From bc818b0b71f9d7b941bf161809b0140550bf80b8 Mon Sep 17 00:00:00 2001 From: even <philippe.even@loria.fr> Date: Mon, 7 Jan 2019 08:55:58 +0100 Subject: [PATCH] Article: remarks BK updated --- Article/Expe_auto/buroDetail.png | Bin 0 -> 26613 bytes Article/Expe_auto/perfTable.tex | 19 +++-- Article/Expe_hard/hardDetailNew.png | Bin 0 -> 28240 bytes Article/Expe_hard/hardDetailOld.png | Bin 0 -> 28030 bytes Article/Expe_hard/readme.txt | 4 + Article/Fig_notions/bswidth.tex | 12 +-- Article/Fig_notions/escapeLightFirst_full.png | Bin 0 -> 35166 bytes Article/Fig_notions/escapeLightFirst_zoom.png | Bin 0 -> 12916 bytes .../Fig_notions/escapeLightSecond_full.png | Bin 0 -> 32773 bytes .../Fig_notions/escapeLightSecond_zoom.png | Bin 0 -> 12112 bytes Article/Fig_notions/escapeLightThird_full.png | Bin 0 -> 34100 bytes Article/Fig_notions/escapeLightThird_zoom.png | Bin 0 -> 12866 bytes Article/Fig_notions/readme.txt | 34 +++++++++ Article/Fig_synth/res.txt | 70 +++++++++--------- Article/Fig_synth/statsTable.tex | 20 ++--- Article/biblio.bib | 4 +- Article/conclusion.tex | 47 ++++++------ Article/expe.tex | 44 +++-------- Article/expeAuto.tex | 33 +++++---- Article/expeHard.tex | 36 +++++---- Article/method.tex | 66 +++++++++-------- 21 files changed, 213 insertions(+), 176 deletions(-) create mode 100755 Article/Expe_auto/buroDetail.png create mode 100644 Article/Expe_hard/hardDetailNew.png create mode 100644 Article/Expe_hard/hardDetailOld.png create mode 100644 Article/Fig_notions/escapeLightFirst_full.png create mode 100644 Article/Fig_notions/escapeLightFirst_zoom.png create mode 100644 Article/Fig_notions/escapeLightSecond_full.png create mode 100644 Article/Fig_notions/escapeLightSecond_zoom.png create mode 100644 Article/Fig_notions/escapeLightThird_full.png create mode 100644 Article/Fig_notions/escapeLightThird_zoom.png create mode 100644 Article/Fig_notions/readme.txt diff --git a/Article/Expe_auto/buroDetail.png b/Article/Expe_auto/buroDetail.png 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\multicolumn{1}{c|}{$N$} -& \multicolumn{1}{c|}{$L$ (pixels)} & \multicolumn{1}{c|}{$W$ (pixels)} \\ +Measure $M$ & \multicolumn{1}{c|}{$T$} & \multicolumn{1}{c|}{$N$} +& \multicolumn{1}{c|}{$L$} & \multicolumn{1}{c|}{$W$} \\ \hline -$M_{old}$ on image of \RefFig{fig:auto} & 29.51 & 306 & 38.58 & 2.47 \\ -$M_{new}$ on image of \RefFig{fig:auto} & 25.85 & 352 & 33.25 & 2.17 \\ -$M_{new}/M_{old}$ (\%) +$M_{old}$ on image of \RefFig{fig:auto} +& 29.51 ms & 306 segments & 38.58 pixels & 2.47 pixels \\ +$M_{new}$ on image of \RefFig{fig:auto} +& 25.85 ms & 352 segments & 33.25 pixels & 2.17 pixels \\ +\hline \hline +$M_{new}/M_{old}$ (\%) & & & & \\ +\hspace{0.4cm} on image of \RefFig{fig:auto} & \multicolumn{1}{l|}{87.60} & \multicolumn{1}{l|}{115.03} & \multicolumn{1}{l|}{86.18} & \multicolumn{1}{l|}{87.85} \\ -\hline -$M_{new}/M_{old}$ (\%) & & & & \\ -on CannyLines images +\hspace{0.4cm} on the set of test images & & & & \\ +\hspace{0.4cm} on CannyLines images & 86.02 $\pm$ 2.44 & 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+selectionner le coin haut gauche de l'image depuis le +point (346, 140). diff --git a/Article/Fig_notions/bswidth.tex b/Article/Fig_notions/bswidth.tex index 5393c1f..3211f8c 100644 --- a/Article/Fig_notions/bswidth.tex +++ b/Article/Fig_notions/bswidth.tex @@ -1,7 +1,7 @@ \begin{picture}(220,60) \multiput(0,6)(2,-6){2}{\line(3,1){150}} - \multiput(0,8)(30,6){8}{\color{red}{\line(5,1){10}}} - \multiput(0,18)(30,6){8}{\color{red}{\line(5,1){10}}} + \multiput(0,8)(30,6){8}{\color{blue}{\line(5,1){10}}} + \multiput(0,18)(30,6){8}{\color{blue}{\line(5,1){10}}} \put(45,21){\circle*{3}} \put(55,21){\circle*{3}} \put(65,21){\circle*{3}} @@ -15,8 +15,8 @@ \put(140,36){\vector(0,1){10}} \put(140,62.66){\vector(0,-1){10}} \put(120,58){$\mu_{i-1}$} - \put(160,30){\color{red}{\vector(0,1){10}}} - \put(160,60){\color{red}{\vector(0,-1){10}}} - \put(164,36){\color{red}{$\mu_i$}} - \put(180,60){\color{red}{$\mathcal{B}_{i}$}} + \put(160,30){\color{blue}{\vector(0,1){10}}} + 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bas a droite avec les fleches +i - i pour voir les scans bounds +p pour le screenshot -> structure.png +I pour voir les scans +p pour le screenshot -> structure.png +Avec gimp, selection de la zone (516,70) (174,250) + + + +Le meme exemple a servi a produire une premiere figure escape +sur le segment P1 (181, 226), P2 (178, 205) +Avec gimp, selection de la zone (159,115) (355,203) + + + +Seg_escape est le code qui a fourni escape*_*.png +a partir de test_escape.txt +En vue principale : +Ctrl-q pour basculer entre scan statique ou adaptatif +En vue d'analyse (touche 1) : +i pour selectionner les vues de scan +Ctrl-j pour visualiser la selection utilisateur +Avec gimp, selection de la zone (333,227)(344,208) + + +Production des images plus claires : +6 y pour avoir un niveau de sombreur a 30 +Avec gimp, selection de la zone (58,127)(520,275) +pour avoir des images 454x148 a l'arrivee. diff --git a/Article/Fig_synth/res.txt b/Article/Fig_synth/res.txt index ff45cfc..d6862a9 100644 --- a/Article/Fig_synth/res.txt +++ b/Article/Fig_synth/res.txt @@ -1,36 +1,38 @@ -1000 cartes avec 1000 segments noirs sur fond blanc -re-estimation de la largeur en retirant un biais de 1.4 - RESULTS FOR THE OLD DETECTOR -69.719 (pm 20.3805) segments searches (local min) / image -25.23 (pm 6.65638) provided segments / image -10.766 (pm 1.96395) provided long segments / image -2.298 (pm 2.82935) undetected segments per image -88.3997 (pm 4.31352) % of points found -2.27666 (pm 1.50916) % of points found more than once (redetections) -32.2193 (pm 13.8132) % false points produced -Precision : 0.732884 (pm 0.0844506) -Biased width : 4.57922 (0.38789) per matched segment -Width : 3.37696 (0.350989) per matched segment -Width difference : 0.64275 (0.319964) per matched segment -Absolute width difference : 0.874094 (0.288227) per matched segment -Angle difference : 0.0497484 (0.756378) degrees per matched segment -Absolute angle difference : 1.2933 (0.92141) per matched segment -Absolute long edge angle difference : 0.44657 (0.55775) per matched segment +66.841 (pm 23.0353) segments searches (local min) / image +25.351 (pm 7.16695) provided segments / image +10.41 (pm 1.84318) provided long segments / image +2.527 (pm 2.54081) undetected segments per image +Recall : 89.0911 (pm 3.94178) % of points found +2.40181 (pm 1.52098) % of points found more than once (redetections) +34.8326 (pm 16.4621) % false points produced +Precision : 0.718919 (pm 0.0973014) +Statistical precision : 0.727566 (pm 0.0969161) +Statistical recall : 0.891995 (pm 0.0394028) +Statistical F-measure : 0.798543 (pm 0.0677593) +Biased width : 4.64042 (0.340364) per matched segment +Width : 3.42451 (0.334641) per matched segment +Width difference : 0.717033 (0.34932) per matched segment +Absolute width difference : 0.920479 (0.309156) per matched segment +Angle difference : -0.246099 (1.33358) degrees per matched segment +Absolute angle difference : 1.48162 (1.41907) per matched segment +Absolute long edge angle difference : 0.542687 (1.08617) per matched segment RESULTS FOR THE NEW DETECTOR -63.6 (pm 17.4179) segments searches (local min) / image -23.722 (pm 4.90028) provided segments / image -11.619 (pm 2.08619) provided long segments / image -0.475 (pm 0.756272) undetected segments per image -89.813 (pm 3.17276) % of