text:
\section{Evolution of DICE coefficients}
\Cref{fig:dice-extended} shows the evolution of the individual DICE coefficients, for gray matter (GM), white matter (WM) and cerebrospinal fluid (CSF), as well as their mean dice, extending \cref{fig:dice}. Where available, we also included the proposed algorithm with the Battacharyya kernel.

\begin{figure*}[ht]
  \centerfloat%
  \def0.9{.9}%
  \def0.25{0.0}
  \subfloat[\scriptsize{MRBrainS: T1$\to$T2-FLAIR; GM}]{
    \scalebox{\scale}{
      \begin{tikzpicture}        \begin{axis}[ymin=0.25, ymax=0.9,
          grid=both, minor tick num=2,
          axis lines=center,
          legend style={at={(0.01,0.01)},anchor=south west},
          xlabel=epoch,
          x label style={anchor=north east}]
          \addCSVplot[blue, name path=A1, smooth]          {MRBrains_AdaptSegNet}{T2_FLAIR_DC_1}{amin};
          \addlegendentry{AdaptSegNet \cite{tsai2018learning}};
          \addCSVplot[red, name path=A2, smooth]          {MRBrains_RobNet_T2_FLAIR}{T2_FLAIR_DC_1}{amin};
          \addlegendentry{Proposed};
          \addCSVplot[green, name path=A3, smooth]          {MRBrains_RobNet_T2_FLAIR_bhattacharyya}{T2_FLAIR_DC_1}{amin};
          \addlegendentry{Proposed (Bhattacharyya)};

          \addCSVplot[blue, name path=B1,smooth]          {MRBrains_AdaptSegNet}{T2_FLAIR_DC_1}{amax};
          \addCSVplot[red, name path=B2, smooth]          {MRBrains_RobNet_T2_FLAIR}{T2_FLAIR_DC_1}{amax};
          \addCSVplot[green, name path=B3, smooth]          {MRBrains_RobNet_T2_FLAIR_bhattacharyya}{T2_FLAIR_DC_1}{amax};

          \tikzfillbetween[of=A1 and B1]{blue, opacity=0.2};
          \tikzfillbetween[of=A2 and B2]{red, opacity=0.2};
          \tikzfillbetween[of=A3 and B3]{green, opacity=0.2};
        \end{axis}
      \end{tikzpicture}}
  }
  \subfloat[\scriptsize{MRBrainS: T1$\to$T2-FLAIR; WM}]{
    \scalebox{\scale}{
      \begin{tikzpicture}        \begin{axis}[ymin=0.25, ymax=0.9,
          grid=both, minor tick num=2,
          axis lines=center,
          legend style={at={(0.01,0.01)},anchor=south west},
          xlabel=epoch,
          x label style={anchor=north east}]
          \addCSVplot[blue, name path=A1, smooth]          {MRBrains_AdaptSegNet}{T2_FLAIR_DC_2}{amin};
          \addlegendentry{AdaptSegNet \cite{tsai2018learning}};
          \addCSVplot[red, name path=A2, smooth]          {MRBrains_RobNet_T2_FLAIR}{T2_FLAIR_DC_2}{amin};
          \addlegendentry{Proposed};
          \addCSVplot[green, name path=A3, smooth]          {MRBrains_RobNet_T2_FLAIR_bhattacharyya}{T2_FLAIR_DC_2}{amin};
          \addlegendentry{Proposed (Bhattacharyya)};

          \addCSVplot[blue, name path=B1,smooth]          {MRBrains_AdaptSegNet}{T2_FLAIR_DC_2}{amax};
          \addCSVplot[red, name path=B2, smooth]          {MRBrains_RobNet_T2_FLAIR}{T2_FLAIR_DC_2}{amax};
          \addCSVplot[green, name path=B3, smooth]          {MRBrains_RobNet_T2_FLAIR_bhattacharyya}{T2_FLAIR_DC_2}{amax};

          \tikzfillbetween[of=A1 and B1]{blue, opacity=0.2};
          \tikzfillbetween[of=A2 and B2]{red, opacity=0.2};
          \tikzfillbetween[of=A3 and B3]{green, opacity=0.2};
        \end{axis}
      \end{tikzpicture}}
  }
  \subfloat[\scriptsize{MRBrainS: T1$\to$T2-FLAIR; CSF}]{
    \scalebox{\scale}{
      \begin{tikzpicture}        \begin{axis}[ymin=0.25, ymax=0.9,
          grid=both, minor tick num=2,
          axis lines=center,
          legend style={at={(0.01,0.01)},anchor=south west},
          xlabel=epoch,
          x label style={anchor=north east}]
          \addCSVplot[blue, name path=A1, smooth]          {MRBrains_AdaptSegNet}{T2_FLAIR_DC_3}{amin};
          \addlegendentry{AdaptSegNet \cite{tsai2018learning}};
          \addCSVplot[red, name path=A2, smooth]          {MRBrains_RobNet_T2_FLAIR}{T2_FLAIR_DC_3}{amin};
          \addlegendentry{Proposed};
          \addCSVplot[green, name path=A3, smooth]          {MRBrains_RobNet_T2_FLAIR_bhattacharyya}{T2_FLAIR_DC_3}{amin};
          \addlegendentry{Proposed (Bhattacharyya)};

          \addCSVplot[blue, name path=B1,smooth]          {MRBrains_AdaptSegNet}{T2_FLAIR_DC_2}{amax};
          \addCSVplot[red, name path=B2, smooth]          {MRBrains_RobNet_T2_FLAIR}{T2_FLAIR_DC_3}{amax};
          \addCSVplot[green, name path=B3, smooth]          {MRBrains_RobNet_T2_FLAIR_bhattacharyya}{T2_FLAIR_DC_3}{amax};

          \tikzfillbetween[of=A1 and B1]{blue, opacity=0.2};
          \tikzfillbetween[of=A2 and B2]{red, opacity=0.2};
          \tikzfillbetween[of=A3 and B3]{green, opacity=0.2};
        \end{axis}
      \end{tikzpicture}}
  }
  \subfloat[\scriptsize{MRBrainS: T1$\to$T2-FLAIR; Mean}]{
    \scalebox{\scale}{
      \begin{tikzpicture}        \begin{axis}[ymin=0.25, ymax=0.9,
          grid=both, minor tick num=2,
          axis lines=center,
          legend style={at={(0.01,0.01)},anchor=south west},
          xlabel=epoch,
          x label style={anchor=north east}]
          \addCSVplot[blue, name path=A1, smooth]          {MRBrains_AdaptSegNet}{T2_FLAIR_DC}{amin};
          \addlegendentry{AdaptSegNet \cite{tsai2018learning}};
          \addCSVplot[red, name path=A2, smooth]          {MRBrains_RobNet_T2_FLAIR}{T2_FLAIR_DC}{amin};
          \addlegendentry{Proposed};
          \addCSVplot[green, name path=A3, smooth]          {MRBrains_RobNet_T2_FLAIR_bhattacharyya}{T2_FLAIR_DC}{amin};
          \addlegendentry{Proposed (Bhattacharyya)};

          \addCSVplot[blue, name path=B1,smooth]          {MRBrains_AdaptSegNet}{T2_FLAIR_DC}{amax};
          \addCSVplot[red, name path=B2, smooth]          {MRBrains_RobNet_T2_FLAIR}{T2_FLAIR_DC}{amax};
          \addCSVplot[green, name path=B3, smooth]          {MRBrains_RobNet_T2_FLAIR_bhattacharyya}{T2_FLAIR_DC}{amax};

          \tikzfillbetween[of=A1 and B1]{blue, opacity=0.2};
          \tikzfillbetween[of=A2 and B2]{red, opacity=0.2};
          \tikzfillbetween[of=A3 and B3]{green, opacity=0.2};
        \end{axis}
      \end{tikzpicture}}
  }

  \def0.25{0.0}
  \subfloat[\scriptsize{MRBrainS: T2-FLAIR$\to$T1; GM}]{
    \scalebox{\scale}{
      \begin{tikzpicture}        \begin{axis}[ymin=0.25, ymax=0.9,
          grid=both, minor tick num=2,
          axis lines=center,
          legend style={at={(0.01,0.01)},anchor=south west},
          xlabel=epoch,
          x label style={anchor=north east}]
          \addCSVplot[blue, name path=A1, smooth]          {MRBrains_AdaptSegNet_T1_from_T2_FLAIR}{T1_DC_1}{amin};
          \addlegendentry{AdaptSegNet \cite{tsai2018learning}};
          \addCSVplot[red, name path=A2, smooth]          {MRBrains_RobNet_T1_from_T2_FLAIR}{T1_DC_1}{amin};
          \addlegendentry{Proposed};

          \addCSVplot[blue, name path=B1,smooth]          {MRBrains_AdaptSegNet_T1_from_T2_FLAIR}{T1_DC_1}{amax};
          \addCSVplot[red, name path=B2, smooth]          {MRBrains_RobNet_T1_from_T2_FLAIR}{T1_DC_1}{amax};

          \tikzfillbetween[of=A1 and B1]{blue, opacity=0.2};
          \tikzfillbetween[of=A2 and B2]{red, opacity=0.2};
        \end{axis}
      \end{tikzpicture}}
  }
  \subfloat[\scriptsize{MRBrainS: T2-FLAIR$\to$T1; WM}]{
    \scalebox{\scale}{
      \begin{tikzpicture}        \begin{axis}[ymin=0.25, ymax=0.9,
          grid=both, minor tick num=2,
          axis lines=center,
          legend style={at={(0.01,0.01)},anchor=south west},
          xlabel=epoch,
          x label style={anchor=north east}]
          \addCSVplot[blue, name path=A1, smooth]          {MRBrains_AdaptSegNet_T1_from_T2_FLAIR}{T1_DC_2}{amin};
          \addlegendentry{AdaptSegNet \cite{tsai2018learning}};
          \addCSVplot[red, name path=A2, smooth]          {MRBrains_RobNet_T1_from_T2_FLAIR}{T1_DC_2}{amin};
          \addlegendentry{Proposed};

          \addCSVplot[blue, name path=B1,smooth]          {MRBrains_AdaptSegNet_T1_from_T2_FLAIR}{T1_DC_2}{amax};
          \addCSVplot[red, name path=B2, smooth]          {MRBrains_RobNet_T1_from_T2_FLAIR}{T1_DC_2}{amax};

          \tikzfillbetween[of=A1 and B1]{blue, opacity=0.2};
          \tikzfillbetween[of=A2 and B2]{red, opacity=0.2};
        \end{axis}
      \end{tikzpicture}}
  }
  \subfloat[\scriptsize{MRBrainS: T2-FLAIR$\to$T1; CSF}]{
    \scalebox{\scale}{
      \begin{tikzpicture}        \begin{axis}[ymin=0.25, ymax=0.9,
          grid=both, minor tick num=2,
          axis lines=center,
          legend style={at={(0.01,0.01)},anchor=south west},
          xlabel=epoch,
          x label style={anchor=north east}]
          \addCSVplot[blue, name path=A1, smooth]          {MRBrains_AdaptSegNet_T1_from_T2_FLAIR}{T1_DC_3}{amin};
          \addlegendentry{AdaptSegNet \cite{tsai2018learning}};
          \addCSVplot[red, name path=A2, smooth]          {MRBrains_RobNet_T1_from_T2_FLAIR}{T1_DC_3}{amin};
          \addlegendentry{Proposed};

          \addCSVplot[blue, name path=B1,smooth]          {MRBrains_AdaptSegNet_T1_from_T2_FLAIR}{T1_DC_2}{amax};
          \addCSVplot[red, name path=B2, smooth]          {MRBrains_RobNet_T1_from_T2_FLAIR}{T1_DC_3}{amax};

          \tikzfillbetween[of=A1 and B1]{blue, opacity=0.2};
          \tikzfillbetween[of=A2 and B2]{red, opacity=0.2};
        \end{axis}
      \end{tikzpicture}}
  }
  \subfloat[\scriptsize{MRBrainS: T2-FLAIR$\to$T1; Mean}]{
    \scalebox{\scale}{
      \begin{tikzpicture}        \begin{axis}[ymin=0.25, ymax=0.9,
          grid=both, minor tick num=2,
          axis lines=center,
          legend style={at={(0.01,0.01)},anchor=south west},
          xlabel=epoch,
          x label style={anchor=north east}]
          \addCSVplot[blue, name path=A1, smooth]          {MRBrains_AdaptSegNet_T1_from_T2_FLAIR}{T1_DC}{amin};
          \addlegendentry{AdaptSegNet \cite{tsai2018learning}};
          \addCSVplot[red, name path=A2, smooth]          {MRBrains_RobNet_T1_from_T2_FLAIR}{T1_DC}{amin};
          \addlegendentry{Proposed};

          \addCSVplot[blue, name path=B1,smooth]          {MRBrains_AdaptSegNet_T1_from_T2_FLAIR}{T1_DC}{amax};
          \addCSVplot[red, name path=B2, smooth]          {MRBrains_RobNet_T1_from_T2_FLAIR}{T1_DC}{amax};

          \tikzfillbetween[of=A1 and B1]{blue, opacity=0.2};
          \tikzfillbetween[of=A2 and B2]{red, opacity=0.2};
        \end{axis}
      \end{tikzpicture}}
  }

