* Finished to implement the changes requested by PA on 08/24.

* Committed Surface_reconstruction_statistics.xls with PA changes committed on 08/24.
* Fixed figures numbering.

Surface_reconstruction_points_3/doc_tex/Surface_reconstruction_points_3/apss.tex

@@ -10,7 +10,6 @@ Even though the \ccc{CGAL::APSS_reconstruction_function} class can be used direc
 
 % Insert image APSS.jpg/eps
 \begin{center}
-    \label{Surface_reconstruction_points_3-fig-APSS}
     % Image
     \begin{ccTexOnly}
         \includegraphics[width=0.5\textwidth]{Surface_reconstruction_points_3/APSS} % omit .eps suffix
@@ -23,6 +22,7 @@ Even though the \ccc{CGAL::APSS_reconstruction_function} class can be used direc
         \caption{APSS surface reconstruction from 10K
                  points sampled with a Minolta laser scanner.}
         % later: add computed function
+        \label{Surface_reconstruction_points_3-fig-APSS}
     \end{figure}
 \end{center}
 

Surface_reconstruction_points_3/doc_tex/Surface_reconstruction_points_3/case_studies.tex

@@ -13,9 +13,8 @@ Ideally the current implementation of the Poisson surface reconstruction method
 
 % Insert image bimba.jpg/.eps
 \begin{center}
-    \label{Surface_reconstruction_points_3-fig-bimba}
     \begin{ccTexOnly}
-  \includegraphics[width=1.0\textwidth]{Surface_reconstruction_points_3/bimba}
+        \includegraphics[width=1.0\textwidth]{Surface_reconstruction_points_3/bimba}
     \end{ccTexOnly}
     \begin{ccHtmlOnly}
         <img width="80%" border=0 src="./bimba.jpg"><P>
@@ -24,14 +23,14 @@ Ideally the current implementation of the Poisson surface reconstruction method
         \caption{Poisson reconstruction.
                  Left: 120K points sampled on a statue (Minolta laser scanner).
                  Right: reconstructed surface mesh.}
+        \label{Surface_reconstruction_points_3-fig-bimba}
     \end{figure}
 \end{center}
 
 % Insert image eros.jpg/.eps
 \begin{center}
-    \label{Surface_reconstruction_points_3-fig-eros}
     \begin{ccTexOnly}
-\includegraphics[width=1.0\textwidth]{Surface_reconstruction_points_3/eros}
+        \includegraphics[width=1.0\textwidth]{Surface_reconstruction_points_3/eros}
     \end{ccTexOnly}
     \begin{ccHtmlOnly}
         <img width="80%" border=0 src="./eros.jpg"><P>
@@ -39,6 +38,7 @@ Ideally the current implementation of the Poisson surface reconstruction method
     \begin{figure}[h]
         \caption{Left: 120K points sampled on a statue (Minolta laser scanner).
                  Right: reconstructed surface mesh.}
+        \label{Surface_reconstruction_points_3-fig-eros}
     \end{figure}
 \end{center}
 
@@ -46,9 +46,8 @@ The algorithm is fairly robust to anisotropic sampling and to noise. It is also
 
 % Insert image holes_good.jpg/.eps
 \begin{center}
-    \label{Surface_reconstruction_points_3-fig-holes_good}
     \begin{ccTexOnly}
-\includegraphics[width=1.0\textwidth]{Surface_reconstruction_points_3/holes_good}
+        \includegraphics[width=1.0\textwidth]{Surface_reconstruction_points_3/holes_good} % omit .eps suffix
     \end{ccTexOnly}
     \begin{ccHtmlOnly}
         <img width="80%" border=0 src="./holes_good.jpg"><P>
@@ -59,6 +58,7 @@ The algorithm is fairly robust to anisotropic sampling and to noise. It is also
                  to the scanning technology.
                  Right: reconstructed surface mesh and closeup.
                  The holes are properly closed.}
+        \label{Surface_reconstruction_points_3-fig-holes_good}
     \end{figure}
 \end{center}
 