points found -1.83739 (pm 1.3875) % of points found more than once (redetections) -22.5376 (pm 10.2339) % false points produced -Precision : 0.799399 (pm 0.0701648) -Biased width : 4.49693 (0.320961) per matched segment -Width : 3.26288 (0.297711) per matched segment -Width difference : 0.408348 (0.27149) per matched segment -Absolute width difference : 0.741648 (0.24851) per matched segment -Angle difference : 0.0354951 (0.641921) degrees per matched segment -Absolute angle difference : 0.982936 (0.696344) per matched segment -Long edge absolute angle difference : 0.480284 (0.568648) per matched segment - +62.393 (pm 17.1718) segments searches (local min) / image +24.351 (pm 5.02624) provided segments / image +11.145 (pm 1.91824) provided long segments / image +0.637 (pm 0.909978) undetected segments per image +Recall : 90.0194 (pm 2.77084) % of points found +1.78012 (pm 1.21784) % of points found more than once (redetections) +23.7471 (pm 8.87023) % false points produced +Precision : 0.791264 (pm 0.0630463) +Statistical precision : 0.791896 (pm 0.0630431) +Statistical recall : 0.900763 (pm 0.0277026) +Statistical F-measure : 0.84169 (pm 0.0416617) +Biased width : 4.5098 (0.252717) per matched segment +Width : 3.28158 (0.239712) per matched segment +Width difference : 0.462984 (0.255638) per matched segment +Absolute width difference : 0.764102 (0.231734) per matched segment +Angle difference : -0.141146 (0.721153) degrees per matched segment +Absolute angle difference : 1.05426 (0.801184) per matched segment +Long edge absolute angle difference : 0.529121 (0.684013) per matched segment diff --git a/Article/Fig_synth/statsTable.tex b/Article/Fig_synth/statsTable.tex index b4da315..33c04ff 100644 --- a/Article/Fig_synth/statsTable.tex +++ b/Article/Fig_synth/statsTable.tex @@ -3,18 +3,20 @@ Detector : & \multicolumn{3}{c|}{old} & \multicolumn{3}{c|}{new} \\ \hline Detected blurred segments per image -& 25.23 & $\pm$ & 6.66 & 23.72 & $\pm$ & 4.90 \\ +& 25.35 & $\pm$ & 7.17 & 24.35 & $\pm$ & 5.03 \\ Detected long (> 40 pixels) blurred segments per image -& 10.77 & $\pm$ & 1.96 & 11.62 & $\pm$ & 2.09 \\ +& 10.41 & $\pm$ & 1.84 & 11.14 & $\pm$ & 1.92 \\ Undetected input segments per image -& 2.30 & $\pm$ & 2.83 & 0.47 & $\pm$ & 0.76 \\ -Ratio of true detection (\%) : $\#(D\cap S)/\#S$ -& 88.40 & $\pm$ & 4.31 & 89.81 & $\pm$ & 3.17 \\ -Precision (\%) : $\#(D\cap S)/\#D$ -& 73.29 & $\pm$ & 8.45 & 79.94 & $\pm$ & 7.02 \\ +& 2.53 & $\pm$ & 2.54 & 0.64 & $\pm$ & 0.91 \\ +Precision (\%) : $P = \#(D\cap S)/\#D$ +& 72.76 & $\pm$ & 9.69 & 79.19 & $\pm$ & 6.30 \\ +Recall (ratio of true detection) (\%) : $R = \#(D\cap S)/\#S$ +& 89.20 & $\pm$ & 3.94 & 90.08 & $\pm$ & 2.77 \\ +F-measure (harmonic mean) (\%) : $F = 2\times P\times R/(P+R)$ +& 79.85 & $\pm$ & 6.78 & 84.17 & $\pm$ & 4.17 \\ Width difference (in pixels) to matched input segment -& 0.87 & $\pm$ & 0.29 & 0.74 & $\pm$ & 0.24 \\ +& 0.92 & $\pm$ & 0.31 & 0.76 & $\pm$ & 0.23 \\ Angle difference (in degrees) to matched input segment -& 1.29 & $\pm$ & 0.92 & 0.98 & $\pm$ & 0.70 \\ +& 1.48 & $\pm$ & 1.42 & 1.05 & $\pm$ & 0.80 \\ \hline \end{tabular} diff --git a/Article/biblio.bib b/Article/biblio.bib index 5df469a..90f6b92 100755 --- a/Article/biblio.bib +++ b/Article/biblio.bib @@ -32,7 +32,7 @@ @inproceedings{DebledAl05, - title = {Blurred Segments Decomposition in Linear Time}, + title = {Blurred segments decomposition in linear time}, author = {Debled-Rennesson, Isabelle and Feschet, Fabien and Rouyer-Degli, Jocelyne}, booktitle = {Proc. of Int. Conf. on DGCI}, @@ -43,7 +43,7 @@ pages = {371-382}, optaddress = {Poitiers, France}, optmonth = {April}, - publisher = {Springer} + optpublisher = {Springer} } diff --git a/Article/conclusion.tex b/Article/conclusion.tex index 240817f..3347917 100755 --- a/Article/conclusion.tex +++ b/Article/conclusion.tex @@ -3,36 +3,39 @@ \label{sec:conclusion} This paper introduced a new straight edge detector based on a local analysis of -the image gradient and on the use of blurred segments to vehiculate an +the image gradient and on the use of blurred segments to embed an estimation of the edge thickness. It relies on directional scans of the image around maximal values of the gradient magnitude, that have previously been presented in \cite{KerautretEven09}. -Despite of good performances achieved, the former approach suffers of two -major drawbacks: the inaccurate estimation of the blurred segment width -and orientation, and the lack of guarantee that it is completely detected. -These limitations were solved through the integration of two new concepts: +%Despite of good performances achieved, the former approach suffers of two +%major drawbacks: the inaccurate estimation of the blurred segment width +%and orientation, and the lack of guarantee that it is completely detected. +%These limitations were solved through the integration of two new concepts: +%adaptive directional scans that continuously adjust the scan strip +%to the detected blurred segment direction; +The main limitations of the former approach were solved through the integration +of two new concepts: adaptive directional scans that continuously adjust the scan strip -to the detected blurred segment direction; +to the detected edge direction; the control of the assigned width based on the observation of the -blurred segment thickenning in the early stage of its expansion. +blurred segment growth. +Expected gains in accuracy and execution time were confirmed by the +held experiments. -Expected gains in execution time linked to the suppression of a useless -repetition of the fine tracking stage were confirmed by the experiments -both in supervised and unsupervised contexts. -The residual weakness is the high sensitivity to the initial conditions -despite of the valuable enhancement brought by the duplication of the -initial detection. -Disturbing gradient perturbations in the early stage of the edge expansion, -possibly due to the presence of close edges, can deeply affect the output -blurred segment. -In supervised context, the user can easily select a favourable area where +A residual weakness of the approach is the sensitivity to the initial +conditions. +In supervised context, the user can select a favourable area where the awaited edge is dominant. -But this default remains quite sensible in unsupervised context. - -In future works, we intend to provide some solutions for this drawback -by scoring the detection result on the base of a characterization of the -initial context. +This task is made quite easier, thanks to the stabilization produced by +the duplication of the initial detection. +But in unsupervised context, gradient perturbations in the early stage of +the edge expansion, msotly due to the presence of close edges, can deeply +affect the result. +In future works, we intend to provide solutions to this drawback +by scoring the detection result on the basis of a characterization of the +local context. +% Then experimental validation of the consistency of the estimated width and orientation values on real situations are planned in different application fields. diff --git a/Article/expe.tex b/Article/expe.tex index 25b1d56..9454e82 100755 --- a/Article/expe.tex +++ b/Article/expe.tex @@ -11,6 +11,12 @@ For a fair comparison, the process flow of the former method (the initial detection followed by two refinement steps) is integrated as