  \def0.9{0.9}%
  \def0.25{0.25}%
  \subfloat[\scriptsize{iSEG: T1$\to$T2; GM}]{
    \scalebox{\scale}{
      \begin{tikzpicture}
        \begin{axis}[ymin=0.25, ymax=0.9,
          grid=both, minor tick num=2,
          axis lines=center,
          xlabel=epoch,
          x label style={anchor=north east}]
          \addCSVplot[blue, name path=A1, smooth]          {iSEG_AdaptSegNet}{T2_DC_1}{amin};
          \addlegendentry{AdaptSegNet \cite{tsai2018learning}};
          \addCSVplot[red, name path=A2, smooth]          {iSEG_RobNet}{T2_DC_1}{amin};
          \addlegendentry{Proposed};
          \addCSVplot[green, name path=A3, smooth]          {iSEG_RobNet_bhattacharyya}{T2_DC_1}{amin};
          \addlegendentry{Proposed (Bhattacharyya)};

          \addCSVplot[blue, name path=B1,smooth]          {iSEG_AdaptSegNet}{T2_DC_1}{amax};
          \addCSVplot[red, name path=B2, smooth]          {iSEG_RobNet}{T2_DC_1}{amax};
          \addCSVplot[green, name path=B3, smooth]          {iSEG_RobNet_bhattacharyya}{T2_DC_1}{amax};

          \tikzfillbetween[of=A1 and B1]{blue, opacity=0.2};
          \tikzfillbetween[of=A2 and B2]{red, opacity=0.2};
          \tikzfillbetween[of=A3 and B3]{green, opacity=0.2};
        \end{axis}
      \end{tikzpicture}}
  }
  \subfloat[\scriptsize{iSEG: T1$\to$T2; WM}]{
    \scalebox{\scale}{
      \begin{tikzpicture}
        \begin{axis}[ymin=0.25, ymax=0.9,
          grid=both, minor tick num=2,
          axis lines=center,
          xlabel=epoch,
          x label style={anchor=north east}]
          \addCSVplot[blue, name path=A1, smooth]          {iSEG_AdaptSegNet}{T2_DC_2}{amin};
          \addlegendentry{AdaptSegNet \cite{tsai2018learning}};
          \addCSVplot[red, name path=A2, smooth]          {iSEG_RobNet}{T2_DC_2}{amin};
          \addlegendentry{Proposed};
          \addCSVplot[green, name path=A3, smooth]          {iSEG_RobNet_bhattacharyya}{T2_DC_2}{amin};
          \addlegendentry{Proposed (Bhattacharyya)};

          \addCSVplot[blue, name path=B1,smooth]          {iSEG_AdaptSegNet}{T2_DC_2}{amax};
          \addCSVplot[red, name path=B2, smooth]          {iSEG_RobNet}{T2_DC_2}{amax};
          \addCSVplot[green, name path=B3, smooth]          {iSEG_RobNet_bhattacharyya}{T2_DC_2}{amax};

          \tikzfillbetween[of=A1 and B1]{blue, opacity=0.2};
          \tikzfillbetween[of=A2 and B2]{red, opacity=0.2};
          \tikzfillbetween[of=A3 and B3]{green, opacity=0.2};
        \end{axis}
      \end{tikzpicture}}
  }
  \subfloat[\scriptsize{iSEG: T1$\to$T2; CSF}]{
    \scalebox{\scale}{
      \begin{tikzpicture}
        \begin{axis}[ymin=0.25, ymax=0.9,
          grid=both, minor tick num=2,
          axis lines=center,
          xlabel=epoch,
          x label style={anchor=north east}]
          \addCSVplot[blue, name path=A1, smooth]          {iSEG_AdaptSegNet}{T2_DC_3}{amin};
          \addlegendentry{AdaptSegNet \cite{tsai2018learning}};
          \addCSVplot[red, name path=A2, smooth]          {iSEG_RobNet}{T2_DC_3}{amin};
          \addlegendentry{Proposed};
          \addCSVplot[green, name path=A3, smooth]          {iSEG_RobNet_bhattacharyya}{T2_DC_3}{amin};
          \addlegendentry{Proposed (Bhattacharyya)};

          \addCSVplot[blue, name path=B1,smooth]          {iSEG_AdaptSegNet}{T2_DC_3}{amax};
          \addCSVplot[red, name path=B2, smooth]          {iSEG_RobNet}{T2_DC_3}{amax};
          \addCSVplot[green, name path=B3, smooth]          {iSEG_RobNet_bhattacharyya}{T2_DC_3}{amax};

          \tikzfillbetween[of=A1 and B1]{blue, opacity=0.2};
          \tikzfillbetween[of=A2 and B2]{red, opacity=0.2};
          \tikzfillbetween[of=A3 and B3]{green, opacity=0.2};
        \end{axis}
      \end{tikzpicture}}
  }
  \subfloat[\scriptsize{iSEG: T1$\to$T2; Mean}]{
    \scalebox{\scale}{
      \begin{tikzpicture}
        \begin{axis}[ymin=0.25, ymax=0.9,
          grid=both, minor tick num=2,
          axis lines=center,
          xlabel=epoch,
          x label style={anchor=north east}]
          \addCSVplot[blue, name path=A1, smooth]          {iSEG_AdaptSegNet}{T2_DC}{amin};
          \addlegendentry{AdaptSegNet \cite{tsai2018learning}};
          \addCSVplot[red, name path=A2, smooth]          {iSEG_RobNet}{T2_DC}{amin};
          \addlegendentry{Proposed};
          \addCSVplot[green, name path=A3, smooth]          {iSEG_RobNet_bhattacharyya}{T2_DC}{amin};
          \addlegendentry{Proposed (Bhattacharyya)};

          \addCSVplot[blue, name path=B1,smooth]          {iSEG_AdaptSegNet}{T2_DC}{amax};
          \addCSVplot[red, name path=B2, smooth]          {iSEG_RobNet}{T2_DC}{amax};
          \addCSVplot[green, name path=B3, smooth]          {iSEG_RobNet_bhattacharyya}{T2_DC}{amax};

          \tikzfillbetween[of=A1 and B1]{blue, opacity=0.2};
          \tikzfillbetween[of=A2 and B2]{red, opacity=0.2};
          \tikzfillbetween[of=A3 and B3]{green, opacity=0.2};
        \end{axis}
      \end{tikzpicture}}
  }

  \def0.25{0.25}
  \def0.9{0.9}
  \subfloat[\scriptsize{iSEG: T2$\to$T1; GM}]{
    \scalebox{\scale}{
      \begin{tikzpicture}
        \begin{axis}[ymin=0.25, ymax=0.9,
          grid=both, minor tick num=2,
          axis lines=center,
          xlabel=epoch,
          x label style={anchor=north east}]
          \addCSVplot[blue, name path=A1, smooth]          {iSEG_AdaptSegNet_T1_from_T2}{T1_DC_1}{amin};
          \addlegendentry{AdaptSegNet \cite{tsai2018learning}};
          \addCSVplot[red, name path=A2, smooth]          {iSEG_RobNet_T1_from_T2}{T1_DC_1}{amin};
          \addlegendentry{Proposed};

          \addCSVplot[blue, name path=B1,smooth]          {iSEG_AdaptSegNet_T1_from_T2}{T1_DC_1}{amax};
          \addCSVplot[red, name path=B2, smooth]          {iSEG_RobNet_T1_from_T2}{T1_DC_1}{amax};

          \tikzfillbetween[of=A1 and B1]{blue, opacity=0.2};
          \tikzfillbetween[of=A2 and B2]{red, opacity=0.2};
        \end{axis}
      \end{tikzpicture}}
  }
  \subfloat[\scriptsize{iSEG: T2$\to$T1; WM}]{
    \scalebox{\scale}{
      \begin{tikzpicture}
        \begin{axis}[ymin=0.25, ymax=0.9,
          grid=both, minor tick num=2,
          axis lines=center,
          xlabel=epoch,
          x label style={anchor=north east}]
          \addCSVplot[blue, name path=A1, smooth]          {iSEG_AdaptSegNet_T1_from_T2}{T1_DC_2}{amin};
          \addlegendentry{AdaptSegNet \cite{tsai2018learning}};
          \addCSVplot[red, name path=A2, smooth]          {iSEG_RobNet_T1_from_T2}{T1_DC_2}{amin};
          \addlegendentry{Proposed};

          \addCSVplot[blue, name path=B1,smooth]          {iSEG_AdaptSegNet_T1_from_T2}{T1_DC_2}{amax};
          \addCSVplot[red, name path=B2, smooth]          {iSEG_RobNet_T1_from_T2}{T1_DC_2}{amax};

          \tikzfillbetween[of=A1 and B1]{blue, opacity=0.2};
          \tikzfillbetween[of=A2 and B2]{red, opacity=0.2};
        \end{axis}
      \end{tikzpicture}}
  }
  \subfloat[\scriptsize{iSEG: T2$\to$T1; CSF}]{
    \scalebox{\scale}{
      \begin{tikzpicture}
        \begin{axis}[ymin=0.25, ymax=0.9,
          grid=both, minor tick num=2,
          axis lines=center,
          xlabel=epoch,
          x label style={anchor=north east}]
          \addCSVplot[blue, name path=A1, smooth]          {iSEG_AdaptSegNet_T1_from_T2}{T1_DC_3}{amin};
          \addlegendentry{AdaptSegNet \cite{tsai2018learning}};
          \addCSVplot[red, name path=A2, smooth]          {iSEG_RobNet_T1_from_T2}{T1_DC_3}{amin};
          \addlegendentry{Proposed};

          \addCSVplot[blue, name path=B1,smooth]          {iSEG_AdaptSegNet_T1_from_T2}{T1_DC_3}{amax};
          \addCSVplot[red, name path=B2, smooth]          {iSEG_RobNet_T1_from_T2}{T1_DC_3}{amax};

          \tikzfillbetween[of=A1 and B1]{blue, opacity=0.2};
          \tikzfillbetween[of=A2 and B2]{red, opacity=0.2};
        \end{axis}
      \end{tikzpicture}}
  }
  \subfloat[\scriptsize{iSEG: T2$\to$T1; Mean}]{
  \scalebox{\scale}{
  \begin{tikzpicture}
    \begin{axis}[ymin=0.25, ymax=0.9,
      grid=both, minor tick num=2,
      axis lines=center,
      xlabel=epoch,
      x label style={anchor=north east}]
      \addCSVplot[blue, name path=A1, smooth]      {iSEG_AdaptSegNet_T1_from_T2}{T1_DC}{amin};
      \addlegendentry{AdaptSegNet \cite{tsai2018learning}};
      \addCSVplot[red, name path=A2, smooth]      {iSEG_RobNet_T1_from_T2}{T1_DC}{amin};
      \addlegendentry{Proposed};

      \addCSVplot[blue, name path=B1,smooth]      {iSEG_AdaptSegNet_T1_from_T2}{T1_DC}{amax};
      \addCSVplot[red, name path=B2, smooth]      {iSEG_RobNet_T1_from_T2}{T1_DC}{amax};

      \tikzfillbetween[of=A1 and B1]{blue, opacity=0.2};
      \tikzfillbetween[of=A2 and B2]{red, opacity=0.2};
    \end{axis}
  \end{tikzpicture}}
  }
  \caption{Evolution of (validation) DICE coefficients over epochs. The minimum and maximum observed value over the three cross-validation runs is plotted, and the area in between is shaded.}
  \label{fig:dice-extended}
\end{figure*}

\section{Impact of the kernel choice}
\label{sec:impact-kernel-choice-extended}

In addition to squared Euclidean distance and the Bhattacharyya kernel, we also performed experiments with KL divergence and, again, found that it has negligible impact on the over-all performance. The results, extending \cref{table:bhattacharyya}, are detailed in \cref{tab:kernel-choice-extended}.