@@ -66,17 +66,17 @@ The algorithm is in general not robust to outliers, although a few outliers do n
 
 % Insert image outliers.jpg/.eps
 \begin{center}
-    \label{Surface_reconstruction_points_3-fig-outliers}
     \begin{ccTexOnly}
-\includegraphics[width=1.0\textwidth]{Surface_reconstruction_points_3/outliers}    \end{ccTexOnly}
+        \includegraphics[width=1.0\textwidth]{Surface_reconstruction_points_3/outliers} % omit .eps suffix
+    \end{ccTexOnly}
     \begin{ccHtmlOnly}
         <img width="80%" border=0 src="./outliers.jpg"><P>
     \end{ccHtmlOnly}
     \begin{figure}[h]
         \caption{Left: 70K points sampled on an elephant with few
-                 outliers emphasized with circles.
-                 % careful: show circles not disks
+                 outliers emphasized with disks.
                  Right: reconstructed surface mesh.}
+        \label{Surface_reconstruction_points_3-fig-outliers}
     \end{figure}
 \end{center}
 
@@ -86,7 +86,8 @@ The algorithm works well even when the inferred surface is composed of several c
 
 \subsubsection{Contouring Parameters}
 
-Our implementation of the Poisson surface reconstruction algorithm computes an implicit function represented as a piecewise linear function over the tetrahedra of a 3D Delaunay triangulation constructed from the input points then refined through Delaunay refinement. For this reason any iso-surface is also piecewise linear and hence may contain sharp creases. As the contouring algorithm \ccc{CGAL::make_surface_mesh()} expects a smooth implicit function these sharp creases may create spurious clusters of vertices in the final reconstructed surface mesh when setting a small mesh sizing or surface approximation error parameter (see Figure~\ref{Surface_reconstruction_points_3-fig-contouring_bad}). One way to avoid these spurious clusters consists of adjusting the mesh sizing and surface approximation parameters large enough compared to the average sampling density (obtained through \ccc{CGAL::compute_average_spacing()}) so that the contouring algorithm ``perceives'' a smooth iso-surface. We recommend to use the following contouring parameters:
+Our implementation of the Poisson surface reconstruction algorithm computes an implicit function represented as a piecewise linear function over the tetrahedra of a 3D Delaunay triangulation constructed from the input points then refined through Delaunay refinement. For this reason, any iso-surface is also piecewise linear and hence may contain sharp creases. As the contouring algorithm \ccc{CGAL::make_surface_mesh()} expects a smooth implicit function these sharp creases may create spurious clusters of vertices in the final reconstructed surface mesh when setting a small mesh sizing or surface approximation error parameter (see Figure~\ref{Surface_reconstruction_points_3-fig-contouring_bad}).\\
+One way to avoid these spurious clusters consists of adjusting the mesh sizing and surface approximation parameters large enough compared to the average sampling density (obtained through \ccc{CGAL::compute_average_spacing()}) so that the contouring algorithm ``perceives'' a smooth iso-surface. We recommend to use the following contouring parameters:
 \begin{itemize}
 \item Max triangle radius: at least 100 times the average spacing.
 \item Approximation distance: at least 0.25 times the average spacing.
@@ -95,9 +96,8 @@ Our implementation of the Poisson surface reconstruction algorithm computes an i
 % PA: we are missing the number of input points here.
 % Insert image contouring_bad.jpg/.eps
 \begin{center}
-    \label{Surface_reconstruction_points_3-fig-contouring_bad}
     \begin{ccTexOnly}
-\includegraphics[width=1.0\textwidth]{Surface_reconstruction_points_3/contouring_bad}
+        \includegraphics[width=1.0\textwidth]{Surface_reconstruction_points_3/contouring_bad}
     \end{ccTexOnly}
     \begin{ccHtmlOnly}
         <img width="80%" border=0 src="./contouring_bad.jpg"><P>
@@ -108,6 +108,7 @@ Our implementation of the Poisson surface reconstruction algorithm computes an i
                  Right: surface reconstructed with approximation
                  distance = 0.15 * average spacing.
                  Notice the spurious cluster on the chick.}
+        \label{Surface_reconstruction_points_3-fig-contouring_bad}
     \end{figure}
 \end{center}
 
