-DEsigning a 2-D median filter basically consists in defining a square window $H(i,j)$ for each pixel $I(i,j)$ of the input image, containing $n\times n$ pixels and centered on $I(i,j)$. The output value $I'(i,j)$ is the median value of the gray level values of the $n\times n$ pixels of $H(i,j)$. Figure \ref{fig:median_1} illustrates this principle with an example of a 5x5 median filter applied on pixel $I(5,6)$. The output value is the median value of the 25 values of the dark gray window centered on pixel $I(5,6)$.
- The generic filtering method is given by Algorithm \ref{algo_median_generic}. After the data transfer stage of line \ref{algo_median_generic:memcpyH2D} which copies data from CPU memory to GPU texture memory, the actual median computing occurs between lines \ref{algo_median_generic:cptstart} and lines \ref{algo_median_generic:cptend}, before the final transfer which copies data back to CPU memory at line \ref{algo_median_generic:memcpyD2H}. Obviously, on key issue is the selection method that identifies the median value. But, as shown in figure \ref{fig:median_overlap}, since two neighboring pixels share part of the values to be sorted, a second key issue is how to rule redundancy between consecutive positions of the running window $H(i,j)$.
-As mentioned earlier, the selection of the median value can be performed by por than one technique, using either histogram-based or sorting methods, each of them having its own benefits and drawbacks as will be discussed further down.
+Designing a 2-D median filter basically consists in defining a square window $H(i,j)$ for each pixel $I(i,j)$ of the input image, containing $n\times n$ pixels and centered on $I(i,j)$. The output value $I'(i,j)$ is the median value of the gray level values of the $n\times n$ pixels of $H(i,j)$. Figure \ref{fig:median_1} illustrates this principle with an example of a 5x5 median filter applied on pixel $I(5,6)$. The output value is the median value of the 25 values of the dark gray window centered on pixel $I(5,6)$.
+Figure \ref{fig:sap_examples} shows an example of a $512\times 512$ pixel image, corrupted by a \textit{salt and pepper} noise and the denoised versions, output respectively by a $3\times 3$, a $5\times 5$ and a 2 iterations $3\times 3 $ median filter.
+\begin{figure}
+\centering
+ \subfigure[Airplane image, corrupted by salt and pepper noise of density 0.25]{\label{img:sap_example_ref} \includegraphics[width=5cm]{Chapters/chapter3/img/airplane_sap25.png}}\qquad
+ \subfigure[Image denoised by a $3\times 3$ median filter]{\label{img:sap_example_med3} \includegraphics[width=5cm]{Chapters/chapter3/img/airplane_sap25_med3.png}}\\
+ \subfigure[Image denoised by a $5\times 5$ median filter]{\label{img:sap_example_med5} \includegraphics[width=5cm]{Chapters/chapter3/img/airplane_sap25_med5.png}}\qquad
+ \subfigure[Image denoised by 2 iterations of a $3\times 3$ median filter]{\label{img:sap_example_med3_it2} \includegraphics[width=5cm]{Chapters/chapter3/img/airplane_sap25_med3_it2.png}}\\
+ \caption{Example of median filtering, applied to salt \& pepper noise reduction.}
+ \label{fig:sap_examples}
+\end{figure}
+
+ The generic filtering method is given by Algorithm \ref{algoMedianGeneric}. After the data transfer stage of the first line, which copies data from CPU memory to GPU texture memory, the actual median computing occurs, before the final transfer which copies data back to CPU memory at the last line. Obviously, one key issue is the selection method that identifies the median value. But, as shown in figure \ref{fig:median_overlap}, since two neighboring pixels share part of the values to be sorted, a second key issue is how to rule redundancy between consecutive positions of the running window $H(i,j)$.
+As mentioned earlier, the selection of the median value can be performed by more than one technique, using either histogram-based or sorting methods, each of them having its own benefits and drawbacks as will be discussed further down.