\begin{table*}[ht]
  \small
  \caption{DICE coefficients when training with squared Euclidean distance, Bhattacharyya distance and KL divergence.}
  \begin{tabular}{lcccc}
    \toprule
    &
        & Sq.\ Euclidian & Bhattacharyya & KL divergence  \\
                \midrule
    & GM
        & $\printMaxPercentWithStd{iSEG_RobNet}{T2_DC}{T2_DC_1}{mean}$
                     & $\printMaxPercentWithStd{iSEG_RobNet_bhattacharyya}{T2_DC}{T2_DC_1}{mean}$
                                     & $\printMaxPercentWithStd{iSEG_RobNet_KL_divergence}{T2_DC}{T2_DC_1}{mean}$\\
    Source: iSEG(T1)  &  WM
        & $\printMaxPercentWithStd{iSEG_RobNet}{T2_DC}{T2_DC_2}{mean}$
                     & $\printMaxPercentWithStd{iSEG_RobNet_bhattacharyya}{T2_DC}{T2_DC_2}{mean}$
                                     & $\printMaxPercentWithStd{iSEG_RobNet_KL_divergence}{T2_DC}{T2_DC_2}{mean}$\\
    Target: iSEG(T2)  & CSF
        & $\printMaxPercentWithStd{iSEG_RobNet}{T2_DC}{T2_DC_3}{mean}$
                     & $\printMaxPercentWithStd{iSEG_RobNet_bhattacharyya}{T2_DC}{T2_DC_3}{mean}$
                                     & $\printMaxPercentWithStd{iSEG_RobNet_KL_divergence}{T2_DC}{T2_DC_3}{mean}$\\
    & Mean
        & $\printMaxPercentWithStd{iSEG_RobNet}{T2_DC}{T2_DC}{mean}$
                     & $\printMaxPercentWithStd{iSEG_RobNet_bhattacharyya}{T2_DC}{T2_DC}{mean}$
                                         & $\printMaxPercentWithStd{iSEG_RobNet_KL_divergence}{T2_DC}{T2_DC}{mean}$\\
    \midrule
    & GM
        & $\printMaxPercentWithStd{MRBrains_RobNet_T2_FLAIR}{T2_FLAIR_DC}{T2_FLAIR_DC_1}{mean}$
                     & $\printMaxPercentWithStd{MRBrains_RobNet_T2_FLAIR_bhattacharyya}{T2_FLAIR_DC}{T2_FLAIR_DC_1}{mean}$
                                     & $\printMaxPercentWithStd{MRBrains_RobNet_T2_FLAIR_KL_divergence}{T2_FLAIR_DC}{T2_FLAIR_DC_1}{mean}$\\
    Source: MRB(T1)  &  WM
        & $\printMaxPercentWithStd{MRBrains_RobNet_T2_FLAIR}{T2_FLAIR_DC}{T2_FLAIR_DC_2}{mean}$
                     & $\printMaxPercentWithStd{MRBrains_RobNet_T2_FLAIR_bhattacharyya}{T2_FLAIR_DC}{T2_FLAIR_DC_2}{mean}$
                                     & $\printMaxPercentWithStd{MRBrains_RobNet_T2_FLAIR_KL_divergence}{T2_FLAIR_DC}{T2_FLAIR_DC_2}{mean}$\\
    Target: MRB(T2) &  CSF
        & $\printMaxPercentWithStd{MRBrains_RobNet_T2_FLAIR}{T2_FLAIR_DC}{T2_FLAIR_DC_3}{mean}$
                     & $\printMaxPercentWithStd{MRBrains_RobNet_T2_FLAIR_bhattacharyya}{T2_FLAIR_DC}{T2_FLAIR_DC_3}{mean}$
                                     & $\printMaxPercentWithStd{MRBrains_RobNet_T2_FLAIR_KL_divergence}{T2_FLAIR_DC}{T2_FLAIR_DC_3}{mean}$\\
    &  Mean
        & $\printMaxPercentWithStd{MRBrains_RobNet_T2_FLAIR}{T2_FLAIR_DC}{T2_FLAIR_DC}{mean}$
                     & $\printMaxPercentWithStd{MRBrains_RobNet_T2_FLAIR_bhattacharyya}{T2_FLAIR_DC}{T2_FLAIR_DC}{mean}$
                                     & $\printMaxPercentWithStd{MRBrains_RobNet_T2_FLAIR_KL_divergence}{T2_FLAIR_DC}{T2_FLAIR_DC}{mean}$\\
    \bottomrule
  \end{tabular}
  \label{tab:kernel-choice-extended}
\end{table*}

\section{Introduction}

Semantic segmentation is of pivotal importance towards high-level understanding of image content, which is useful in a breadth of application areas, from autonomous driving to health care, for instance.
Particularly, in medical imaging, segmentation facilitates clinical tasks, including disease diagnosis, treatment and follow-up, among others. Modern medical segmentation approaches rely on deep learning techniques, which
have demonstrated outstanding performances in a breadth of applications \cite{dolz20183d,dolz2018hyperdense,litjens2017survey}. Despite their success, generalization of trained models to new scenarios may be hampered
if the gap between data distributions across domains is large. A trivial solution to address this issue would be to re-annotate images from different domains and re-train or fine-tune the deep models. Nevertheless,
obtaining such massive amounts of labeled data is a cumbersome process which, for some applications, may require user expertise, resulting in a prohibitive and unrealistic solution.

 To tackle this problem, unsupervised domain adaptation (UDA) techniques have been widely investigated. These methods aim at learning robust classifiers, or other predictors, in the
presence of a \textit{shift} between source and target distributions when the target data is unlabeled. An important body of recent literature formulates UDA as a domain divergence minimization.
In this scenario, the goal is typically to minimize the discrepancy between distributions across domains at the inputs \cite{bousmalis2017unsupervised,chen2018semantic,hoffman2017cycada,russo2018source,sankaranarayanan2017generate,wu2018dcan} or at intermediate-feature levels \cite{ganin2015unsupervised,ghifary2016deep,kamnitsas2017unsupervised,liu2018detach,long2015learning,long2016unsupervised,tzeng2017adversarial}, while leveraging labeled source examples to retain discriminative power on the feature space. Generative pixel-level techniques align the image appearance between domains, so that the target data `style' is transferred to source data, or vice-versa \cite{bousmalis2017unsupervised,chen2018semantic,russo2018source,shrivastava2017learning,zhang2018task}.
Then, supervised learning with the newly generated synthetic data is performed to train a segmentation network on transformed data. A downside of these approaches is that they perform satisfactorily only
for small images and narrow domain shifts, which limits their applicability. Feature-level UDA models follow a similar distribution alignment but in the feature space instead \cite{dou2018unsupervised,ganin2015unsupervised,kamnitsas2017unsupervised,long2015learning,tzeng2017adversarial}. Within the current paradigm of learning domain-invariant representations, domain adversarial training \cite{ganin2015unsupervised,tzeng2017adversarial} and maximum mean discrepancies (MMD) \cite{long2015learning,sun2016deep,yan2017mind} have become very popular choices.

For semantic segmentation problems, adversarial training models \cite{goodfellow2014generative} are currently dominating the recent literature \cite{chen2017no,chen2018road,dou2018pnp,kamnitsas2017unsupervised,hoffman2016fcns,hong2018conditional,saito2018maximum,tsai2018learning,vu2018advent}.
Such models alternate the training of two networks: a discriminator that learns a decision boundary between source and target features and a segmentation network
that uses the learned decision boundary, thereby matching feature distribution across domains.
Some other approaches rely on generative networks, which yield target images conditioned on the source, or vice-versa, aligning both domains at the pixel level \cite{cai2019towards,huo2018synseg,murez2018image,sankaranarayanan2017generate,zhang2018translating,zhao2019supervised}.

While adversarial training achieved outstanding performances in image classification, our numerical evidence and rational intuition suggest that it may not be generally suitable for segmentation tasks.
First, in segmentation, learning a discriminator boundary is much more complex than classification as it solves for predictions in an exponentially large label space. Intuitively,
a large label space implies large spaces of possible solutions for discriminator boundaries and target predictions, both of which are latent. Therefore, as we
will see later in our experiments, alternating both adversarial and prediction tasks in segmentation might cause much more significant training instabilities than in image classification tasks.
Furthermore, most of adversarial methods perform feature adaptation at many levels of abstraction. However, a large label space makes the hypothesis that source and target domains share the same
multi-level feature representations less likely to be valid. While the inputs can be significantly different from one domain to another, the output (label) space in semantic segmentation convey very rich information
related to the spatial layout and local context, which is shared across domains (See Fig. \ref{fig:domaindiscrepancy}). Inspired by this observation, Tsai \etal \cite{tsai2018learning} proposed
adversarial training in the output (softmax segmentation) space, achieving better performance than features-matching approaches on the Cityscapes dataset. Leveraging this information is even more
meaningful in medical images, where label (output) statistics remain domain-independent, up to geometric transformations, despite significant differences in image inputs across domains.
Nevertheless, following the trend in UDA approches for natural image segmentation, adversarial learning has become the \textit{de facto} choice in medical image segmentation \cite{chen2019synergistic,dou2018pnp,gholami2018novel,javanmardi2018domain,kamnitsas2017unsupervised,zhang2018task,zhao2019supervised}.

It is worth mentioning that some recent natural image segmentation works \cite{zhang2017curriculum,zou2018unsupervised} pointed out that adversarial models for classification
do not translate well to segmentation. These studies showed that similar or better performances can be achieved by other alternatives.
The authors of \cite{zou2018unsupervised} tackled the problem with self-training, which generates masks of unlabeled target images via the network's own predictions. In a different approach,
Zhang \etal \cite{zhang2017curriculum} adopted a curriculum learning approach, enforcing consistency of global label distributions such as region proportions. Finally, in the context of classification, the authors
of \cite{shu2018dirt} pointed out that UDA based on adversarial training may not be sufficient for models with high capacity, which is the case in segmentation. They empirically proved that, for sufficiently
deep architectures, jointly achieving small source generalization error and feature divergence does not imply high accuracy on the target task.

\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{ICCV_DomainsDiff.png}
\caption{
The stat-of-the-art domain adaptation method in \cite{tsai2018learning} proposed adversarial training in the output (softmax segmentation) space, achieving better performance than features-matching approaches.
This is motivated by the fact that input images can be significantly different from one domain to another, whereas the output (label) space in semantic segmentation
is shared across domains and conveys very rich information related to the spatial layout and local context. Leveraging this information is even more
meaningful in medical images, where label (output) statistics remain domain-independent, up to geometric transformations, despite significant differences in image inputs across domains.}
\label{fig:domaindiscrepancy}
\end{figure}

Minimization of distribution matching losses is a principled approach to domain adaptation in the context of image classification, e.g., MDD \cite{long2015learning,sun2016deep,yan2017mind}. However, it is largely
overlooked in adapting segmentation networks, which is currently dominated by adversarial models. We propose a class of loss functions, which encourage direct kernel density matching in the network-output space,
up to some geometric transformations computed from unlabeled inputs. Rather than using an intermediate domain discriminator, our direct approach unifies distribution matching and segmentation in a single loss. Therefore,
it simplifies segmentation adaptation by avoiding extra adversarial steps, while improving quality, stability and efficiency of training. We juxtapose our approach to the state-of-art segmentation method in \cite{tsai2018learning}, which performs distribution matching with a two-step adversarial learning in the network-output space. In the challenging task of adapting brain segmentation across different magnetic resonance images (MRI) modalities, our approach achieves significantly better performance than adversarial output adaption, both in terms of accuracy and stability.

\begin{figure*}[h!]
  \centering
  \subfloat[Adverserial (Discriminator)]{
    \includegraphics[width=0.32\textwidth]{Discriminator.png}
    \label{fig:conceptualcomparison:a}
  }
  \subfloat[Adverserial (Segmenter)]{
    \includegraphics[width=0.32\textwidth]{Generator.png}
    \label{fig:conceptualcomparison:b}
  }
  \subfloat[Direct Distribution Matching]{
    \includegraphics[width=0.32\textwidth]{Direct_Distribution_Matching.png}
    \label{fig:conceptualcomparison:c}
  }
  \caption{A conceptual juxtaposition of adversarial training in the network-output space \cite{tsai2018learning} (\labelcref{fig:conceptualcomparison:a,fig:conceptualcomparison:b}) and our direct kernel density matching (\labelcref{fig:conceptualcomparison:c}).}
\label{fig:conceptualcomparison}
\end{figure*}

\section{Formulation}
\label{sec:method}

Consider an unsupervised domain-adaptation setting with two distinct subsets: $\mathcal L = \{(X_i, Y_i)\}_{i = 1, \dots, n}$ contains labeled source-domain images $X_i$ and
the corresponding ground-truth segmentations $Y_i$, and $\mathcal U = \{(X_{i}, X'_{i})\}_{i = n+1, \dots, n+m}$ contains {\em unlabeled} image pairs, each involving a source
image $X_i$ and a target image $X'_i$. For each labeled source image $X_i: \Omega \subset {\mathbb R}^{2,3} \rightarrow \mathbb{R}$, $ i = 1, \dots, n$, the ground-truth labeling
$Y_i \in \{0, 1\}^{L \times |\Omega|}$ is a matrix whose columns are binary vectors, encoding the assignment of pixel $p \in \Omega$ to one of $L$ classes (segmentation regions):
${\mathbf y}_i(p) = (y_i(1,p), \dots, y_i (L,p)) \in \{0,1\}^L$. For any image $X$,
let ${\mathbf s}_{\mathbf{\theta}}(p, X) = \big(s_{\mathbf{\theta}}(1, p, X), \dots, s_{\mathbf{\theta}} (L, p, X)\big) \in [0,1]^L$ denote the probability vector of
softmax outputs for pixel $p$, with $\mathbf{\theta}$ the trainable parameters of the network. For the sake of simplicity, we will omit the subscript $\mathbf{\theta}$ in the following.

