From 69fe8483859e6204735808a021848294dcc99d56 Mon Sep 17 00:00:00 2001 From: =?utf8?q?Bj=C3=B8rn=20Rustad?= Date: Fri, 16 May 2014 16:10:51 +0200 Subject: [PATCH] Figures in the result section --- results.tex | 147 +++++++++++++++++++++++++++++++++++++++++++++++++--- 1 file changed, 141 insertions(+), 6 deletions(-) diff --git a/results.tex b/results.tex index ed0d873..89275da 100644 --- a/results.tex +++ b/results.tex @@ -1,10 +1,145 @@ -% Dette eksempelet er laget for article-dokumentklassen. Hvis -% skriver i 'book'-dokumentklassen vil du kanskje bytte ut -% \section med \chapter, \subsection med \section, osv... +\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. -- 2.47.3