an option into the code of the new detector, so that both methods rely on the same optimized basic routines. +During all these experiments, only the blurred segment size and its +orientation compared to the initial stroke were tested at the end of +the initial detection, and only the segment size was tested at the end +of the fine tracking stage. +All the other tests, sparsity or fragmentation, were disabled. +The segment minimal size was set to 5 pixels, except where precised. The first test (\RefFig{fig:synth}) compares the performance of both detectors on a set of 1000 synthesized images containing 10 randomly @@ -18,20 +24,14 @@ placed input segments with random width between 2 and 5 pixels. The absolute value of the difference of each found segment to its matched input segment is measured. On such perfect image, the numerical error on the gradient extraction -biases the line width measures. This bias was estimated in quasi ideal -context (only one input segment, thus no risk of perturbation) +biases the line width measures. This bias was first estimated using 1000 +images containing only one input segment (no possible interaction) and the found value (1.4 pixel) was taken into account in the test. -Although the effect of the old detector weaknesses should be reduced in -this low gradient noise context, the results of \RefTab{tab:synth} show +The results of \RefTab{tab:synth} show slightly better width and angle measurements for the new detector. The new detector shows more precise, with a smaller amount of false detections and succeeds in finding most of the input segments. -The second test (\RefFig{fig:hard}) visually compares the results of both -detectors on quite noisy images, also difficult to process for other -detectors from the literature. -The new detector provides less outliers and misaligned segments, and -globally more relevant informations to infere the structure of the brick wall. \begin{figure}[h] %\center \begin{tabular}{ @@ -65,29 +65,7 @@ $S$ is the set of all the input segments, $D$ the set of all the detected blurred segments.} \label{tab:synth} \end{table} -\begin{figure} -%\center - \begin{tabular}{ - c@{\hspace{0.1cm}}c@{\hspace{0.1cm}}c@{\hspace{0.1cm}}} - \includegraphics[width=0.32\textwidth]{Fig_method/parpaings.png} & - \includegraphics[width=0.32\textwidth]{Expe_hard/hardOld.png} & - \includegraphics[width=0.32\textwidth]{Expe_hard/hardNew.png} - \begin{picture}(1,1) - {\color{dwhite}{ - \put(-286,4.5){\circle*{8}} - \put(-171,4.5){\circle*{8}} - \put(-58,4.5){\circle*{8}} - }} - \put(-288.5,2){a} - \put(-173.5,2){b} - \put(-60.5,2){c} - \end{picture} - \end{tabular} - \caption{Detection results on quite textured images: - one of the tested images (a), - the segments found by the old detector (b) - and those found by the new detector (c).} - \label{fig:hard} -\end{figure} \input{expeAuto} + +\input{expeHard} diff --git a/Article/expeAuto.tex b/Article/expeAuto.tex index c46db99..8538b88 100755 --- a/Article/expeAuto.tex +++ b/Article/expeAuto.tex @@ -1,16 +1,13 @@ - -The third campaign of tests aims at evaluating the performance of the new -detector with respect to the previous one on a selection of more standard -images. +The next experiments aim at evaluating the performance of the new +detector with respect to the previous one on a test set composed of a +selection of 20 real images. +One of them is displayed on \RefFig{fig:auto}. Compared measures $M$ are the execution time $T$, the amount $N$ of detected -blurred segments, the mean length $L$ and the mean width $W$ of the detected -segments. +blurred segments, their mean length $L$ and their mean width $W$. For the sake of objectivity, these results are also