We propose to minimize the following loss function:
\begin{align}
\label{density-matching-loss}
  {\cal F}(\theta) &= \sum_{i=1}^n \sum_{p \in \Omega} {\cal H}\big({\mathbf y}_i (p), {\mathbf s} (p, X_i)\big) \nonumber\\*
                   &+ \lambda \sum_{i=n+1}^{n+m} \sum_{p \in \Omega} {\cal D} \big({\mathbf s} (p, X_i), {\mathbf s} (p, {\cal T}(X'_i))\big) ,
\end{align}
where
\begin{itemize}
\item $\mathcal D(\mathbf s,\mathbf s')$ evaluates the discrepancy between two probability
distributions $\mathbf s$ and $\mathbf s'$, e.g., the KL divergence. It is possible to
choose $\mathcal D(\cdot,\cdot) = - \mathcal K(\cdot,\cdot)$, with some kernel function $\mathcal K$ defined over a pair
of probability vectors, e.g., a probability product kernel \cite{Jebara2004}
${\cal K}(\mathbf s,\mathbf s') = \sum_{l=1}^L s(l)^\rho s'(l)^\rho$, with $s(l)$ denoting the $l$\textsuperscript{th}
component of $\mathbf s$ and\footnote{Notice that $\rho=\frac{1}{2}$ corresponds to the well-known Bhattacharyya coefficient.} $\rho \in ]0, 1]$.
\Cref{Discrepancy_measures} lists a few choices of $\cal D$ including some kernel functions.
\begin{table}
\renewcommand{\arraystretch}{1}
\centering
    \caption{\small{Examples of choices for pairwise discrepancy functions ${\cal D}({\mathbf s},{\mathbf s}')$ for probability simplex vectors ${\mathbf s}$ and ${\mathbf s}'$,
      including some kernel-based functions ${\cal D} = - {\cal K}$. For RBF (Gaussian) kernel, $\sigma$ is the the kernel width.
            Superscript $t$ denotes transposition.}}
  \label{tab:ex_ker}
\begin{tabular}{p{0.4\textwidth}p{0.4\textwidth}}
  \toprule
  Function & $-\mathcal D(\mathbf s, \mathbf s')$ \\
  \midrule
    RBF kernel & $-\exp(-\|{\mathbf s} - {\mathbf s}'\|^2/\sigma)$\\
  Bhattacharyya kernel & $-\sqrt{{\mathbf s}^t{\mathbf s}'}$ \\
  KL divergence & ${\mathbf s}^t \ln \frac{{\mathbf s}}{{\mathbf s}'}$ \\
  Squared Euclidean distance & $\|{\mathbf s} - {\mathbf s}'\|^2$ \\
  \bottomrule
\end{tabular}
\label{Discrepancy_measures}
\end{table}

\item ${\cal T}$ is a geometric transformation, which aligns pairs of unlabeled images, for instance, using a standard automatic cross-modality registration algorithm \cite{Oliveira-Tavares-14}.

\item ${\cal H}$ denotes standard cross-entropy loss for labeled source-domain images: ${\cal H}({\mathbf y}_i (p), {\mathbf s} (p, X_i)) = - {\mathbf y}_i^t(p) \ln {\mathbf s} (p, X_i)$, with superscript $t$ denoting transposition.
\item $\lambda$ is a non-negative multiplier.
 \end{itemize}

The second term in our model in \eqref{density-matching-loss} encourages the density of network outputs (softmax segmentations) in the target
domain to closely match the density of those in the source domain.
Our loss in \eqref{density-matching-loss} encourages direct kernel
density matching in the network-output space. \cref{fig:conceptualcomparison} juxtaposes conceptually our direct matching (\cref{fig:conceptualcomparison:c}) to the state-of-art
method in \cite{tsai2018learning}, which pursues a two-step adversarial learning in the network-output space (\cref{fig:conceptualcomparison:a,fig:conceptualcomparison:b}), so as to achieve the same
goal as our loss: matching the source and target distributions of label predictions. The data points in the Figure depict networks outputs
(softmax segmentations) in $\{0,1\}^{L \times |\Omega|}$, with the blue points
corresponding to the source and dashed points to the target.

The model in \cite{tsai2018learning} alternates the training of two networks: (i) a discriminator (\cref{fig:conceptualcomparison:a}),
which learns a decision boundary $D(S(X))$ that distinguishes between source and target outputs; and (ii) a segmentation network that uses the learned decision
boundary, thereby encouraging the target outputs to be similar to those in the source (\cref{fig:conceptualcomparison:b}). Rather than using an intermediate domain
discriminator, our direct method (\cref{fig:conceptualcomparison:c}) unifies distribution matching and segmentation in a single loss. Therefore, it simplifies segmentation
adaptation by avoiding extra adversarial steps, while improving both the quality, stability and efficiency of training. While adversarial training achieved outstanding
performances in image classification, our numerical evidence and intuition suggest that it may not be suitable for segmentation, in which case learning a discriminator boundary
is much more complex as it solves for predictions in an exponentially large label space. In fact, intuitively, a large label space implies large spaces of possible solutions
for discriminator boundaries and target predictions, both of which are latent; see dashed boundaries and data points in \cref{fig:conceptualcomparison:a}.
Therefore, alternating both adversarial and prediction tasks in segmentation might cause much more significant instabilities than in image classification tasks, as we
will see later in our experiments. Another important difference between our approach and adversarial training is that we account for the fact that target and source label
predictions are similar up to some geometric transformations. Such a prior information is very common and useful in medical
imaging problems but adversarial approaches do not have mechanisms to take advantage of it.

\section{Experiments}

In this section we describe and present the numerical experiments and results to validate the proposed unsupervised domain adaptation approach. Particularly, we evaluated our approach in the challenging task of brain tissue segmentation on magnetic resonance imaging (MRI). First, we show the performance of our method when it is trained and tested on different image protocols and scans across modalities are perfectly aligned. Then, we evaluate the impact of not having images perfectly aligned, which corresponds to having images from different subjects in the second term of equation (\ref{density-matching-loss}). In these experiments, we compare the proposed method with AdaptSegNet \cite{tsai2018learning}. And last, we investigated the effect of employing different kernels to evaluate the discrepancy between the source and target probability distributions in (\ref{density-matching-loss}).

\subsection{Experimental details}

\subsubsection{Dataset}
We performed numerical studies in two public segmentation benchmarks: MRBrainS2013 \cite{mendrik2015mrbrains} and iSEG2017 \cite{iSEG} challenge. The MRBrainS dataset contains 5 training scans with ground truth and 15 unlabeled scans of adult brains for testing. On the other hand, the iSEG dataset focus on infant brains and it is composed by 10 training and 13 testing scans. We tested our algorithm on the T1 and T2-FLAIR modalities of MRBrainS and T1, T2 of iSEG. In both cases, the segmentation task consists of finding a pixel-wise classification of white matter (WM), gray matter (GM) and cerebrospinal fluid (CSF).

Original T2 images from the iSEG Challenge were resampled into an isotropic $1 \times 1 \times 1 \si{\cubic\milli\meter}$ resolution and then aligned onto their corresponding T1 images with a simple affine registration method. The sequences from the MRBrains Challenge were also aligned by rigid registration, using the Elastix software \cite{klein2010elastix}.

\subsubsection{Training}
We first evaluate our approach when images across domains are perfectly aligned. In this scenario, we assume that the training data $(\mathcal L, \mathcal U)$ consists of two distinct subsets, where $\mathcal L = \{(X_1, Y_1), \dots ,(X_n, Y_n)\}$ contains images $X_i$ from the source domain with their corresponding ground truth $y_i$, and $\mathcal U = \{(X_{n+1}, X'_{n+1}), \dots ,(X_{n+m}, X'_{n+m})\}$ contains unlabeled pairs of aligned source and target data, respectively. The calculation of the loss for one batch is detailed in \cref{alg:loss}, where the permutation $\pi = \mathrm{id}$ denotes the identity.
In order to test performance when the assumption of alignment between $X_i$ and $X'_i$ is violated, we also perform experiments with shuffled target data, by passing a random permutation $\pi$ of $\{1, \dots, n\}$ to \cref{alg:loss}. By performing preliminary experiments, we found that the choice of distance functions $\mathcal D$ does not significantly alter performance (cf.\ \cref{sec:impact-kernel-choice}). We performed all experiments with squared Euclidean distance $\mathcal D(\mathbf s, \mathbf s') = \|\mathbf s - \mathbf s'\|^2$.

\begin{algorithm}
    \small
    \DontPrintSemicolon
    \KwIn{batch size $t$, distance function $\mathcal D$, permutation $\pi$ of $\{1, \dots, m\}$,
    network $\mathbf{s}(\cdot, \cdot)$, transformation $\mathcal{T}$, Lagrange multiplier $\lambda$}
    \KwData{%
    $\mathcal L = \{(X_1, Y_1), \dots ,(X_n, Y_n)\}$,
    $\mathcal U = \{(X_{n+1}, X'_{n+1}), \dots ,(X_{n+m}, X'_{n+m})\}$}
    \KwOut{loss $L$ for one random batch}
    \Begin{
        $\mathcal{I}_0 \leftarrow \RandomSample(\{1,\dots,n\}, t)$\;
    $\mathcal{I}_1 \leftarrow \RandomSample(\{1,\dots,m\}, t)$\;
    $L \leftarrow 0$\;
    \For{$i \in \mathcal I_0$}{
    $\displaystyle L \leftarrow L - \sum_{p \in \Omega}\sum_{l=1}^L y_i(l, p) \cdot
      \log s(l, p, X_i)$
    }
    \For{$i \in \mathcal I_1$}{
    ${\displaystyle L \leftarrow L + \lambda \sum_{p \in \Omega}
    \mathcal{D}\big(\mathbf{s}(p, X_{n+i}), \mathbf{s}(p, \mathcal T(X'_{n + \pi(i)}))\big)}$
    }
    }
    \caption{Computing the loss for one random batch. The function \texttt{RandomSample}$(\mathcal A, k)$ selects $k$ elements from the set $\mathcal A$ uniformly, independently at random, without replacement.}
    \label{alg:loss}
    \label{algo}
\end{algorithm}

Due to the limited size of the training set, we employed a leave-one-out-cross-validation strategy, where $n-1$ images were used for training, leaving the remaining image for evaluation. Furthermore, the unlabeled testing sequences were employed in the unsupervised term of \cref{density-matching-loss}.

Each experiment was performed three times with different evaluation data and the average as well as the empirical standard deviation over these three runs is reported.

\subsubsection{Baselines}
\label{sssec:models}

\paragraph{Lower and upper bounds.} In order to evaluate the impact of the adaptation approaches we trained the segmentation network in a supervised manner on the source and target data, providing a lower and upper bound for the expected unsupervised domain adaptation results. While network trained on source images is referred to as \emph{No adaptation}, the segmentation network directly trained on the target domain is referred to as the \emph{oracle}.

\paragraph{Adversarial state-of-the-art approach.} In addition, we compare the proposed approach with the adversarial method proposed in \cite{tsai2018learning}. For a fair comparison, we used the same segmentation network for the proposed and the adversarial approach. Furthermore, we kept the discriminator network architecture, but set the strides of two of the five convolutional layers to one due to a different input size for the discriminator network. The Lagrange multiplier for training the segmentation network was chosen to be $\lambda_{\mathrm{adv}} = 0.1$.

\subsubsection{Implementation details}
We used a slightly modified UNet \cite{Ronneberger2015U} for the segmentation task, operating on 2D slices. Particularly, the employed network follows the original implementation \cite{Ronneberger2015U}, but the depth is reduced by one, i.e., max-pool is performed only three times instead of four. The input size is $(120, 120)$, resulting in a lowest resolution of $(11, 11)$ and an output size of $(28, 28)$. We used ReLU activation functions and did not include dropout, to avoid any regularization that does not originate from our proposed domain adaptation strategy. The Lagrange multiplier $\lambda = 0.1$ was equal for all experiments. The input images are sliced along the z-axis to provide the input for the segmentation network.

For the adversarial approach of \cite{tsai2018learning}, we used the same segmentation network (U-Net) as described above to facilitate a fair comparison. To keep matters simple, we chose the ``single-level'' strategy, performing the domain adaptation only on the output layer. We chose the same discriminator model as in~\cite{tsai2018learning}. However, to avoid collapse of the discriminator output due to the small input size $(28, 28)$, we changed the stride of the third an fourth 2D convolution layer from two to one.