@@ -122,9 +123,8 @@ The reconstruction algorithm expects a sufficiently dense point set. Although th
 
 % Insert image sampling.jpg/.eps
 \begin{center}
-    \label{Surface_reconstruction_points_3-fig-sampling}
     \begin{ccTexOnly}
-\includegraphics[width=0.8\textwidth]{Surface_reconstruction_points_3/sampling}     \end{ccTexOnly}
+        \includegraphics[width=0.8\textwidth]{Surface_reconstruction_points_3/sampling}     \end{ccTexOnly}
     \begin{ccHtmlOnly}
         <img width="80%" border=0 src="./sampling.jpg"><P>
     \end{ccHtmlOnly}
@@ -135,6 +135,7 @@ The reconstruction algorithm expects a sufficiently dense point set. Although th
                  Right: point set simplified to 1K points then reconstructed
                  (all input points are depicted with normals). The thin
                  feature is not reconstructed.}
+        \label{Surface_reconstruction_points_3-fig-sampling}
     \end{figure}
 \end{center}
 
@@ -145,9 +146,8 @@ The reconstruction is devised to solve for an implicit function which is an appr
 
 % Insert image holes_bad.jpg/.eps
 \begin{center}
-    \label{Surface_reconstruction_points_3-fig-holes_bad}
     \begin{ccTexOnly}
-\includegraphics[width=0.8\textwidth]{Surface_reconstruction_points_3/holes_bad}
+        \includegraphics[width=0.8\textwidth]{Surface_reconstruction_points_3/holes_bad}
     \end{ccTexOnly}
     \begin{ccHtmlOnly}
         <img width="80%" border=0 src="./holes_bad.jpg"><P>
@@ -158,19 +158,19 @@ The reconstruction is devised to solve for an implicit function which is an appr
                  Right: reconstructed surface mesh. The surface is
                  properly closed on the fingers and also closed
                  at the wrist but in a less plausible manner.}
+        \label{Surface_reconstruction_points_3-fig-holes_bad}
     \end{figure}
 \end{center}
 
 
 \subsubsection{Wrongly Oriented Normals}
 
-The Poisson surface reconstruction approaches solves for an implicit function whose gradient best matches a set of input normals. Because it solves this problem in the least squares sense it is robust to few isolated wrongly oriented (flipped) normals. Nevertheless a cluster of wrongly oriented normals leads to an incorrect implicit function and hence to spurious geometric or even topological distortion (see Figure~\ref{Surface_reconstruction_points_3-fig-flipped_normals}).
+The Poisson surface reconstruction approaches solves for an implicit function whose gradient best matches a set of input normals. Because it solves this problem in the least squares sense, it is robust to few isolated wrongly oriented (flipped) normals. Nevertheless a cluster of wrongly oriented normals leads to an incorrect implicit function and hence to spurious geometric or even topological distortion (see Figure~\ref{Surface_reconstruction_points_3-fig-flipped_normals}).
 
 % Insert image flipped_normals.jpg/.eps
 \begin{center}
-    \label{Surface_reconstruction_points_3-fig-flipped_normals}
     \begin{ccTexOnly}
-\includegraphics[width=0.8\textwidth]{Surface_reconstruction_points_3/flipped_normals}
+        \includegraphics[width=0.8\textwidth]{Surface_reconstruction_points_3/flipped_normals}
     \end{ccTexOnly}
     \begin{ccHtmlOnly}
         <img width="80%" border=0 src="./flipped_normals.jpg"><P>
@@ -179,6 +179,7 @@ The Poisson surface reconstruction approaches solves for an implicit function wh
         \caption{Left: points sampled on a sphere with a cluster
                  of wrongly oriented normals.
                  Right: reconstructed surface mesh with a spurious bump.}
+        \label{Surface_reconstruction_points_3-fig-flipped_normals}
     \end{figure}
 \end{center}
 
