changed template

added chapters
added bib

tex/chapters/abstract.tex

@@ -0,0 +1 @@
+This is the abstract stract stract

tex/chapters/conclusion.tex

@@ -0,0 +1,2 @@
+\section{Conclusion}
+The conclusion goes here.

tex/chapters/experiments.tex

@@ -0,0 +1,2 @@
+\section{Experiments}
+

tex/chapters/introduction.tex

@@ -0,0 +1,7 @@
+\section{Introduction}
+
+\cite{Deinzer01-CIV}
+% KDE wellknown nonparametic estimation method
+% Flexibility is paid with slow speed
+% Finding optimal bandwidth
+% Expensive computation

tex/chapters/kde.tex

@@ -0,0 +1,29 @@
+\section{Binned Kernel Density Estimation}
+% KDE by rosenblatt and parzen
+% general KDE
+% Gauss Kernel
+% Formula Gauss KDE
+% -> complexity/operation count
+% Binned KDE
+% Binned Gauss KDE
+% -> complexity/operation count
+
+The histogram is a simple and for a long time the most used non-parametric estimator.
+However, its inability to produce a continuous estimate dismisses it for many applications where a smooth distribution is assumed.
+In contrast, the KDE is often the preferred tool because of its ability to produce a continuous estimate and its flexibility.
+Given $n$ independently observed realizations of the observation set $X=(x_1,\dots,x_n)$, the kernel density estimate $\hat{f}_n$ of the density function $f$ of the underlying distribution is given with
+\begin{equation}
+\label{eq:kde}
+\hat{f}_n = \frac{1}{nh} \sum_{i=1}^{n} K \left(  \frac{x-X_i}{h} \right)  \text{,} %= \frac{1}{n} \sum_{i=1}^{n} K_h(x-x_i)
+\end{equation}
+where $K$ is the kernel function and $h\in\R^+$ is an arbitrary smoothing parameter called bandwidth.
+While any density function can be used as the kernel function $K$ (such that $\int K(u) \dop{u} = 1$), a variety of popular choices of the kernel function $K$ exits.
+In practice the Gaussian kernel is commonly used:
+\begin{equation}
+K(u)=\frac{1}{\sqrt{2\pi}} \expp{- \frac{u^2}{2} }
+\end{equation}
+
+\begin{equation}
+\hat{f}_n = \frac{1}{nh\sqrt{2\pi}} \sum_{i=1}^{n} \expp{-\frac{(x-X_i)^2}{2h^2}}
+\end{equation}
+

tex/chapters/mvg.tex

@@ -0,0 +1,22 @@
+\section{Moving Average Filter}
+% Basic box filter formula
+% Recursive form
+% Gauss Blur Filter
+% Repetitive Box filter to approx Gauss
+% Simple multipass, n/m approach, extended box filter
+The moving average filter is a simplistic filter which takes an input function $x$ and produces a second function $y$.
+A single output value is computed by taking the average of a number of values symmetrical around a single point in the input.
+The number of values in the average can also be seen as the width $w=2r+1$, where $r$ is the \qq{radius} of the filter.
+The computation of an output value using a moving average filter of radius $r$ is defined as
+\begin{equation}
+\label{eq:symMovAvg}
+y[i]=\frac{1}{2r+1} \sum_{j=-r}^{r}x[i+j] \text{.}
+\end{equation}
+
+It is well-known that a moving average filter can approximate a Gaussian filter by repetitive recursive computations.
+
+
+
+As is known the Gaussian filter is parametrized by its standard deviation $\sigma$.
+To approximate a Gaussian filter one needs to express a given $\sigma$ in terms of moving average filters.
+

tex/chapters/relatedwork.tex

@@ -0,0 +1,5 @@
+\section{Related work}
+% original work rosenblatt/parzen
+% binned version silverman, scott, härdle
+% -> Fourier transfom
+% other approaches Fast Gaussian Transform

tex/chapters/usage.tex

@@ -0,0 +1,2 @@
+\section{Usage}
+%wie benutzen wir das ganze jetzt? auf was muss ich achten?