Implementation was done in TensorFlow, and experiments were run on a server equipped with a NVidia Titan V GPU with 12 GB memory. For all networks, we employed the Adam~\cite{Kingma2014Adam} optimizer with learning rate $\mathrm{lr} = 0.0001$ and a batch size of $32$. The code is publicly available at \url{https://github.com/anonymauthor/DDMSegNet}

\subsubsection{Evaluation}

Our evaluation involves a quantitative and a qualitative component. In terms of quantitative evaluation, we resorted to the common Dice coefficient, widely employed in medical image segmentation, to compare the performance of the different methods introduced in Section \ref{sssec:models}. The Dice coefficient can be expressed as:

\begin{eqnarray}
\DICE( \hat{Y} , Y )= \frac{2 | \hat{Y} \cap Y | }{| \hat{Y} | + | Y |} .
\end{eqnarray}

Since the images on the datasets are actually volumetric data, the reported dice values are computed over the 3D entire volume.
\begin{table*}[ht!]
\small
\caption{Domain adaptation results on MRBrains and iSEG dataset, showing the mean Dice coefficient over the three classes (i.e., GM, WM and CSF).}
\makebox[\textwidth][c]{
\begin{tabular}{lllcccc}
\toprule
&       &        & \multicolumn{4}{c}{Mean Dice}              \\
       \midrule
         &          &      & Oracle                        & No adaptation                 & AdaptSegNet \cite{tsai2018learning} & Proposed                      \\
\midrule
Source   & Target   &      & Target$\longrightarrow$Target & Source$\longrightarrow$Target & Source$\longrightarrow$Target                        & Source$\longrightarrow$Target \\
\midrule
MRB (T1) & MRB (T2-FLAIR)
& GM
& $\printMaxPercentWithStd{MRBrains_UNet_T2_FLAIR}{T2_FLAIR_DC}{T2_FLAIR_DC_1}{mean}$
& $\printMaxPercentWithStd{MRBrains_UNet_T2_FLAIR_from_T1}{T2_FLAIR_DC}{T2_FLAIR_DC_1}{mean}$
& $\printMaxPercentWithStd{MRBrains_AdaptSegNet}{T2_FLAIR_DC}{T2_FLAIR_DC_1}{mean}$
& $\printMaxPercentWithStd{MRBrains_RobNet_T2_FLAIR}{T2_FLAIR_DC}{T2_FLAIR_DC_1}{mean}$        \\
 &  & WM
& $\printMaxPercentWithStd{MRBrains_UNet_T2_FLAIR}{T2_FLAIR_DC}{T2_FLAIR_DC_2}{mean}$
& $\printMaxPercentWithStd{MRBrains_UNet_T2_FLAIR_from_T1}{T2_FLAIR_DC}{T2_FLAIR_DC_2}{mean}$
& $\printMaxPercentWithStd{MRBrains_AdaptSegNet}{T2_FLAIR_DC}{T2_FLAIR_DC_2}{mean}$
& $\printMaxPercentWithStd{MRBrains_RobNet_T2_FLAIR}{T2_FLAIR_DC}{T2_FLAIR_DC_2}{mean}$
\\
& & CSF
& $\printMaxPercentWithStd{MRBrains_UNet_T2_FLAIR}{T2_FLAIR_DC}{T2_FLAIR_DC_3}{mean}$
& $\printMaxPercentWithStd{MRBrains_UNet_T2_FLAIR_from_T1}{T2_FLAIR_DC}{T2_FLAIR_DC_3}{mean}$
& $\printMaxPercentWithStd{MRBrains_AdaptSegNet}{T2_FLAIR_DC}{T2_FLAIR_DC_3}{mean}$
& $\printMaxPercentWithStd{MRBrains_RobNet_T2_FLAIR}{T2_FLAIR_DC}{T2_FLAIR_DC_3}{mean}$  \\
&  & Mean
& $\printMaxPercentWithStd{MRBrains_UNet_T2_FLAIR}{T2_FLAIR_DC}{T2_FLAIR_DC}{mean}$
& $\printMaxPercentWithStd{MRBrains_UNet_T2_FLAIR_from_T1}{T2_FLAIR_DC}{T2_FLAIR_DC}{mean}$
& $\printMaxPercentWithStd{MRBrains_AdaptSegNet}{T2_FLAIR_DC}{T2_FLAIR_DC}{mean}$
& $\printMaxPercentWithStd{MRBrains_RobNet_T2_FLAIR}{T2_FLAIR_DC}{T2_FLAIR_DC}{mean}$         \\
\midrule
MRB (T2-FLAIR) & MRB (T1)
& GM
& $\printMaxPercentWithStd{MRBrains_UNet}{T1_DC}{T1_DC_1}{mean}$
& $\printMaxPercentWithStd{MRBrains_UNet_T2_FLAIR}{T1_DC}{T1_DC_1}{mean}$
& $\printMaxPercentWithStd{MRBrains_AdaptSegNet_T1_from_T2_FLAIR}{T1_DC}{T1_DC_1}{mean}$
& $\printMaxPercentWithStd{MRBrains_RobNet_T1_from_T2_FLAIR}{T1_DC}{T1_DC_1}{mean}$        \\
 &  & WM
& $\printMaxPercentWithStd{MRBrains_UNet}{T1_DC}{T1_DC_2}{mean}$
& $\printMaxPercentWithStd{MRBrains_UNet_T2_FLAIR}{T1_DC}{T1_DC_2}{mean}$
& $\printMaxPercentWithStd{MRBrains_AdaptSegNet_T1_from_T2_FLAIR}{T1_DC}{T1_DC_2}{mean}$
& $\printMaxPercentWithStd{MRBrains_RobNet_T1_from_T2_FLAIR}{T1_DC}{T1_DC_2}{mean}$
\\
& & CSF
& $\printMaxPercentWithStd{MRBrains_UNet}{T1_DC}{T1_DC_3}{mean}$
& $\printMaxPercentWithStd{MRBrains_UNet_T2_FLAIR}{T1_DC}{T1_DC_3}{mean}$
& $\printMaxPercentWithStd{MRBrains_AdaptSegNet_T1_from_T2_FLAIR}{T1_DC}{T1_DC_3}{mean}$
& $\printMaxPercentWithStd{MRBrains_RobNet_T1_from_T2_FLAIR}{T1_DC}{T1_DC_3}{mean}$  \\
&  & Mean
& $\printMaxPercentWithStd{MRBrains_UNet}{T1_DC}{T1_DC}{mean}$
& $\printMaxPercentWithStd{MRBrains_UNet_T2_FLAIR}{T1_DC}{T1_DC}{mean}$
& $\printMaxPercentWithStd{MRBrains_AdaptSegNet_T1_from_T2_FLAIR}{T1_DC}{T1_DC}{mean}$
& $\printMaxPercentWithStd{MRBrains_RobNet_T1_from_T2_FLAIR}{T1_DC}{T1_DC}{mean}$         \\
\midrule
iSEG (T1) & iSEG (T2)
& GM
& $\printMaxPercentWithStd{iSEG_UNet_T2}{T2_DC}{T2_DC_1}{mean}$
& $\printMaxPercentWithStd{iSEG_UNet}{T2_DC}{T2_DC_1}{mean}$
& $\printMaxPercentWithStd{iSEG_AdaptSegNet}{T2_DC}{T2_DC_1}{mean}$
& $\printMaxPercentWithStd{iSEG_RobNet}{T2_DC}{T2_DC_1}{mean}$        \\
 &  & WM
& $\printMaxPercentWithStd{iSEG_UNet_T2}{T2_DC}{T2_DC_2}{mean}$
& $\printMaxPercentWithStd{iSEG_UNet}{T2_DC}{T2_DC_2}{mean}$
& $\printMaxPercentWithStd{iSEG_AdaptSegNet}{T2_DC}{T2_DC_2}{mean}$
& $\printMaxPercentWithStd{iSEG_RobNet}{T2_DC}{T2_DC_2}{mean}$
\\
& & CSF
& $\printMaxPercentWithStd{iSEG_UNet_T2}{T2_DC}{T2_DC_3}{mean}$
& $\printMaxPercentWithStd{iSEG_UNet}{T2_DC}{T2_DC_3}{mean}$
& $\printMaxPercentWithStd{iSEG_AdaptSegNet}{T2_DC}{T2_DC_3}{mean}$
& $\printMaxPercentWithStd{iSEG_RobNet}{T2_DC}{T2_DC_3}{mean}$  \\
&  & Mean
& $\printMaxPercentWithStd{iSEG_UNet_T2}{T2_DC}{T2_DC}{mean}$
& $\printMaxPercentWithStd{iSEG_UNet}{T2_DC}{T2_DC}{mean}$
& $\printMaxPercentWithStd{iSEG_AdaptSegNet}{T2_DC}{T2_DC}{mean}$
& $\printMaxPercentWithStd{iSEG_RobNet}{T2_DC}{T2_DC}{mean}$         \\
\midrule
iSEG (T2) & iSEG (T1)
& GM
& $\printMaxPercentWithStd{iSEG_UNet}{T1_DC}{T1_DC_1}{mean}$
& $\printMaxPercentWithStd{iSEG_UNet_T2}{T1_DC}{T1_DC_1}{mean}$
& $\printMaxPercentWithStd{iSEG_AdaptSegNet_T1_from_T2}{T1_DC}{T1_DC_1}{mean}$
& $\printMaxPercentWithStd{iSEG_RobNet_T1_from_T2}{T1_DC}{T1_DC_1}{mean}$        \\
 &  & WM
& $\printMaxPercentWithStd{iSEG_UNet}{T1_DC}{T1_DC_2}{mean}$
& $\printMaxPercentWithStd{iSEG_UNet_T2}{T1_DC}{T1_DC_2}{mean}$
& $\printMaxPercentWithStd{iSEG_AdaptSegNet_T1_from_T2}{T1_DC}{T1_DC_2}{mean}$
& $\printMaxPercentWithStd{iSEG_RobNet_T1_from_T2}{T1_DC}{T1_DC_2}{mean}$
\\
& & CSF
& $\printMaxPercentWithStd{iSEG_UNet}{T1_DC}{T1_DC_3}{mean}$
& $\printMaxPercentWithStd{iSEG_UNet_T2}{T1_DC}{T1_DC_3}{mean}$
& $\printMaxPercentWithStd{iSEG_AdaptSegNet_T1_from_T2}{T1_DC}{T1_DC_3}{mean}$
& $\printMaxPercentWithStd{iSEG_RobNet_T1_from_T2}{T1_DC}{T1_DC_3}{mean}$  \\
&  & Mean
& $\printMaxPercentWithStd{iSEG_UNet}{T1_DC}{T1_DC}{mean}$
& $\printMaxPercentWithStd{iSEG_UNet_T2}{T1_DC}{T1_DC}{mean}$
& $\printMaxPercentWithStd{iSEG_AdaptSegNet_T1_from_T2}{T1_DC}{T1_DC}{mean}$
& $\printMaxPercentWithStd{iSEG_RobNet_T1_from_T2}{T1_DC}{T1_DC}{mean}$         \\
            \bottomrule
\end{tabular}}
\label{table:aligned}
\end{table*}

\subsection{Results}
\label{sssec:results}

\subsubsection{Precise image alignment.}
\Cref{table:aligned} reports the class-specific and mean results when pairs of unlabeled images are perfectly aligned (permutation $\pi = \mathrm{id}$ in \cref{algo}). Looking at the results achieved by the oracle we can observe that without any adaptation strategy the performance dramatically drops, particularly for the WM. The adaptation strategy proposed in \cite{tsai2018learning} is able to infer target domain information during learning and recover segmentation performance. For example, when shifting from T1 to T2 AdaptSegNet improves the mean performance by at least
{\readValue[max]{iSEG_AdaptSegNet}{T2_DC}{mean}{T2_DC}\pgfmathsetmacro{\adaptISEG}{\CSVnumber}%
  \readValue[max]{iSEG_UNet}{T2_DC}{mean}{T2_DC}\pgfmathsetmacro{\baselineISEG}{\CSVnumber}%
  \readValue[max]{MRBrains_AdaptSegNet}{T2_FLAIR_DC}{mean}{T2_FLAIR_DC}\pgfmathsetmacro{\adaptMRB}{\CSVnumber}%
  \readValue[max]{MRBrains_UNet_T2_FLAIR_from_T1}{T2_FLAIR_DC}{mean}{T2_FLAIR_DC}\pgfmathsetmacro{\baselineMRB}{\CSVnumber}%
  \pgfmathsetmacro{\CSVnumber}{100 * min(\adaptISEG - \baselineISEG, \adaptMRB - \baselineMRB)}%
  $\pgfmathprintnumber[fixed,precision=1,]{\CSVnumber}\%$}%
with respect to the \textit{No adaptation} network in both MRBrains and iSEG images. Despite this improvement, there is still a considerable gap compared to the oracle, with a difference of
{\readValue[max]{iSEG_AdaptSegNet}{T2_DC}{mean}{T2_DC}\pgfmathsetmacro{\adaptISEG}{\CSVnumber}%
  \readValue[max]{iSEG_UNet_T2}{T2_DC}{mean}{T2_DC}\pgfmathsetmacro{\baselineISEG}{\CSVnumber}%
  \pgfmathsetmacro{\CSVnumber}{100 * (\baselineISEG - \adaptISEG)}%
  $\pgfmathprintnumber[fixed,precision=1,]{\CSVnumber}\%$}
and
{\readValue[max]{MRBrains_AdaptSegNet}{T2_FLAIR_DC}{mean}{T2_FLAIR_DC}\pgfmathsetmacro{\adaptMRB}{\CSVnumber}%
  \readValue[max]{MRBrains_UNet_T2_FLAIR}{T2_FLAIR_DC}{mean}{T2_FLAIR_DC}\pgfmathsetmacro{\baselineMRB}{\CSVnumber}%
  \pgfmathsetmacro{\CSVnumber}{100 * (\baselineMRB - \adaptMRB)}%
  $\pgfmathprintnumber[fixed,precision=1,]{\CSVnumber}\%$}
for iSEG and MRBrains, respectively. On the other hand, the increased performance achieved by our method is more pronounced, getting closer to the performance of the oracle. Particularly, in all the four settings, differences with respect to training the network on target images and our method are in the range between
{\readValue[max]{iSEG_RobNet}{T2_DC}{mean}{T2_DC}\pgfmathsetmacro{\robi}{\CSVnumber}%
  \readValue[max]{iSEG_UNet_T2}{T2_DC}{mean}{T2_DC}\pgfmathsetmacro{\basei}{\CSVnumber}%
  \readValue[max]{MRBrains_RobNet_T2_FLAIR}{T2_FLAIR_DC}{mean}{T2_FLAIR_DC}\pgfmathsetmacro{\robii}{\CSVnumber}%
  \readValue[max]{MRBrains_UNet_T2_FLAIR}{T2_FLAIR_DC}{mean}{T2_FLAIR_DC}\pgfmathsetmacro{\baseii}{\CSVnumber}%
  \readValue[max]{iSEG_RobNet_T1_from_T2}{T1_DC}{mean}{T1_DC}\pgfmathsetmacro{\robiii}{\CSVnumber}%
  \readValue[max]{iSEG_UNet}{T1_DC}{mean}{T1_DC}\pgfmathsetmacro{\baseiii}{\CSVnumber}%
  \readValue[max]{MRBrains_RobNet_T1_from_T2_FLAIR}{T1_DC}{mean}{T1_DC}\pgfmathsetmacro{\robiv}{\CSVnumber}%
  \readValue[max]{MRBrains_UNet}{T1_DC}{mean}{T1_DC}\pgfmathsetmacro{\baseiv}{\CSVnumber}%
  \pgfmathsetmacro{\mymin}{100 * min(\basei - \robi, \baseii - \robii, \baseiii - \robiii, \baseiv - \robiv)}%
  \pgfmathsetmacro{\mymax}{100 * max(\basei - \robi, \baseii - \robii, \baseiii - \robiii, \baseiv - \robiv)}%
  $\pgfmathprintnumber[fixed,precision=1,]{\mymin} - \pgfmathprintnumber[fixed,precision=1,]{\mymax}\%$}. Furthermore, in most cases, the standard deviation is largely decreased by employing the proposed approach rather than the adversarial method. Another interesting finding when independently analyzing the class-specific results is that the proposed method reliably follows the behaviour of the oracle. For each of the four analyzed settings, the class segmentation rank for both oracle and proposed approach remains the same.