@@ -186,13 +187,12 @@ The Poisson surface reconstruction approaches solves for an implicit function wh
 \subsubsection{Noise and Outliers}
 
 A large amount of noise inevitably impacts on the reconstruction (see Figure~\ref{Surface_reconstruction_points_3-fig-noise}, top) and the current implementation does not provide any mean to trade data fitting for smoothness. Nevertheless if the signal-to-noise ratio is sufficiently high and/or the
-surface approximation and sizing parameters set for contouring the iso-surface is large with respect to the noise level the output surface mesh will appear smooth (not shown). If the user wants to produce a smooth and detailed output surface mesh we recommend to apply smoothing through \ccc{CGAL::jet_smooth_point_set()} ((see Figure~\ref{Surface_reconstruction_points_3-fig-noise}, bottom).
+surface approximation and sizing parameters set for contouring the iso-surface is large with respect to the noise level the output surface mesh will appear smooth (not shown). If the user wants to produce a smooth and detailed output surface mesh, we recommend to apply smoothing through \ccc{CGAL::jet_smooth_point_set()} ((see Figure~\ref{Surface_reconstruction_points_3-fig-noise}, bottom).
 
 % Insert image noise.jpg/.eps
 \begin{center}
-    \label{Surface_reconstruction_points_3-fig-noise}
     \begin{ccTexOnly}
-\includegraphics[width=0.8\textwidth]{Surface_reconstruction_points_3/noise}
+        \includegraphics[width=0.8\textwidth]{Surface_reconstruction_points_3/noise}
     \end{ccTexOnly}
     \begin{ccHtmlOnly}
         <img width="80%" border=0 src="./noise.jpg"><P>
@@ -203,6 +203,7 @@ surface approximation and sizing parameters set for contouring the iso-surface i
                  Top-right: reconstructed surface mesh.
                  Bottom-left: smoothed point set.
                  Bottom-right: reconstructed surface mesh.}
+        \label{Surface_reconstruction_points_3-fig-noise}
     \end{figure}
 \end{center}
 
@@ -215,9 +216,8 @@ The current reconstruction algorithm is not able to recover the sharp creases an
 
 % Insert image sharp_features.jpg/.eps
 \begin{center}
-    \label{Surface_reconstruction_points_3-fig-sharp_features}
     \begin{ccTexOnly}
-\includegraphics[width=0.8\textwidth]{Surface_reconstruction_points_3/sharp_features}
+        \includegraphics[width=0.8\textwidth]{Surface_reconstruction_points_3/sharp_features}
     \end{ccTexOnly}
     \begin{ccHtmlOnly}
         <img width="80%" border=0 src="./sharp_features.jpg"><P>
@@ -227,16 +227,7 @@ The current reconstruction algorithm is not able to recover the sharp creases an
                  sharp features (creases, darts and corners).
                  Right: reconstructed surface mesh with smoothed
                  creases.}
+        \label{Surface_reconstruction_points_3-fig-sharp_features}
     \end{figure}
 \end{center}
 
-
-
-%====================================================
-% PA: I propose to comment this: this is rather the
-% failure of the mst stuff - we can have users which
-% provide oriented normals
-%====================================================
-%\subsubsection{Several Connected Components}
-%This package does not support point sets with several clusters of points. The main limitation is that \ccc{CGAL::mst_orient_normals()} cannot orient coherently the normals of several clusters of points. The contouring phase (i.e. the call to \ccc{make_surface_mesh()}) also requires a different initialization to handle several connected components.
-

Surface_reconstruction_points_3/doc_tex/Surface_reconstruction_points_3/introduction.tex

@@ -4,7 +4,6 @@ This \cgal\ component implements two surface reconstruction methods which take a
 
