Avant pull

MMVII/Doc/Paper/Epipolar_ipol/Epipolar_ipol.tex

@@ -77,6 +77,7 @@
 
 
 \newcommand{\PiVert}{\widetilde{\pi}}
+\newcommand{\PiZVert}{\widetilde{\pi}_1^{\mathcal{Z}} }
 %\newcommand{\PiOT}{\Pi^{12}}
 %\newcommand{\PiTO}{\Pi_{2\rightarrow 1}}
 
@@ -779,10 +780,6 @@ \subsubsection{Why should it work ?}
 
 
 
-\subsubsection{Epipolar resampling without the localisation model}
-
-As described above, the method cannot work in general when there is 
-a functionnal correspondance $p_1=F(p_2)$ between tie points.
 
 %---------------------------------------------
 %---------------------------------------------
@@ -933,6 +930,47 @@ \subsubsection{Estimating inverse function}
 is $d+4$ in our implementation). These has no inconvenient as long the redunduncy
 is high enough.
 
+%---------------------------------------------
+%---------------------------------------------
+%---------------------------------------------
+
+\subsection{Epipolar resampling without the localisation model}
+
+The question we adress here is : \emph{"is it possible to use
+the proposed method  for computing epipolar geometry
+when we have only  tie points computed from images but no geometric model"}.  In fact
+there is not binary simple answer as there pro and cons to solve this question .
+
+\noindent {\underline {\bf Pro: }}  algorithm~\ref{AlgoGlob} only use tie points and a
+direction for computing the epipolar geometry. For this computation,
+it does not matter if the tie points are extracted from the geometric model
+(as with algorithm~\ref{AlgoGenData}) or from an image 
+processing method, like SIFT (\cite{LOWE}) , that do not require any
+\emph{a priori} information on image geometry. So as long as we
+are able to know the directions the method can be used.
+
+
+\noindent {\underline {\bf Cons:}} when the tie points comes from an image computation,
+then there exist some function relation between them :
+
+\begin{itemize}
+   \item suppose the relief can be describe a function $Z=\mathcal{Z}(X,Y)$,
+         and note $S^\mathcal{Z}$  the corresponding surface;
+   \item for a point $p_1$ of $I_1$, note $ \PiZVert (p_1)$
+         the intersection of  $\BundO(p_1)$ and the surface  $S^\mathcal{Z}$;
+   \item we see now there exist a functionnal relation between all the homologous
+         points $(p_1,p_2)$ corresponding to equation 
+\end{itemize}
+
+\begin{equation}
+   p_2 = (\pi_2 \circ  \PiZVert) (p_1) = F^\mathcal{Z}(p_1)
+\end{equation}
+
+
+But, as discussed in \ref{WhyWork}, it is not possible, in the most general
+case, to recover epipolar geometry from set of homologous points when there exist
+a functionnal relation between them.
+
 
 %---------------------------------------------
 %---------------------------------------------

src/uti_phgrm/CPP_CreateEpip.cpp

@@ -178,6 +178,7 @@ if (MPD_MM())
 
 
 
+    int aNbTens=0;
     for (int aKX=0 ; aKX<= aNbX ; aKX++)
     {
         // Barrycentrik weighting, 
@@ -245,10 +246,16 @@ if (MPD_MM())
                 {
                     Pt2dr aDir2 = vunit(aVPIm2.back()-aVPIm2[0]);
                     aSomTens2 = aSomTens2 + aDir2 * aDir2; // On double l'angle pour en faire un tenseur
+                    aNbTens++;
                 }
             }
         }
     }
+    if (!ForCheck)
+    {
+       std::cout << "Number points for tensor " << aNbTens << "\n";
+       ELISE_ASSERT(aNbTens!=0,"Cannot compute direction no valide point");
+    }
     Pt2dr aRT = Pt2dr::polar(aSomTens2,0.0);
     return Pt2dr::FromPolar(1.0,aRT.y/2.0); // Divide angle as it was multiplied
 }