Qualitative results of these models are depicted in Figure \ref{fig:visual}. Specifically, cross-sectional 2D MRI images of two given patients are shown, for both source and target domains, along with the corresponding ground truth and segmentation masks obtained by the different models. We can observe that if no adaptation method is applied, the model trained on the source domain completely fail to segment the target image. Including an adaptation adversarial module visually improves the segmentation, which aligns with the numerical values reported in Table \ref{table:aligned}. Having a closer look to the AdaptSegNet segmentation we observe that while the CSF (in brown) seems to correlate with the ground truth, both white and gray matter (in yellow and green, respectively) only capture global information, being imprecise in local details. This can be due to the fact that appearance of this particular structure remains similar across domains, whereas intensity distribution of white and gray matter highly differ between source and target domains. Indeed, this observation also holds for the \textit{No adaptation} setting, where CSF segmentation obtains the best performance for domain adaptation on MRBrains. Contrary, the proposed direct distribution matching method is able to correctly capture differences between images, satisfactorily adapting both domains.

\begin{figure*}[h!]
\centering
\includegraphics[width=\textwidth]{ICCV-2019.png}
\caption{Visual results for two MRBrains subjects achieved by the different models in the case of adapting a MR T1-trained model to MR T2 images (\textit{top}), and a MR T2-trained model to MR T1 images (\textit{bottom}). These images were randomly selected from one of the three runs.}
\label{fig:visual}
\end{figure*}

\subsubsection{Sensitivity to image disalignment.}
\label{}

In our first experiments we used perfectly aligned images, but different protocols as source and target class. In order to test the performance when the assumption of alignment between $X_i$ and $X'_i$ is violated, we then randomly shuffle the target data $(X'_{n+1}, \dots, X'_{n+m})$ (random permutation in \cref{algo}), leading to a different pair of images in the unsupervised term.

To define a lower bound in this experiment, we simply compute the Dice coefficient across patients employing the provided labels. In Fig. \ref{fig:disalignment}, it can be observed that even though the brains across patients are somehow aligned, overlapping between the classes is very low. This is reflected in the poor Dice score reported in \cref{table:alignment}, where the mean Dice value across patients is equal to \printCompareDCPercent[1]{iseg}{avg}{mean}. Performing the adaptation with AdapSegNet improves the segmentation performance in the target by roughly
{\readValue[max]{iSEG_AdaptSegNet_shuffled}{T2_DC}{mean}{T2_DC}\pgfmathsetmacro{\adapti}{\CSVnumber}%
  \readValue[max]{iSEG_AdaptSegNet_T1_from_T2_shuffled}{T1_DC}{mean}{T1_DC}\pgfmathsetmacro{\adaptii}{\CSVnumber}%
  \readDCValue{iseg}{avg}{mean}\pgfmathsetmacro{\basei}{\CSVnumber}%
  \pgfmathsetmacro{\myval}{100 * ((\adapti + \adaptii)/2 - \basei))}%
  $\pgfmathprintnumber[fixed,precision=0,]{\myval}\%$}. On the other hand, the proposed approach achieves similar results than the adversarial method, while having a reduced complexity. It is worth mentioning that AdapSegNet does not leverage the alignment between images, as shown for example in the T2 to T1 adaptation scenario on iSEG data. When images in $\mathcal U$ are aligned, AdapSegNet achieves a mean DICE of \printMaxPercent{iSEG_AdaptSegNet_T1_from_T2}{T1_DC}{T1_DC}{mean} (\cref{table:aligned}), similar to the case of non-aligned images, i.e., \printMaxPercent{iSEG_AdaptSegNet_T1_from_T2_shuffled}{T1_DC}{T1_DC}{mean} (\cref{table:alignment}).

On the contrary, the proposed framework exploits this information, which results in a performance increase of
{\readValue[max]{iSEG_RobNet_T1_from_T2}{T1_DC}{mean}{T1_DC}\pgfmathsetmacro{\CSVnumberi}{\CSVnumber}%
  \readValue[max]{iSEG_RobNet_T1_from_T2_shuffled}{T1_DC}{mean}{T1_DC}%
  \pgfmathsetmacro{\CSVnumber}{100 * (\CSVnumberi - \CSVnumber)}$\pgfmathprintnumber[fixed,precision=1,]{\CSVnumber}\%$}
and
{\readValue[max]{iSEG_RobNet}{T2_DC}{mean}{T2_DC}\pgfmathsetmacro{\CSVnumberi}{\CSVnumber}%
  \readValue[max]{iSEG_RobNet_shuffled}{T2_DC}{mean}{T2_DC}%
  \pgfmathsetmacro{\CSVnumber}{100 * (\CSVnumberi - \CSVnumber)}$\pgfmathprintnumber[fixed,precision=1,]{\CSVnumber}\%$}
when adapting from T2 to T1 and T1 to T2, respectively (\cref{table:aligned,table:alignment}), if the data is aligned.

\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{Misalignment.png}
\caption{Disalignment found across iSEG dataset subjects. For simplicity, we display only one target class on these images. Different colors represent the WM labels for different patients. Each image shows a different pair of images from different scans. Best viewed in colour.}
\label{fig:disalignment}
\end{figure}

\begin{table*}[ht!]
\small
\caption{Domain adaptation results on the iSEG dataset when there is misalignment between the images.}
\begin{tabular}{llcccc}
\toprule
 &   & \multicolumn{4}{c}{Mean Dice} \\
\midrule
 &  & & Original alignment & AdaptSegNet \cite{tsai2018learning} & Proposed  \\
Source & Target &  & Source$\longrightarrow$Target & Source$\longrightarrow$Target & Source$\longrightarrow$Target  \\
\midrule
iSEG(T1) & iSEG(T2) & GM
& $\printCompareDCPercentWithStd[1]{iseg}{1}{mean}$
& $\printMaxPercentWithStd{iSEG_AdaptSegNet_shuffled}{T2_DC}{T2_DC_1}{mean}$
& $\printMaxPercentWithStd{iSEG_RobNet_shuffled}{T2_DC}{T2_DC_1}{mean}$\\
 &  & WM
& $\printCompareDCPercentWithStd[1]{iseg}{2}{mean}$
& $\printMaxPercentWithStd{iSEG_AdaptSegNet_shuffled}{T2_DC}{T2_DC_2}{mean}$
& $\printMaxPercentWithStd{iSEG_RobNet_shuffled}{T2_DC}{T2_DC_2}{mean}$\\
 &  & CSF
& $\printCompareDCPercentWithStd[1]{iseg}{3}{mean}$
& $\printMaxPercentWithStd{iSEG_AdaptSegNet_shuffled}{T2_DC}{T2_DC_3}{mean}$
& $\printMaxPercentWithStd{iSEG_RobNet_shuffled}{T2_DC}{T2_DC_3}{mean}$\\
 &  & Mean
& $\printCompareDCPercentWithStd[1]{iseg}{avg}{mean}$
& $\printMaxPercentWithStd{iSEG_AdaptSegNet_shuffled}{T2_DC}{T2_DC}{mean}$
& $\printMaxPercentWithStd{iSEG_RobNet_shuffled}{T2_DC}{T2_DC}{mean}$\\
\midrule
iSEG(T2) & iSEG(T1) & GM
& $\printCompareDCPercentWithStd[1]{iseg}{1}{mean}$
& $\printMaxPercentWithStd{iSEG_AdaptSegNet_T1_from_T2_shuffled}{T1_DC}{T1_DC_1}{mean}$
& $\printMaxPercentWithStd{iSEG_RobNet_T1_from_T2_shuffled}{T1_DC}{T1_DC_1}{mean}$\\
 &  & WM
& $\printCompareDCPercentWithStd[1]{iseg}{2}{mean}$
& $\printMaxPercentWithStd{iSEG_AdaptSegNet_T1_from_T2_shuffled}{T1_DC}{T1_DC_2}{mean}$
& $\printMaxPercentWithStd{iSEG_RobNet_T1_from_T2_shuffled}{T1_DC}{T1_DC_2}{mean}$\\
 & & CSF
& $\printCompareDCPercentWithStd[1]{iseg}{3}{mean}$
& $\printMaxPercentWithStd{iSEG_AdaptSegNet_T1_from_T2_shuffled}{T1_DC}{T1_DC_3}{mean}$
& $\printMaxPercentWithStd{iSEG_RobNet_T1_from_T2_shuffled}{T1_DC}{T1_DC_3}{mean}$\\
 &  & Mean
& $\printCompareDCPercentWithStd[1]{iseg}{avg}{mean}$
& $\printMaxPercentWithStd{iSEG_AdaptSegNet_T1_from_T2_shuffled}{T1_DC}{T1_DC}{mean}$
& $\printMaxPercentWithStd{iSEG_RobNet_T1_from_T2_shuffled}{T1_DC}{T1_DC}{mean}$\\
\bottomrule
\end{tabular}
\label{table:alignment}
\end{table*}

\subsubsection{Training stability.}

Adversarial learning strategies are known to be unstable during training. Particularly, for UDA adversarial based approaches this often results in segmentators that produce meaningless outputs. Thus, in addition to segmentation performance, we want to compare our method to adversarial in terms of learning convergence. Figure \ref{fig:dice} depicts the testing evolution of the mean 3D DICE coefficient for AdaptSegNet and our proposed approach, evaluated every 5 epochs. It can be observed that in both datasets, MRBrains and iSEG, training is very unstable for the adversarial approach, not clearly converging in the MRBrains dataset (\textit{left plot}). As a consequence, the performance can be highly different depending on the number of trained epochs.

On the other hand, the proposed method shows a significantly better stability, smoothly converging as the network is trained.

\begin{figure}[ht]
  \centering
  \subfloat[\scriptsize{MRBrainS: T1$\to$T2-FLAIR}]{
    \begin{scaletikzpicturetowidth}{.48\textwidth}
      \scalebox{\tikzscale}{
        \begin{tikzpicture}          \begin{axis}[ymin=0.0, ymax=0.85,
            grid=both, minor tick num=2,
            axis lines=center,
            legend style={at={(0.01,0.01)},anchor=south west},
            xlabel=epoch,
            x label style={anchor=north east}]
            \addCSVplot[blue, name path=A1, smooth]            {MRBrains_AdaptSegNet}{T2_FLAIR_DC}{amin};
            \addlegendentry{AdaptSegNet \cite{tsai2018learning}};
            \addCSVplot[red, name path=A2, smooth]            {MRBrains_RobNet_T2_FLAIR}{T2_FLAIR_DC}{amin};
            \addlegendentry{Proposed};

            \addCSVplot[blue, name path=B1,smooth]            {MRBrains_AdaptSegNet}{T2_FLAIR_DC}{amax};
            \addCSVplot[red, name path=B2, smooth]            {MRBrains_RobNet_T2_FLAIR}{T2_FLAIR_DC}{amax};

            \tikzfillbetween[of=A1 and B1]{blue, opacity=0.2};
            \tikzfillbetween[of=A2 and B2]{red, opacity=0.2};
          \end{axis}
          \begin{pgfonlayer}{background}
            \fill[overlay,white] (-10,-10) rectangle (10,10);
          \end{pgfonlayer}
        \end{tikzpicture}}
    \end{scaletikzpicturetowidth}
    \label{fig:dice-mrbrains}
  }
  \subfloat[\scriptsize{iSEG: T1$\to$T2}]{
    \begin{scaletikzpicturetowidth}{.48\textwidth}
      \scalebox{\tikzscale}{
        \begin{tikzpicture}
          \begin{axis}[ymin=0.25, ymax=0.85,
            grid=both, minor tick num=2,
            axis lines=center,
            xlabel=epoch,
            x label style={anchor=north east}]
            \addCSVplot[blue, name path=A1, smooth]            {iSEG_AdaptSegNet}{T2_DC}{amin};
            \addlegendentry{AdaptSegNet \cite{tsai2018learning}};
            \addCSVplot[red, name path=A2, smooth]            {iSEG_RobNet}{T2_DC}{amin};
            \addlegendentry{Proposed};