compared to the same measurements made on the 20 images data base used for the CannyLine line segment detector \cite{LuAl15}. -\RefTab{tab:auto} gives the measures obtained on one of the selected images -(\RefFig{fig:auto}) and the result of a systematic test on the CannyLine -data base. +\RefTab{tab:auto} gives the achieved results. \begin{figure}[h] %\center \begin{tabular}{ @@ -20,7 +17,8 @@ data base. % \includegraphics[width=0.32\textwidth]{Expe_auto/coloredNew.png} \\ \includegraphics[width=0.32\textwidth]{Expe_auto/bsOld.png} & \includegraphics[width=0.32\textwidth]{Expe_auto/bsNew.png} \\ - & \includegraphics[width=0.22\textwidth]{Expe_auto/dssDetailOld.png} & + \includegraphics[width=0.22\textwidth]{Expe_auto/buroDetail.png} & + \includegraphics[width=0.22\textwidth]{Expe_auto/dssDetailOld.png} & \includegraphics[width=0.22\textwidth]{Expe_auto/dssDetailNew.png} \begin{picture}(1,1) {\color{red}{ @@ -28,25 +26,30 @@ data base. \put(-5.5,31){\vector(-2,-1){20}} \put(-133.5,31){\framebox(28,9)} \put(-117.5,31){\vector(-2,-1){20}} + \put(-247.5,31){\framebox(28,9)} + \put(-231.5,31){\vector(-2,-1){20}} }} {\color{dwhite}{ \put(-291,32.5){\circle*{8}} \put(-177,32.5){\circle*{8}} \put(-63,32.5){\circle*{8}} + \put(-302,4.5){\circle*{8}} \put(-188,4.5){\circle*{8}} \put(-75,4.5){\circle*{8}} }} \put(-293.5,30){a} \put(-179.5,30){b} \put(-65.5,30){c} - \put(-191,2){d} - \put(-77.5,2){e} + \put(-305,2){d} + \put(-191,2){e} + \put(-77.5,2){f} \end{picture} \end{tabular} - \caption{Automatic detection on standard images: + \caption{Automatic detection on real images: an input image (a), the segments found by the old detector (b) and those found by the new detector (c), and a detail of the - enclosing digital segments for both old (d) and new (e) detectors.} + image (d) and the enclosing digital segments for both old (e) + and new (f) detectors.} \label{fig:auto} \end{figure} \begin{table} @@ -69,7 +72,7 @@ Found edges are thus more fragmented. The relevance of this behavior depends strongly on application requirements. Therefore the control of the assigned width is left as an option, the user can let or cancel it. -In both case, it could be interesting to combine the detector with a tool +In both case, it could be useful to combine the detector with a tool to merge aligned segments. %Although these observations in unsupervised context should be reproduced diff --git a/Article/expeHard.tex b/Article/expeHard.tex index 087e0df..be775d9 100755 --- a/Article/expeHard.tex +++ b/Article/expeHard.tex @@ -1,29 +1,33 @@ - -The second test (\RefFig{fig:hard}) visually compares the results of -both detectors on quite difficult images with a lot of gradient noise. -The new detector provides less outliers and misaligned segments, and -globally more relevant informations to infere the structure of the brick wall. -\begin{figure}[h] -%\center +The last test visually compares the results of both detectors on quite textured +images, also difficult to process for other detectors from the literature. +The minimal size parameter was raised to 12 pixels to reject small segments +considered as outliers. +On the example of \RefFig{fig:hard}, the new detector provides less residual +outliers and misaligned segments, and globally more relevant informations +to infere the structure of the brick wall. +\begin{figure} + \center \begin{tabular}{ c@{\hspace{0.1cm}}c@{\hspace{0.1cm}}c@{\hspace{0.1cm}}} - \includegraphics[width=0.32\textwidth]{Fig_method/parpaings.png} & - \includegraphics[width=0.32\textwidth]{Fig_hard/hardOld.png} & - \includegraphics[width=0.32\textwidth]{Fig_hard/hardNew.png} + \includegraphics[width=0.205\textwidth]{Fig_method/parpaings.png} & + \includegraphics[width=0.32\textwidth]{Expe_hard/hardDetailOld.png} & + \includegraphics[width=0.32\textwidth]{Expe_hard/hardDetailNew.png} \begin{picture}(1,1) + {\color{red}{ + \put(-302,34){\framebox(29,11.5)} + }} {\color{dwhite}{ - \put(-286,4.5){\circle*{8}} + \put(-266,4.5){\circle*{8}} \put(-171,4.5){\circle*{8}} \put(-58,4.5){\circle*{8}} }} - \put(-288.5,2){a} + \put(-268.5,2){a} \put(-173.5,2){b} \put(-60.5,2){c} \end{picture} \end{tabular} - \caption{Detection results on quite textured images: - one of the tested images (a), - the segments found by the old detector (b) - and those found by the new detector (c).} + \caption{Results on quite textured images: test image (a), + detail (top left corner) on the segments found by the old + detector (b) and on those found by the new detector (c).} \label{fig:hard} \end{figure} diff --git a/Article/method.tex b/Article/method.tex index e9e5f8f..d4640a5 100755 --- a/Article/method.tex +++ b/Article/method.tex @@ -37,8 +37,8 @@ The output segment $\mathcal{B}'$ is finally tested according to the application needs. Too short, too sparse or too fragmented segments can be rejected. Length, sparsity or fragmentation thresholds are intuitive parameters left at the end user disposal. -None of these tests are activated for the experimental stage in order -to put forward achievable performance. +%None of these tests are activated for the experimental stage in order +%to put forward achievable performance. \subsection{Adaptive directional scan} @@ -51,36 +51,36 @@ A second search is then run using another directional scan aligned on the detected segment (\RefFig{fig:escape} b). In the given example, an outlier added to the initial segment leads to a wrong orientation value. -But even in case of a correct detection, this estimated orientation -is subject to the numerization rounding, and the longer the real segment -to detect, the higher the probability to fail again on a blurred segment -escape from the directional scan. +But even in case of a correct detection, this estimated orientation is +subject to the numerization rounding, and the longer the real segment is, +the higher the probability gets to fail again on an escape from the scan strip. \begin{figure}[h] \center \begin{tabular}{c@{\hspace{0.2cm}}c} - \includegraphics[width=0.48\textwidth]{Fig_notions/escapeFirst_zoom.png} & - \includegraphics[width=0.48\textwidth]{Fig_notions/escapeSecond_zoom.png} \\ + \includegraphics[width=0.48\textwidth]{Fig_notions/escapeLightFirst_zoom.png} & + \includegraphics[width=0.48\textwidth]{Fig_notions/escapeLightSecond_zoom.png} \\ \multicolumn{2}{c}{ - \includegraphics[width=0.62\textwidth]{Fig_notions/escapeThird_zoom.png}} + \includegraphics[width=0.62\textwidth]{Fig_notions/escapeLightThird_zoom.png}} \begin{picture}(1,1)(0,0) {\color{dwhite}{ - \put(-260,87.5){\circle*{8}} - \put(-86,87.5){\circle*{8}} - \put(-172,7.5){\circle*{8}} + \put(-260,78.5){\circle*{8}} + \put(-86,78.5){\circle*{8}} + \put(-172,4.5){\circle*{8}} }} - \put(-263,85){a} - \put(-89,85){b} - \put(-175,5){c} + \put(-262.5,76){a} + \put(-89,75.5){b} + \put(-174.5,2){c} \end{picture} \end{tabular} \caption{Aborted detections on side escapes of static directional scans and successful detection using an adaptive directional scan. The last points added to the left of the blurred segment during initial detection (a) lead to a bad estimation of its - orientation, and thus to an incomplete fine detection with a - classical directional scan (b). An adaptive directional scan - can continue the segment expansion as far as necessary (c). + orientation, and thus to an incomplete fine tracking with a + classical directional scan (b). An adaptive directional scan at + the place of the static one allows to continue the segment + expansion as far as necessary (c). On the pictures, the input selection is drawn in red color, the scan strip bounds in blue and the detected blurred segment in green.