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+\section{Image restoration results}
+Although the theory behind the graph cut image restoration algorithm has
+been the main focus of this project, we will look at some results when
+applying the algorithm to different noisy input images.
-\section{Results}
-Method noise is the original image subtracted from the output image. It
-should not containt too many features.
+The two main parameters available to the user of the algorithm are the
+$\beta$ parameter and the neighborhood specification. With $\beta$ being
+the weight of the total variation in the energy function, larger values
+will give more smoothing in the output image. By changing the pixel
+neighborhoods we can change the reach of the smoothing, and maybe try to
+reduce some visual effects introduced by the discretization.
+
+Measuring the performance of the method is hard, especially as different
+applications have different measures for what is a ``good'' output
+image. We will in this section consider an original image with
+artificially added noise, and try to remove the noise to obtain an
+output image as close to the original as possible.
+
+The most obvious approach is to just look at the two images and see how
+much alike they are, something that makes sense especially if the output
+is made for the eye to see. One can also consider the \emph{method
+noise} which is the difference between the noisy image and the de-noised
+version. If noise is independent of the original image, one would also
+hope that the method noise would not contain too many features from the
+original image, since it is only the noise we want to remove.
+
+\begin{figure}
+ \centering
+ \begin{subfigure}[t]{0.3\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{../image-restoration/figures/lena512.png}
+ \caption{Original image}
+ \end{subfigure}
+ ~
+ \begin{subfigure}[t]{0.3\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{../image-restoration/figures/normal/noisy.png}
+ \caption{Gaussian noise, $\mu = 0$, $\sigma = 30$.}
+ \end{subfigure}
+ ~
+ \begin{subfigure}[t]{0.3\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{../image-restoration/figures/laplace/noisy.png}
+ \caption{Laplace noise, $\mu = 0$, $\lambda = 30$.}
+ \end{subfigure}
+ \caption{
+ The classical Lena Söderberg portrait, with two different types
+ of additive noise.
+ }
+ \label{fig:lena_and_gaussian}
+\end{figure}
+
+Figure \ref{fig:lena_and_gaussian} shows the Lena Söderberg portrait
+which has been used as a test image in digital imaging countless times.
+Gaussian and Laplace noise has been added. Since the pixel values in
+these gray scale images are limited to the range $\{0, \ldots, 255\}$,
+we have to truncate the pixel value if the addition of noise makes it
+exit the interval.
+
+\begin{figure}
+ \centering
+ \begin{subfigure}[t]{0.30\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{../image-restoration/figures/normal/restored_10.png}
+ \caption{$\beta = 10$}
+ \end{subfigure}
+ ~
+ \begin{subfigure}[t]{0.30\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{../image-restoration/figures/normal/restored_30.png}
+ \caption{$\beta = 30$}
+ \end{subfigure}
+ ~
+ \begin{subfigure}[t]{0.30\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{../image-restoration/figures/normal/restored_50.png}
+ \caption{$\beta = 50$}
+ \end{subfigure}
+
+ \centering
+ \begin{subfigure}[t]{0.30\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{../image-restoration/figures/normal/method_10.png}
+ \end{subfigure}
+ ~
+ \begin{subfigure}[t]{0.30\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{../image-restoration/figures/normal/method_30.png}
+ \end{subfigure}
+ ~
+ \begin{subfigure}[t]{0.30\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{../image-restoration/figures/normal/method_50.png}
+ \end{subfigure}
+ \caption{
+ \fixme{GAUSSIAN}
+ The first row shows restored images for different $\beta$
+ parameter using a size four neighborhood. In the second row the
+ method noise is shown around a gray value of $127$ without any
+ scaling.
+ }
+\end{figure}
+
+\begin{figure}
+ \centering
+ \begin{subfigure}[t]{0.30\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{../image-restoration/figures/laplace/restored_10.png}
+ \caption{$\beta = 10$}
+ \end{subfigure}
+ ~
+ \begin{subfigure}[t]{0.30\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{../image-restoration/figures/laplace/restored_30.png}
+ \caption{$\beta = 30$}
+ \end{subfigure}
+ ~
+ \begin{subfigure}[t]{0.30\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{../image-restoration/figures/laplace/restored_50.png}
+ \caption{$\beta = 50$}
+ \end{subfigure}
+
+ \centering
+ \begin{subfigure}[t]{0.30\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{../image-restoration/figures/laplace/method_10.png}
+ \end{subfigure}
+ ~
+ \begin{subfigure}[t]{0.30\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{../image-restoration/figures/laplace/method_30.png}
+ \end{subfigure}
+ ~
+ \begin{subfigure}[t]{0.30\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{../image-restoration/figures/laplace/method_50.png}
+ \end{subfigure}
+ \caption{
+ \fixme{LAPLACE, should run with different norm.}
+ }
+\end{figure}
\subsection{Image segmentation}
Some figures maybe. Showing the segmentation for different parameters.
projects / prosjektoppgave / commitdiff