            \addCSVplot[blue, name path=B1,smooth]            {iSEG_AdaptSegNet}{T2_DC}{amax};
            \addCSVplot[red, name path=B2, smooth]            {iSEG_RobNet}{T2_DC}{amax};

            \tikzfillbetween[of=A1 and B1]{blue, opacity=0.2};
            \tikzfillbetween[of=A2 and B2]{red, opacity=0.2};
          \end{axis}
          \begin{pgfonlayer}{background}
            \fill[overlay,white] (-10,-10) rectangle (10,10);
          \end{pgfonlayer}
        \end{tikzpicture}}
    \end{scaletikzpicturetowidth}
    \label{fig:dice-iseg}
  }
  \caption{Evolution of mean (validation) DICE coefficient over epochs. The minimum and maximum observed value over the three cross-validation runs is plotted, and the area in between is shaded.}
  \label{fig:dice}
\end{figure}

\subsubsection{Impact of the kernel choice}
\label{sec:impact-kernel-choice}

In addition to L2, we also conducted experiments with the Bhattacharyya kernel on both iSEG and MRBrains13 data. As shown in \cref{table:bhattacharyya}, we found that the kernel choice has negligible impact on the over-all performance.

\begin{table}[ht]
\small
\caption{Dice coefficients when training with squared Euclidean and Bhattacharyya distances.}
\begin{tabular}{lcccc}
\toprule
  &
    & Sq.\ Euclidian & Bhattacharyya \\
      \midrule
 & GM
& $\printMaxPercentWithStd{iSEG_RobNet}{T2_DC}{T2_DC_1}{mean}$
& $\printMaxPercentWithStd{iSEG_RobNet_bhattacharyya}{T2_DC}{T2_DC_1}{mean}$\\
Source: iSEG(T1)  &  WM
& $\printMaxPercentWithStd{iSEG_RobNet}{T2_DC}{T2_DC_2}{mean}$
& $\printMaxPercentWithStd{iSEG_RobNet_bhattacharyya}{T2_DC}{T2_DC_2}{mean}$\\
Target: iSEG(T2)  & CSF
& $\printMaxPercentWithStd{iSEG_RobNet}{T2_DC}{T2_DC_3}{mean}$
& $\printMaxPercentWithStd{iSEG_RobNet_bhattacharyya}{T2_DC}{T2_DC_3}{mean}$\\
  & Mean
& $\printMaxPercentWithStd{iSEG_RobNet}{T2_DC}{T2_DC}{mean}$
& $\printMaxPercentWithStd{iSEG_RobNet_bhattacharyya}{T2_DC}{T2_DC}{mean}$\\
\midrule
& GM
& $\printMaxPercentWithStd{MRBrains_RobNet_T2_FLAIR}{T2_FLAIR_DC}{T2_FLAIR_DC_1}{mean}$
& $\printMaxPercentWithStd{MRBrains_RobNet_T2_FLAIR_bhattacharyya}{T2_FLAIR_DC}{T2_FLAIR_DC_1}{mean}$\\
Source: MRB(T1)  &  WM
& $\printMaxPercentWithStd{MRBrains_RobNet_T2_FLAIR}{T2_FLAIR_DC}{T2_FLAIR_DC_2}{mean}$
& $\printMaxPercentWithStd{MRBrains_RobNet_T2_FLAIR_bhattacharyya}{T2_FLAIR_DC}{T2_FLAIR_DC_2}{mean}$\\
Target: MRB(T2) &  CSF
& $\printMaxPercentWithStd{MRBrains_RobNet_T2_FLAIR}{T2_FLAIR_DC}{T2_FLAIR_DC_3}{mean}$
& $\printMaxPercentWithStd{MRBrains_RobNet_T2_FLAIR_bhattacharyya}{T2_FLAIR_DC}{T2_FLAIR_DC_3}{mean}$\\
 &  Mean
& $\printMaxPercentWithStd{MRBrains_RobNet_T2_FLAIR}{T2_FLAIR_DC}{T2_FLAIR_DC}{mean}$
& $\printMaxPercentWithStd{MRBrains_RobNet_T2_FLAIR_bhattacharyya}{T2_FLAIR_DC}{T2_FLAIR_DC}{mean}$\\
\bottomrule
\end{tabular}
\label{table:bhattacharyya}
\end{table}

\section{Conclusions}

In this paper, we proposed a simple direct distribution matching approach for unsupervised domain adaptation in the context of semantic segmentation of medical images. Unlike all adversarial approaches in this domain, our method aligns data distributions from both domains in the label space. This output space conveys much richer local and global information, which results in better adapted models. Furthermore, as demonstrated in the experimental results, directly matching output distributions has several benefits compared to adversarial learning: superior performance and better training stability.

\section*{Acknowledgments}
\label{sec:acknowledgments}

Dr.\ Georg Pichler and Prof.\ Pablo Piantanida would like to acknowledge support for this project from the CNRS via the International Associated Laboratory (LIA) on Information, Learning and Control. The work of Prof.\ Pablo Piantanida was supported by the European Commission's Marie Sklodowska-Curie Actions (MSCA), through the Marie Sklodowska-Curie IF (H2020-MSCAIF-2017-EF-797805-STRUDEL).

Prof. Jose Dolz would like to thank NVIDIA for the donation of one TITAN V to support his research.

Some computations were made on the supercomputer ``Helios'' from Laval University, managed by Calcul Québec and Compute Canada. The operation of this supercomputer is funded by the Canada Foundation for Innovation (CFI), the ministère de l'Économie, de la science et de l'innovation du Québec (MESI) and the Fonds de recherche du Québec - Nature et technologies (FRQ-NT).

Part of this work was performed using HPC resources from the \href{http://mesocentre.centralesupelec.fr/}{Mésocentre} computing center of CentraleSupélec and École Normale Supérieure Paris-Saclay supported by CNRS and Région Île-de-France.

\myappendix

{\small
\bibliographystyle{ieee}

redpajama_set_name: RedPajamaArXiv


text:
Prince Salman: Palestinians Accept Trump's Proposals 'Or Shut Up'
May 2, 2018 3:21 AM IMEMC News & Agencies Arab World, News Report, Peace process 0
Saudi Arabia's crown prince, Mohammed bin Salman reportedly told a collection of Jewish leaders that Palestinian leadership has no choice but to accept Donald Trump's 'peace' proposal, according to Israeli media.
According to Ma'an News Agency, the meeting reportedly took place behind closed doors in New York, last month, where Mohammed bin Salman disapproved of the leadership of Palestinian Authority President Mahmoud Abbas.
Bin Salman allegedly said: "In the last several decades the Palestinian leadership has missed one opportunity after the other and rejected all the peace proposals it was given."
"It is about time the Palestinians take the proposals and agree to come to the table or shut up and stop complaining."
Those present at the meeting were reportedly "staggered" by the remarks, and criticism of Palestinians.
"There needs to be significant progress toward an agreement with the Palestinians before it will be possible to advance negotiations between Saudi Arabia and the Arab world and Israel.
"The Palestinian issue is not at the top of the Saudi government's agenda…There are much more urgent and more important issues to deal with — such as Iran," he said.
It is reported that Bin Salman and Trump's son-in-law, Jared Kushner — who has been appointed to the administration's team that will oversee the possible brokerage of negotiations between Israel and Palestine — are on friendly terms.
The Saudi crown prince has reportedly pressured Mahmoud Abbas to accept the U.S.' framework of a possible peace deal between Israel and Palestine.
The Palestinian Authority has maintained its position of boycotting the White House since last December. In the aftermath, Palestinian Authority leader Mahmoud Abbas declared that the U.S. was no longer an "honest broker" in the peace talks between the two nations, following Trump's announcement recognizing Jerusalem as the capital of Israel, as well as the relocation of its embassy from Tel Aviv to Jerusalem.
05/01/18 PLO: Palestinians Will Not Be Part of Any Peace Plan Proposed by US
04/01/18 Saudi Prince Meets with AIPAC, anti-BDS Leaders during US Visit
« Palestinian & Israeli Officials Sign Energy Agreement Army Refuses to Disclose Engagement Policy on Gaza Protesters »
IMEMC News & Agencies
Christopher Carlson is a full-time student of Religious Studies at Mount Mercy University, USA. He has been with the IMEMC since 2013. (chris@imemc.org)
Israel Opens Dams, Floods Agricultural Land in Gaza
Opinion: 'We Will Only be Moved as Bodies': Israel and Bedouins Face Off in the Negev
Video: Palestinian Woman Arrested at Al-Aqsa After Alleged Stabbing Attempt
Three Palestinians Detained Near Bethlehem, Including a Former Prisoner

redpajama_set_name: RedPajamaCommonCrawl


text:
Home / Business & Finance / Corporations / What Does the Abbreviation "Ltd." Mean in a Company Name?
What Does the Abbreviation "Ltd." Mean in a Company Name?
By Staff WriterLast Updated Mar 26, 2020 1:48:23 PM ET
Elliott Brown/CC-BY-2.0
"Ltd." is an abbreviation for "limited." When used after a business name, it indicates that the owners and shareholders of the business only have limited responsibility for the company's debts and obligations.
A company cannot simply place "Ltd." after its name for legal protection. In the United States, each state has its own legal requirements for owners to maintain a limited legal liability status. Some states also allow corporations to use "ltd." in the place of "inc."
In some other countries, this abbreviation indicates the business owner is only financially responsible for the amount of money that he or she has personally invested into the business.