 % Insert image introduction.jpg/eps
 \begin{center}
-    \label{Surface_reconstruction_points_3-fig-introduction}
     % Image
     \begin{ccTexOnly}
         \includegraphics[width=1.0\textwidth]{Surface_reconstruction_points_3/introduction} % omit .eps suffix
@@ -18,6 +17,7 @@ This \cgal\ component implements two surface reconstruction methods which take a
                  Left: 17K points sampled on the statue of an
                  elephant with a Minolta laser scanner.
                  Right: reconstructed surface mesh.}
+        \label{Surface_reconstruction_points_3-fig-introduction}
     \end{figure}
 \end{center}
 
@@ -32,7 +32,6 @@ Chapter \ccc{Point_set_processing_3} \ref{chap:point_set_processing_3} describes
 
 % Insert image pipeline.jpg/eps
 \begin{center}
-    \label{Surface_reconstruction_points_3-fig-pipeline}
     % Image
     \begin{ccTexOnly}
         \includegraphics[width=1.0\textwidth]{Surface_reconstruction_points_3/pipeline} % omit .eps suffix
@@ -43,6 +42,7 @@ Chapter \ccc{Point_set_processing_3} \ref{chap:point_set_processing_3} describes
     % Title
     \begin{figure}[h]
         \caption{Common surface reconstruction pipeline.}
+        \label{Surface_reconstruction_points_3-fig-pipeline}
     \end{figure}
 \end{center}
 

Surface_reconstruction_points_3/doc_tex/Surface_reconstruction_points_3/performances.tex

@@ -1,11 +1,11 @@
 \section{Performances}
 \label{surface_reconstruction_section_performances}
 
-We provide some performance numbers for scanning data. We measure the Poisson implicit function computation time, the contouring time for a variety of approximation distances, the memory occupancy as well as the influence of the point set simplification. The machine used is a PC running Linux 32 bits with an Intel CPU Core 2 processor clocked at 3 GHz and with 3 GB of RAM. The software is compiled with g++ 4.3.1 compiler with the 03 option which maximizes speed.
+We provide some performance numbers for scanning data. We measure the Poisson implicit function computation time, the contouring time for a range of approximation distances, the memory occupancy as well as the influence of the point set simplification. The machine used is a PC running Linux 32 bits with an Intel CPU Core 2 processor clocked at 3 GHz and with 3 GB of RAM. The software is compiled with g++ 4.3.1 compiler with the 03 option which maximizes speed.
 
 \subsection{Poisson implicit function}
 
-The point set chosen for benchmarking the Poisson implicit function is the Bimba con Nastrino point set (1.6M points) depicted by Figure~\ref{Surface_reconstruction_points_3-fig-poisson_bench}. We measure the Poisson implicit function computation (i.e., the call to \ccc{Poisson_reconstruction_function::compute_implicit_function()} denoted by Poisson solve hereafter) for this point set as well as for simplified versions obtained through random simplification. The following table provides Poisson solve computation times in seconds for an increasing number of points.
+The point set chosen for benchmarking the Poisson implicit function is the Bimba con Nastrino point set (1.6 million points) depicted by Figure~\ref{Surface_reconstruction_points_3-fig-poisson_bench}. We measure the Poisson implicit function computation (i.e., the call to \ccc{Poisson_reconstruction_function::compute_implicit_function()} denoted by Poisson solve hereafter) for this point set as well as for simplified versions obtained through random simplification. The following table provides Poisson solve computation times in seconds for an increasing number of points.
 
 \begin{tabular}{|c|c|}
   \hline
@@ -23,9 +23,8 @@ The point set chosen for benchmarking the Poisson implicit function is the Bimba
 
