diff --git a/Article/biblio.bib b/Article/biblio.bib index 781258bf9f7feb1ad2b81c6ca64dae32208737a9..c527a0fd24829ec18f416292fa6190900bb4e810 100755 --- a/Article/biblio.bib +++ b/Article/biblio.bib @@ -11,7 +11,7 @@ title = {Blurred segments in gray level images for interactive line extraction}, author = {Kerautret, Bertrand and Even, Philippe}, - booktitle = {Proc. of Int. Workshop on Computer Image Analysis}}, + booktitle = {Proc. of Int. Workshop on Combinatorial Image Analysis}, series = {LNCS}, volume = {5852}, optpublisher = {Springer}, diff --git a/Article/method.tex b/Article/method.tex index c58b4b53f3468c1c3826b580b28b30913a444e3b..9b2093eda000b3d0be03471a421017b6b2495afc 100755 --- a/Article/method.tex +++ b/Article/method.tex @@ -116,9 +116,9 @@ thus producing a useless computational cost. Here the proposed solution is to dynamically align the scan direction to the blurred segment one all along the expansion stage. -At each iteration $i$, the scan strip is updated using the direction -of the blurred segment computed at previous iteration $i-1$. -The adaptive directional scan $ADS$ is then defined by : +At each iteration $i$, the scan strip is aligned on the direction of the +blurred segment $\mathcal{B}_{i-1}$ computed at previous iteration $i-1$. +More generally, an adaptive directional scan $ADS$ is defined by: \begin{equation} %S_i = \mathcal{D}_{i-1} \cap \mathcal{N}_i ADS = \left\{ @@ -126,14 +126,23 @@ S_i = \mathcal{D}_i \cap \mathcal{N}_i \cap \mathcal{I} \left| \begin{array}{l} \delta(\mathcal{N}_i) = - \delta^{-1}(\mathcal{D}_0) \\ \wedge~ h_0(\mathcal{N}_i) = h_0(\mathcal{N}_{i-1}) + p(\mathcal{D}) \\ -\wedge~ \mathcal{D}_{i} = D (\mathcal{B}_{i-1},\varepsilon + k), i > 1 +\wedge~ \mathcal{D}_{i} = \mathcal{D} (C_{i-1}, \vec{D}_{i-1}, w_{i-1}), i > 1 +%\wedge~ \mathcal{D}_{i} = D (\mathcal{B}_{i-1},\varepsilon + k), i > 1 \end{array} \right. \right\} \end{equation} -where $D (\mathcal{B}_i,w)$ is the scan strip aligned to the -detected segment at iteration $i$ with width $w$. -In practice, the scan width is set a little greater than the assigned -width $\varepsilon$ ($k$ is a constant arbitrarily set to 4). -The last clause expresses the update of the scan bounds at iteration $i$. +%where $D (\mathcal{B}_i,w)$ is the scan strip aligned to the +%detected segment at iteration $i$ with width $w$. +%In practice, the scan width is set a little greater than the assigned +%width $\varepsilon$ ($k$ is a constant arbitrarily set to 4). +where $C_{i-1}$, $\vec{D}_{i-1}$ and $w_{i-1}$ are a position, a director +vector and a width observed at iteration $i-1$. +In the scope of the present detector, $C_{i-1}$ is the intersection of +the input selection and the medial axis of $\mathcal{B}_{i-1}$, +$\vec{D}_{i-1}$ the support vector of the narrowest digital straight line +that contains $\mathcal{B}_{i-1}$, +and $w_{i-1}$ a value slightly greater than the minimal width of +$\mathcal{B}_{i-1}$. +So the last clause expresses the update of the scan bounds at iteration $i$. Compared to static directional scans, the scan strip moves while scan lines remain fixed. This behavior ensures a complete detection of the blurred segment even @@ -145,15 +154,15 @@ when the orientation is badly estimated (\RefFig{fig:escape} c). \includegraphics[width=0.48\textwidth]{Fig_notions/escapeFirst_zoom.png} & \includegraphics[width=0.48\textwidth]{Fig_notions/escapeSecond_zoom.png} \\ \multicolumn{2}{c}{ - \includegraphics[width=0.98\textwidth]{Fig_notions/escapeThird_zoom.png}} + \includegraphics[width=0.78\textwidth]{Fig_notions/escapeThird_zoom.png}} \begin{picture}(1,1)(0,0) {\color{dwhite}{ - \put(-260,134.5){\circle*{8}} - \put(-86,134.5){\circle*{8}} + \put(-260,108.5){\circle*{8}} + \put(-86,108.5){\circle*{8}} \put(-172,7.5){\circle*{8}} }} - \put(-263,132){a} - \put(-89,132){b} + \put(-263,106){a} + \put(-89,106){b} \put(-175,5){c} \end{picture} \end{tabular} @@ -195,7 +204,7 @@ $\lambda$ iterations ($\mu_{i+\lambda} = \mu_i$), it is set to a much stricter value able to circumscribe the possible interpretations of the segment, that take into account the digitization margins: \begin{equation} -\varepsilon = \mu_{i+\lambda} + 1/2 +\varepsilon = \mu_{i+\lambda} + \frac{\textstyle 1}{\textstyle 2} \end{equation} This strategy aims at preventing the incorporation of spurious outliers in further parts of the segment.