text:
Jul MAR Apr
31 Jul 2018 - 13 Oct 2019
Collection: Live Web Proxy Crawls
Content crawled via the Wayback Machine Live Proxy mostly by the Save Page Now feature on web.archive.org.
Liveweb proxy is a component of Internet Archive's wayback machine project. The liveweb proxy captures the content of a web page in real time, archives it into a ARC or WARC file and returns the ARC/WARC record back to the wayback machine to process. The recorded ARC/WARC file becomes part of the wayback machine in due course of time.
This content does not have an English version.
This content does not have an Arabic version.
Find out why Mayo Clinic is the right place for your health care. Make an appointment..
Diseases and Conditions A-Z
Tests and Procedures A-Z
Drugs and Supplements A-Z
Find a directory of doctors and departments at all Mayo Clinic campuses. Visit now..
Medical Departments and Centers
Research Centers and Programs
See how Mayo Clinic research and clinical trials advance the science of medicine and improve patient care. Explore now..
Educators at Mayo Clinic train tomorrow's leaders to deliver compassionate, high-value, safe patient care. Choose a degree..
Explore Mayo Clinic's many resources and see jobs available for medical professionals. Get updates..
International Advisory Services
Philanthropy at Mayo Clinic
Your support accelerates powerful innovations in patient care, research and education. Give today..
Patient Care & Health Information
Care at Mayo Clinic
A seizure is a sudden, uncontrolled electrical disturbance in the brain. It can cause changes in your behavior, movements or feelings, and in levels of consciousness. If you have two or more seizures or a tendency to have recurrent seizures, you have epilepsy.
There are many types of seizures, which range in severity. Seizure types vary by where and how they begin in the brain. Most seizures last from 30 seconds to two minutes. A seizure that lasts longer than five minutes is a medical emergency.
Seizures are more common than you might think. Seizures can happen after a stroke, a closed head injury, an infection such as meningitis or another illness. Many times, though, the cause of a seizure is unknown.
Most seizure disorders can be controlled with medication, but management of seizures can still have a significant impact on your daily life. The good news is you can work with your health care professional to balance seizure control and medication side effects.
Seizure care at Mayo Clinic
With a seizure, signs and symptoms can range from mild to severe and vary depending on the type of seizure. Seizure signs and symptoms may include:
A staring spell
Uncontrollable jerking movements of the arms and legs
Loss of consciousness or awareness
Cognitive or emotional symptoms, such as fear, anxiety or deja vu
Doctors generally classify seizures as either focal or generalized, based on how and where abnormal brain activity begins. Seizures may also be classified as unknown onset, if how the seizure began isn't known.
Focal seizures
Focal seizures result from abnormal electrical activity in one area of your brain. Focal seizures can occur with or without loss of consciousness:
Focal seizures with impaired awareness. These seizures involve a change or loss of consciousness or awareness. You may stare into space and not respond normally to your environment or perform repetitive movements, such as hand rubbing, chewing, swallowing or walking in circles.
Focal seizures without loss of consciousness. These seizures may alter emotions or change the way things look, smell, feel, taste or sound, but you don't lose consciousness. These seizures may also result in the involuntary jerking of a body part, such as an arm or leg, and spontaneous sensory symptoms such as tingling, dizziness and flashing lights.
Symptoms of focal seizures may be confused with other neurological disorders, such as migraine, narcolepsy or mental illness.
Generalized seizures
Seizures that appear to involve all areas of the brain are called generalized seizures. Different types of generalized seizures include:
Absence seizures. Absence seizures, previously known as petit mal seizures, often occur in children and are characterized by staring into space or by subtle body movements, such as eye blinking or lip smacking. These seizures may occur in clusters and cause a brief loss of awareness.
Tonic seizures. Tonic seizures cause stiffening of your muscles. These seizures usually affect muscles in your back, arms and legs and may cause you to fall to the ground.
Atonic seizures. Atonic seizures, also known as drop seizures, cause a loss of muscle control, which may cause you to suddenly collapse or fall down.
Clonic seizures. Clonic seizures are associated with repeated or rhythmic, jerking muscle movements. These seizures usually affect the neck, face and arms.
Myoclonic seizures. Myoclonic seizures usually appear as sudden brief jerks or twitches of your arms and legs.
Tonic-clonic seizures. Tonic-clonic seizures, previously known as grand mal seizures, are the most dramatic type of epileptic seizure and can cause an abrupt loss of consciousness, body stiffening and shaking, and sometimes loss of bladder control or biting your tongue.
Seek immediate medical help if any of the following occurs:
The seizure lasts more than five minutes.
Breathing or consciousness doesn't return after the seizure stops.
A second seizure follows immediately.
You have a high fever.
You're experiencing heat exhaustion.
You're pregnant.
You have diabetes.
You've injured yourself during the seizure.
If you experience a seizure for the first time, seek medical advice.
Request an Appointment at Mayo Clinic
Nerve cells (neurons) in the brain create, send and receive electrical impulses, which allow the brain's nerve cells to communicate. Anything that disrupts these communication pathways can lead to a seizure.
The most common cause of seizures is epilepsy. But not every person who has a seizure has epilepsy. Sometimes seizures happen because of:
High fever, which can be associated with an infection such as meningitis
Low blood sodium (hyponatremia), which can happen with diuretic therapy
Medications, such as certain pain relievers, antidepressants or smoking cessation therapies, that lower the seizure threshold
Head trauma that causes an area of bleeding in the brain
Illegal or recreational drugs, such as amphetamines or cocaine
Alcohol abuse, during times of withdrawal or extreme intoxication
Having a seizure at certain times can lead to circumstances that are dangerous for you or others. You might be at risk of:
Falling. If you fall during a seizure, you can injure your head or break a bone.
Drowning. If you have a seizure while swimming or bathing, you're at risk of accidental drowning.
Car accidents. A seizure that causes either loss of awareness or control can be dangerous if you're driving a car or operating other equipment.
Pregnancy complications. Seizures during pregnancy pose dangers to both mother and baby, and certain anti-epileptic medications increase the risk of birth defects. If you have epilepsy and plan to become pregnant, work with your doctor so that he or she can adjust your medications and monitor your pregnancy, as needed.
Emotional health issues. People with seizures are more likely to have psychological problems, such as depression and anxiety. Problems may be a result of difficulties dealing with the condition itself as well as medication side effects.
By Mayo Clinic Staff
Seizures care at Mayo Clinic
Share on: FacebookTwitter
Schachter SC. Evaluation and management of the first seizure in adults. https://www.uptodate.com/contents/search. Accessed May 24, 2017.
Daroff RB, et al. Epilepsies. In: Bradley's Neurology in Clinical Practice. 7th ed. Philadelphia, Pa.: Saunders Elsevier; 2016. https://www.clinicalkey.com. Accessed May 5, 2017.
The epilepsies and seizures: Hope through research. National Institute of Neurological Disorders and Stroke. https://www.ninds.nih.gov/Disorders/Patient-Caregiver-Education/Hope-Through-Research/Epilepsies-and-Seizures-Hope-Through. Accessed May 24, 2017.
Types of seizures. Epilepsy Foundation. http://www.epilepsy.com/learn/types-seizures. Accessed May 24, 2017.
AskMayoExpert. First seizure (adult). Rochester, Minn.: Mayo Foundation for Medical Education and Research; 2014.
Seizure First Aid. Centers for Disease Control and Prevention. https://www.cdc.gov/features/getseizuresmart/index.html. Accessed June 13, 2017.
Haider HA, et al. Neuroimaging in the evaluation of seizures and epilepsy. https://www.uptodate.com/contents/search. Accessed May 24, 2017.
Neurological diagnostic tests and procedures fact sheet. National Institute of Neurological Disorders and Stroke. https://www.ninds.nih.gov/Disorders/Patient-Caregiver-Education/Fact-Sheets/Neurological-Diagnostic-Tests-and-Procedures-Fact. Accessed May 24, 2017.
Schachter SC. Overview of the management of epilepsy in adults. https://www.uptodate.com/contents/search. Accessed May 24, 2017.
Crepeau AZ, et al. Management of adult onset seizures. Mayo Clinic Proceedings. 2017;92:306.
Harden CL, et al. Practice parameter update: Management issues for women with epilepsy — Focus on pregnancy (an evidence-based review): Teratogenesis and perinatal outcomes. Neurology. 2009;73:133.
Diagnosis 101. Epilepsy Foundation. http://www.epilepsy.com/start-here/diagnosis-101. Accessed June 14, 2017.
Seizure first aid. Epilepsy Foundation. http://www.epilepsy.com/learn/treating-seizures-and-epilepsy/seizure-first-aid. Accessed June 14, 2017.
Brown AY. Allscripts EPSi. Mayo Clinic, Rochester, Minn. Feb. 1, 2017.
Crepeau AZ (expert opinion). Mayo Clinic, Phoenix/Scottsdale, Ariz. July 7, 2017.
Van Gompel JJ (expert opinion). Mayo Clinic, Rochester, Minn. May 30, 2018.
Mayo Clinic Minute: Demystifying epilepsy
Mayo Clinic does not endorse companies or products. Advertising revenue supports our not-for-profit mission.
Mayo Clinic Marketplace
Check out these best-sellers and special offers on books and newsletters from Mayo Clinic.
FREE TRIAL — Mayo Clinic Health Letter
4 simple steps to a joy-filled life
Live stronger, longer and healthier at any age
Stop osteoporosis in its tracks
The Mayo Clinic Diet Online
Mayo Clinic is a not-for-profit organization. Make a donation.


Dr. Miao Li, assistant professor, Department of Sociology and School of Philosophy and Social Development at Shandong University, joins New Books in Education to discuss Citizenship Education and Migrant Youth in China: Pathways to the Urban Underclass (Routledge, 2015). Part of the Research in International and Comparative Education series, the book explores China's large floating population of migrants who have flocked to urban areas for employment, despite lagging educational opportunities for their children. Utilizing rich ethnographic data with interviews from teachers, principals, and students, Dr. Li thoroughly explores how global economic realities and national educational policies detrimentally affect people on the micro-level.
For questions or comments on the podcast, you can connect to the host at @PoliticsAndEd.


text:
Chair of Council
Closing date: Tuesday 31 January 2023
Salary: un-renumerated
Contract type: Casual / Working hours: Flexible
Location: Edinburgh , Harbourside House
110 Commercial Street, Edinburgh, EH6 6NF
Purple emperor ©Frank Porch www.flickr.com/photos/prankf
Scotland's leading nature conservation charity, the Scottish Wildlife Trust, is looking for a new Chair Of Council.
Title: Chair of Council
Salary: un-remunerated
Closing date: 31 January 2023, 12 noon
Scotland's leading nature conservation charity, the Scottish Wildlife Trust, is looking for a new Chair.
Do you have the ability, empathy and commitment to make a major contribution to the conservation of Scotland's wildlife and wild places?
Are you an experienced leader?
If so, we would love to hear from you!
We're looking for an outstanding individual with excellent leadership, diplomacy and communication skills, who is used to building consensus and has a natural affinity for cultivating relationships.
Understanding of current conservation challenges and issues would be an advantage, although a focus on maximising long-term impact is more important than in-depth expertise.
This post is eligible for a Disclosure Scotland check.


No problem. I am not trying very hard to sell it, so it may still be around.
As a matter of fact, I do still have it.
Keep it moving folks....nothing to see here.
This was my HP rifle last year in Zwolle, LA at their State HP match. I didn't expect to hit many, but it sure was fun. Now I know a .32-40 is capable of knocking down a ram at 500 meters. Scoped lever guns are fun!
I figured that, but had to ask. Thanks.
What's the word on scoring this year? Same as last year, or will we have scorers?
I think Pat's correct....blue corn chips go better with this show.
Not to be argumentative, but based on a recent (1879 or so) rule change, mules are also allowed now.
Topic: "Post or Bead insert..."
Re: "Post or Bead insert..."
It is in rule 3.1.3 a.
I received 2 of 13 yesterday, one was wrong. So far, I remain skeptical.
Let me know soon, as it is heading to GunBroker today or tomorrow.
Nothing wrong with Weaver bases. I like Millet rings with the Weaver bases, some folks don't care for them. They have several heights to choose from.


text:
Bruce Furst - Weebly
Harvard College Fund Parents Committee - Roles and Responsibilities
Since 2000, Bruce Furst has served as a president of Austin, Texas-based Ashber Corporation, where he maintains responsibility for licensing music content for film productions and negotiating film rights. Outside of this role, Bruce Furst supports the Harvard College Fund Parents Committee.
The Harvard College Fund Parents Committee brings together parent volunteers to foster a sense of community among parents of Harvard students around the world. Committee members help develop relationships between the college and parents and assist in recruiting volunteers. They also attend or host regional events for parents, including Parents Leadership Weekend in Cambridge.
Another important role of committee members is fundraising for the school. Leading by example, committee members who donate at least $1,000 per year belong to the Associates Committee, and those who donate at $5,000 annually earn a spot among the Leadership Gifts Committee. At both levels, parents serve a one-year renewable term.
Parents who donate at least $50,000 per year earn a spot among the Regional Vice Chairs and serve a two-year renewable term. Finally, those who donate at least $100,000 annually may receive a special invitation to serve as co-chairs on the Harvard College Fund Executive Committee. In this role, they serve a two-year renewable term and lead events and meetings throughout the year.
With over 20 years of experience in the entertainment industry, Bruce Furst boasts significant expertise in film and music licensing.
American Society Of Composers
Ashber Corporation
Bruce Furst
Intergalactic Royalty Operations Corporation (iRoc)


text:
Fine Art Valuations
Fine Art Valuations for Insurance and Probate
Haynes Fine Art has been involved with Fine Art Valuation for over 40 years covering most specialist areas of 19th to 21st Century British and European Art. With established links with many of the museum curators and saleroom experts we have networked a comprehensive database from which to source a professional valuation for both insurance and probate purposes. The cost of this service is dependant on location and time scale, a quote for which can be given by telephone or email email@haynesfineart.com
Alternatively paintings can be brought to the gallery and for the nominal cost of £25 each you can leave with a full written valuation, the proceeds from which go directly to our own charitable cause titled The Haynes Fine Art Sports for Schools Campaign. Appointments must be made through Lindsey or Wanda at the gallery on a day when Tony Haynes is expected at the gallery.
It has become all too evident that our children are spending more solitary time in front of a television or playing computer games. This small but valuable charitable drive will help some of our state schools provide healthy sports options whilst at school and during after school activities, many of which are not provided simply down to lack of funding for facilities and equipment. To date we have raised in excess of £20,000 which has been used to fund sports kit and equipment. 'Back in our day' the great outdoors was a place where we were sent to play in both our own time and indeed within our schools. Not only were these the times that we exercised but also where we encountered team work and companionship, above all social skills, something we do not get through being sat in front of a television screen.
For those who have helped fund our charitable work we extend a huge heartfelt thank you and we look forward to future clients who will contribute to our campaign. Upon receipt of your valuation we will ask for the cheque to be made payable directly to the chosen school we are working with at that time. This means 100% of all the money raised shall reach this good cause.
For those State Schools wishing to apply for this funding please forward your application to the gallery by writing and enclosing a self address envelope for us to respond. We are currently committed to projects which are focused on schools local to ourselves. We warmly invite at this time state funded schools in the areas of Worcestershire and Warwickshire.
The History of the Haynes Family
Antique Furniture & Sculpture
Antique Sculpture
Interest Free Payments
Valuations and Probate
Complete this form to receive emails with updates about our stock, events and website news.
By clicking "Join Now", I agree to the Haynes Fine Art Terms and Conditions and Privacy Policy.


Having had a taste for executing things in paralell in kanren let's move over to guile-log. Executing stuff in paralell is similar but we can take advantage of variable binding beeing done directly on the variable and not bound in a binding data structure. The idea is for each engine keep a path EnginePath=[ek,...,e0] that tracks the state of the engine ek being constructed in engine ek-1 etc. When we store a junction point we make sure that the path is stored with it. This is not dramatic addition of data to the logic engine.
Now the backtracker has to unwind the stack and undo bindings and dynamic winds etc. At each paralell junction we store a record of the paralell engines created. when unwinding over such a record either there is an angine in the first element of Path, if so we will install that engine and continue unwinding (adding the engine to the global EnginePath) And making sure that we will still keep the record on the old engines stack. If it is not match, all sub engines will be recursivly cleared and then the unwinding of the stack would continue. This describes the unwinding.
Now engines is just a datastructure consisting of the stack and the object containes extra information that is needed in order for backtracking to work properly.
This should as said int the comments be used by probing fail thunks in the specific brances and when executing those the code backtracks to a specific branch and and leave the siblings untouched. See Dependent Kanren for an example.
How would we do about a zip then? here is the code.
These examples does not work well if one store and restore due to that we mutate varibales. But basically the exact code survives using mutating safe boxes.


Lakes, ponds, streams, wet meadows, marshes, bogs, shallow pools; frequently in wooded regions; often near dead trees or brush (AOU 1983, Pratt et al. 1987). Edges of ponds in taiga (AOU 1983).
Pratt, H.D., P.L. Bruner, and D.G. Berrett. 1987. A Field Guide to the Birds of Hawaii and the Tropical Pacific. Princeton University Press, Princeton, New Jersey. 409 pp. + 45 plates.