\begin{table}%t1
\small
   Maps used in morphological analysis. \\[1mm]
   %\centering
\par
   \begin{tabular}{clll}
   \hline\hline
   Symbol        & Name                    & Description                                   & Eq. \\
   \hline
                 &                         &                                               & \\
   $\Phi$        & Scale Space Map         & Combination filtered density maps $f_{\rm S,n}$ over all levels $n$. & (\ref{eq:scalespace})\\ 
                 &                         &                                               & \\
                 &                         &                                               & \\
\par
   $\mathcal{E}$ & Morphology Mask         & Region of space obeying shape constraint. & (\ref{eq:morphmask})\\ 
                 &                         & $E=1$: locations obeying shape constraint   & (Table~\ref{tab:morph})\\
                 &                         & $E=0$: locations not obeying shape constraints & \\
\par
   $\mathcal{S}$ & Shape Significance Map  & Feature shape fidelity for each point locale. & \\ 
                 &                         & Measures conformance to local shape criteria  & (\ref{eq:significance})\\  
                 &                         &                                               & \\
   $\mathcal{M}$ & Morphology Map          & Soft thresholded version of $\mathcal{S}$.  The threshold selects out the most & \\
                 &                         & locally shape conformant features.  Requires input of a threshold parameter $\beta$ & (\ref{eq:G_geom_1}) \\
                 &                         &                                               & \\
   $\mathcal{I}$ & Morphology Intensity Map   & Map of $\lambda_3$ for blobs,     
                                             $\lambda_2$ for filaments or 
                                             $\lambda_1$ for walls                         & \\
                 &                         & Modulates Morphology map, meant to avoid enhancing noisy low intensity structures 
                                             & (\ref{eq:intensity}) \\
                 &                         &                                               & \\
\par
   $\mathcal{T}$ & Morphology Filter       & Constructed from $\mathcal{I}$ and $\mathcal{M}$. Morphology weighted filter & \\
                 &                         & for the Morphology Mask. Provides each location which obeys the morphology constraint  & \\
                 &                         & with a measure of the strength of morphology signal. & (\ref{eq:morphfilter}) \\
                 &                         &                                               & \\
   $\mathcal{F}$ & Feature Map             & Product of morphology mask $\mathcal{E}$ and corresponding morphology filter $\mathcal{T}$.  & \\
                 &                         & There is one Feature Map for each level in the Scale-Space, representing local structures as & \\
                 &                         & seen on the different scales of the Scale-Space & (\ref{eq:featuremap}) \\
                 &                         &                                               & \\
   $\Psi$        & Scale-Space Map Stack   & Constructed from the $\mathcal{F}_i$ for all levels in the Scale-Space   &   \\
                 &                         & Each pixel in this map is the greatest value of the corresponding pixels & \\
                 &                         &  in  the Feature maps that make up the Scale-Space stack & (\ref{eq:featurestack}) \\
                 &                         &                                               & \\
                 &                         &                                               & \\
   $\mathcal{O}$ & Object Map              & Inclusion of astrophysical and cosmological criteria to select physically recognizable objects & \\
                 &                         & Produced by thresholding Scale-Space Map Stack $\Psi$ &   \\
                 &                         & Threshold criterion determined by cosmological/astrophysical considerations & 
(Sect.~\ref{sec:FeatureDetection}) \\
  \hline
   \end{tabular}
 \end{table}