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\title{Supplementary Materials}

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\maketitle

Fig. (\ref{fig:prep-and-ms-registration})  shows the flowchart for the 'preprocessing' and 'whole slide tissue registration' step of the proposed algorithm and Fig. (\ref{fig:siftregistration}) shows the flowchart for the SIFT registration step of the algorithm. 

\begin{figure*}[!h]
\centering
\includegraphics[clip=true, trim=0.5cm 0cm 1.2cm 1.4cm, width=0.8\textwidth]{prepAndMSRegistration.jpg}
\caption{Figure shows in more details the steps that are carried out in the 'Preprocessing' and 'Whole tissue registration' stages of the proposed algorithm.}
\label{fig:prep-and-ms-registration}
\end{figure*}

\clearpage 

\begin{figure*}[!h]
\centering
\includegraphics[clip=true, trim=0cm 0cm 1.5cm 0cm, width=\textwidth]{SIFTRegistration.jpg}
\caption{ Figure shows the steps that are taken in the 'SIFT registration' stage of the algorithm to register the ROI for subsequent whole slide images.}
\label{fig:siftregistration}
\end{figure*}

\clearpage

Fig.~\ref{fig:siftexamples} shows the SIFT registration results for a few slides of the registered blood vessels. For each example, the top left image shows the best SIFT feature matches for the ROIs in the previous and current slides. Also shown is the selected 3 SIFT matches that resulted in the best alignment of the 2 slides. The image on the right shows the segmentation for the previous slide (blue) mapped on the current slide after performing registration. The segmentation for the current slide is also shown in green. One can see that the two slides are aligned fairly well.\par

\begin{figure*}[!h]
\includegraphics[clip=true, trim=0cm 0cm 0cm 0cm, width=\textwidth]{SIFTExamples.jpg}
\caption{Example of the SIFT registration results. For each example, the left top figure shows the matched SIFT features for the full resolution ROI in the previous and current slide ($ROI^0_{i,i+1}$). The bottom left figure shows the 3 SIFT matches that led to the best alignment between the two slides. The right figure shows segmentation for the previous slide (blue) mapped on the current slide after performing registration. Also shown is the segmentation for the current slide (green). One can see that the two segmentations are reasonably aligned.}
\label{fig:siftexamples}
\end{figure*}

\clearpage
In order to ensure that the proposed registration algorithm and the final registration results after applying fine registration are robust against different sizes of the region of interest (ROI), we considered three different ROI sizes around the blood vessels of interest and performed registration using the proposed algorithm and the competing methods. After applying the proposed algorithm, fine registration was carried out using the work of~\cite{moles2014registration} with the best identified parameter values: $T_\mu = Affine$, $S = MI$, $MSL = 10$, and $Input = Lum$ and another set of values with smaller MSL: $T_\mu = Affine$, $S = MI$, $MSL = 1$, and $Input = Lum$. As shown in Fig.~\ref{fig:differentrois} (Left), the results suggest that performing regional registration after applying the proposed algorithm does not always provide reasonable results for the small-sized ROIs for the experiments with $MSL = 10$. However, regional registration is robust against medium- and large-sized ROIs with $MLS=10$ and different ROI sizes with $MSL = 1$.
Fig.~\ref{fig:differentrois} (Right) compares the registration accuracy of the proposed registration method followed by fine registration with those of the whole tissue registration method (\cite{moles2014registration} 1 Round) and the regional version of this method (\cite{moles2014registration} 2 Rounds) using $MSL = 1$ and $MSL = 10$ for fine registration.  One can see that the registration outputs are more accurate and robust for larger ROI sizes and the algorithm performs better using $MSL = 1$.\\

\begin{figure*}[t]
     \begin{tabular}{cc}
        \includegraphics[clip=true, trim=3cm 4cm 0cm -2cm, width=0.5\textwidth]{MSL1ProposedVsProposedML.jpg}&
        \includegraphics[clip=true, trim=3.2cm 4.4cm 0cm -2cm, width=0.5\textwidth]{MSL1ProposedMLVsML2Rounds.jpg}\\
        \includegraphics[clip=true, trim=3cm -1.5cm 0cm -2cm, width=0.5\textwidth]{MSL10ProposedVsProposedML.jpg}&
        \includegraphics[clip=true, trim=3cm -1.5cm 0cm -2cm, width=0.5\textwidth]{MSL10ProposedMLVsML2Rounds.jpg}\\
      \end{tabular}
      \caption{(Left) shows the registration accuracy using the proposed registration algorithm using different ROI sizes. (small) and (large) refer to the smallest and largest ROIs considered for the blood vessels, respectively (with (large) ROI being 150 pixels bigger than the (small) ROI in both dimensions). Proposed alg. + \cite{moles2014registration} shows the registration accuracy for the proposed registration algorithm followed by fine registration using different ROI sizes. (Right) compares the registration accuracy with those of the competing algorithms (\cite{moles2014registration} 1 Round and 2 Rounds). (Top row) shows the results using $MSL = 1$ for fine registration.  (Bottom row) shows these results for fine registration using $MSL = 10$.}
      \label{fig:differentrois}
\end{figure*}

\clearpage
%Fig. \ref{fig:vessels2} shows a 2D view of the other 10 blood vessels in our experiment that were selected for registration (first column). The resulting 3D reconstructed blood vessels after performing registration using the proposed algorithm are shown in the second and third column, respectively. The fourth and fifth column show 3D reconstruction of the registered lumen masks using the proposed algorithm followed by fine registration, and regional version (\cite{moles2014registration} 2 rounds) of the method by~\cite{moles2014registration} as the registration technique.



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