 % Insert image poisson_bench.jpg/.eps
 \begin{center}
-    \label{Surface_reconstruction_points_3-fig-poisson_bench}
     \begin{ccTexOnly}
-      \includegraphics[width=1.0\textwidth]{Surface_reconstruction_points_3/poisson_bench}
+        \includegraphics[width=1.0\textwidth]{Surface_reconstruction_points_3/poisson_bench}
     \end{ccTexOnly}
     \begin{ccHtmlOnly}
         <img width="80%" border=0 src="./poisson_bench.jpg"><P>
@@ -33,8 +32,9 @@ The point set chosen for benchmarking the Poisson implicit function is the Bimba
     \begin{figure}[h]
         \caption{Poisson implicit function computation duration (in s)
                  against the number of points  for the Bimba con Nastrino
-                 point set with 1.6 million points (shown)
+                 point set with 1.6M points (shown)
                  as well as for simplified versions.}
+        \label{Surface_reconstruction_points_3-fig-poisson_bench}
     \end{figure}
 \end{center}
 
@@ -42,11 +42,12 @@ The point set chosen for benchmarking the Poisson implicit function is the Bimba
 
 \subsection{Contouring}
 
-The point set chosen for benchmarking the contouring stage is the Bimba con Nastrino point set simplified to 120 kpoints. We measure the contouring (i.e. the call to \ccc{make_surface_mesh()}) duration and the reconstruction error (expressed as the average distance from input points to the reconstructed surface) for a variety of approximation distances.
+The point set chosen for benchmarking the contouring stage is the Bimba con Nastrino point set simplified to 120k points. We measure the contouring (i.e. the call to \ccc{make_surface_mesh()}) duration and the reconstruction error for a range of approximation distances.
+The reconstruction error is expressed as the average distance from input points to the reconstructed surface in mm (the Bimba con Nastrino statue is 324 mm tall).
 
 \begin{tabular}{|c|c|c|}
   \hline
-  Approx. distance (*average spacing)    & Contouring duration (sec) & Reconstruction error \\
+  Approx. distance (*average spacing)    & Contouring duration (in s) & Reconstruction error (mm) \\
   \hline
   0.1                                    & 177                       & 0.13 \\
   0.25                                   & 47                        & 0.155 \\
@@ -58,7 +59,6 @@ The point set chosen for benchmarking the contouring stage is the Bimba con Nast
 
 % Insert image contouring_bench.jpg/.eps
 \begin{center}
-    \label{Surface_reconstruction_points_3-fig-contouring_bench}
     \begin{ccTexOnly}
       \includegraphics[width=1.0\textwidth]{Surface_reconstruction_points_3/contouring_bench}
     \end{ccTexOnly}
@@ -66,9 +66,10 @@ The point set chosen for benchmarking the contouring stage is the Bimba con Nast
         <img width="80%" border=0 src="./contouring_bench.jpg"><P>
     \end{ccHtmlOnly}
     \begin{figure}[h]
-        \caption{Contouring duration and reconstruction error
+        \caption{Contouring duration (in s) and reconstruction error (mm)
                  against several approximation distance parameters
-                 for the Bimba con Nastrino point set simplified to 120 kpoints.}
+                 for the Bimba con Nastrino point set simplified to 120k points.}
+        \label{Surface_reconstruction_points_3-fig-contouring_bench}
     \end{figure}
 \end{center}
 
@@ -76,13 +77,13 @@ The point set chosen for benchmarking the contouring stage is the Bimba con Nast
 
 \subsection{Memory}
 
-We measure the memory occupancy for the full Bimba con Nastrino point set (3.8 millions points) as well as for simplified versions.\\
-The Poisson implicit function computation has a memory peak when solving the Poisson linear system using {\sc Taucs} sparse linear solver. For large point sets, it may fail to allocate big chunks of memory due to memory fragmentation.\\
-The exact limit depends of the allocation scheme used by the compiler. In our experiments, a PC running Linux 32 bits can reconstruct the Bimba con Nastrino point set up to 1.6 million points when Windows 32 bits is limited to 1.3 million points.\\
+We measure the memory occupancy for the reconstruction of the full Bimba con Nastrino point set (3.8 millions points) as well as for simplified versions.\\
+The Poisson implicit function computation has a memory peak when solving the Poisson linear system using the {\sc Taucs} sparse linear solver. For large point sets, it may fail to allocate big chunks of memory due to memory fragmentation.\\
+The exact limit depends of the allocation scheme used by the compiler. In our experiments, a PC running Linux 32 bits can reconstruct the Bimba con Nastrino point set up to 1.6M points while Windows 32 bits is limited to 1.3M points.\\
 
