is available and the dataset chosen for evaluation in this thesis \cite{subter} does not contain any explicit data or measurements about the dedata degradation, we had to choose a method of how we would label the data ourselves for evaluation. After considering multiple avenues, we decided to simply label all point clouds created during experiments with artifical smoke present as anomalies and all point clouds from other experiments as normal data. 
+
+    We discussed the challenges and importance of obtaining correctly labeled data in Section~\ref{sec:data}, particularly for evaluation purposes. Since, to our knowledge, no public dataset provides objective labels for LiDAR data degradation in subterranean environments—and the dataset selected for this thesis \cite{subter} lacks explicit measurements of degradation—we had to develop our own labeling approach. After considering several options, we decided to label all point clouds from experiments with artificial smoke as anomalies, while point clouds from experiments without smoke were labeled as normal data.
+
+    %\todo[inline, color=green!40]{this simple labeling method is quite flawed since we do not label based on the actual degradation of the scan (not by some kind of threshold of analog measurement threshold, statistical info about scan) since (TODO FIXME) this would result in training which only learns this given metric (example missing measurement points) which would make this methodology useless since we could simply use that same measurement as an more simple way to quantify the scan's degradation. }
+
+    %This simplistic approach has both Advantages and disadvantages. The approach is simple to implement and provides a clear and straightforward distinction between normal and anomalous data. As a negative, there are clearly point clouds without subjective degradation present in the experiments with added degradation, which-using this method-get labeled as anomalies even though for actual trainging and evaluation purposes they should not be labeleld as such. Since we do not have an objective measure available, we looked into other ways to label the data such as statistical data about missing measurements per point cloud or the aforementioned phenomenon of more erroneous measurements up close to the sensor in degraded environments, but we feared that any statistical property of the data or any combination of them would only result in the method learning to replicate those statistical evaluations rather than to actually quantify the degradation in a generalized way. The classification of wether smoke was present during an experiment or not is different here in that it is not dependent on the data but is rather an expression of the environment itself, during the recording of the data.
+
+    This simplistic labeling approach has both advantages and disadvantages. On the positive side, it is easy to implement and creates a clear distinction between normal and anomalous data. However, its simplicity is also its drawback: some point clouds from experiments with artificial smoke do not exhibit perceptible degradation, yet they are still labeled as anomalies. In an ideal scenario, these point clouds should not be classified as degraded for training and evaluation purposes.
+
+Since an objective measure of degradation is unavailable, we explored alternative labeling methods—such as using statistical properties like the number of missing measurements per point cloud or the higher incidence of erroneous measurements near the sensor in degraded environments. Ultimately, we were concerned that these statistical approaches might lead the method to simply mimic the statistical evaluation rather than to quantify degradation in a generalized and robust manner. Notably, our labeling strategy—based on the presence or absence of smoke—is fundamentally an environmental indicator, independent of the intrinsic data properties recorded during the experiments.
+
+    %\todo[inline]{TODO maybe evaluate based on different thresholds? missing datapoints, number of detected outliers, number of particles in phantom circle around sensor?}
 
 \newchapter{experimental_setup}{Experimental Setup}
     \newsection{autoencoder_architecture}{DeepSAD Autoencoder Architecture}
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