 \begin{tabular}{|c|c|}
   \hline
-  Number of points (kpoints) & Memory occupancy (MBytes) \\
+  Number of points (x1000) & Memory occupancy (MBytes) \\
   \hline
   60                         & 330 \\
   120                        & 660 \\
@@ -95,17 +96,18 @@ The exact limit depends of the allocation scheme used by the compiler. In our ex
 
 % Insert image memory_bench.jpg/.eps
 \begin{center}
-    \label{Surface_reconstruction_points_3-fig-memory_bench}
     \begin{ccTexOnly}
-      \includegraphics[width=1.0\textwidth]{Surface_reconstruction_points_3/memory_bench}
+        \includegraphics[width=1.0\textwidth]{Surface_reconstruction_points_3/memory_bench}
     \end{ccTexOnly}
     \begin{ccHtmlOnly}
         <img width="80%" border=0 src="./memory_bench.jpg"><P>
     \end{ccHtmlOnly}
     \begin{figure}[h]
         \caption{Memory occupancy (in MBytes) against number of points
-                 for the Bimba con Nastrino point set with 1.2 million points
-                 as well as for simplified versions.}
+                 for the Bimba con Nastrino point set with 1.2M points
+                 as well as for simplified versions.
+                 The best fitting line is shown.}
+        \label{Surface_reconstruction_points_3-fig-memory_bench}
     \end{figure}
 \end{center}
 
@@ -113,12 +115,13 @@ The exact limit depends of the allocation scheme used by the compiler. In our ex
 
 \subsection{Point Set Simplification}
 
-Due to memory limitations, it is a common practice to simplify the point sets captured by laser scanners.\\
-We measure the reconstruction error (expressed as the average distance from input points to the reconstructed surface) for the Bimba con Nastrino point set (1.6 million points) as well as for simplified versions. All reconstructions use the recommended contouring parameter approximation distance = 0.25 * the input point set's average spacing.
+Due to the memory limitations described above, we recommend to simplify the point sets captured by laser scanners.\\
+We measure the reconstruction error for the Bimba con Nastrino point set (1.6M points) as well as for simplified versions. All reconstructions use the recommended contouring parameter approximation distance = 0.25 * the input point set's average spacing.
+The reconstruction error is expressed as the average distance from input points to the reconstructed surface in mm (the Bimba con Nastrino statue is 324 mm tall).
 
 \begin{tabular}{|c|c|}
   \hline
-  Number of points (kpoints) & Reconstruction error \\
+  Number of points (x1000) & Reconstruction error (mm) \\
   \hline
   60                         & 0.27 \\
   120                        & 0.15 \\
@@ -132,17 +135,17 @@ We measure the reconstruction error (expressed as the average distance from inpu
 
 % Insert image simplification_bench.jpg/.eps
 \begin{center}
-    \label{Surface_reconstruction_points_3-fig-simplification_bench}
     \begin{ccTexOnly}
-      \includegraphics[width=1.0\textwidth]{Surface_reconstruction_points_3/simplification_bench}
+        \includegraphics[width=1.0\textwidth]{Surface_reconstruction_points_3/simplification_bench}
     \end{ccTexOnly}
     \begin{ccHtmlOnly}
         <img width="80%" border=0 src="./simplification_bench.jpg"><P>
     \end{ccHtmlOnly}
     \begin{figure}[h]
-        \caption{Reconstruction error against number of points
-                 for the Bimba con Nastrino point set with 1.6 million points
+        \caption{Reconstruction error (mm) against number of points
+                 for the Bimba con Nastrino point set with 1.6M points
                  as well as for simplified versions.}
+        \label{Surface_reconstruction_points_3-fig-simplification_bench}
     \end{figure}
 \end{center}