} @@ -108,22 +108,26 @@ ADS = \left\{ 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(\mathcal{N}_i) = h(\mathcal{N}_{i-1}) + p(\mathcal{D}) \\ -\wedge~ \mathcal{D}_{i} = \mathcal{D} (C_{i-1}, \vec{D}_{i-1}, w_{i-1}), i > 1 +\wedge~ h(\mathcal{N}_i) = h(\mathcal{N}_{i-1}) + p(\mathcal{D}_0) \\ +\wedge~ \mathcal{D}_{i} = \mathcal{D} (C_{i-1}, \vec{D}_{i-1}, w_{i-1}), +i > \lambda \end{array} \right. \right\} \end{equation} -where $C_{i-1}$, $\vec{D}_{i-1}$ and $w_{i-1}$ are a position, a director -vector and a width observed at iteration $i-1$. +where $C_{i}$, $\vec{D}_{i}$ and $w_{i}$ are respectively a position, +a director vector and a width observed at iteration $i$. 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 enclosing digital segment $E(\mathcal{B}_{i-1})$, 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 +Compared to static directional scans where the scan strip remains fixed to +the initial line $\mathcal{D}_0$, here the scan strip moves while scan lines remain fixed. -This behavior ensures a complete detection of the blurred segment even -when the orientation is badly estimated (\RefFig{fig:escape} c). +This behavior ensures a complete detection of the blurred segment even when +the orientation of $\mathcal{D}_0$ is badly estimated (\RefFig{fig:escape} c). +In practice, it is started after $\lambda = 20$ iterations when the observed +direction becomes more stable. \subsection{Control of the assigned width} @@ -131,15 +135,15 @@ The assigned width $\varepsilon$ to the blurred segment recognition algorithm is initially set to a large value $\varepsilon_0$ in order to allow the detection of large blurred segments. Then, when no more augmentation of the minimal width is observed after -$\lambda$ iterations ($\mu_{i+\lambda} = \mu_i$), it is set to a much +$\tau$ iterations ($\mu_{i+\tau} = \mu_i$), 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} + \frac{\textstyle 1}{\textstyle 2} +\varepsilon = \mu_{i+\tau} + \frac{\textstyle 1}{\textstyle 2} \end{equation} This strategy aims at preventing the incorporation of spurious outliers in further parts of the segment. -Setting the observation distance to a constant value $\lambda = 20$ seems +Setting the observation distance to a constant value $\tau = 20$ seems appropriate in most experimented situations. \subsection{Supervised blurred segment detection} @@ -221,7 +225,7 @@ $2~\varepsilon_{ini}$, and $M_j$ is used as start point of the blurred segment; \item the occupancy mask is filled in with the points of the dilated blurred segments $\mathcal{B}_j''$ at the end of each successful detection -(a 21 pixels bowl is used); +(a 21 pixels neighborhood is used); \item points marked as occupied are rejected when selecting candidates for the blurred segment extension in the fine tracking step. \end{enumerate} @@ -240,8 +244,8 @@ the borders. At each position, the multi-detection algorithm is run to collect all the segments found under the stroke. In the present work, the stroke sweeping step $\delta$ is set to 10 pixels. -The automatic detection of blurred segments in a whole image is left -available for testing in an online demonstration at the following address: \\ +The automatic detection of blurred segments in a whole image is left available +for testing from an online demonstration at the following address: \\ \href{http://ipol-geometry.loria.fr/~kerautre/ipol_demo/AdaptDirBS_IPOLDemo}{ \small{\url{ http://ipol-geometry.loria.fr/~kerautre/ipol_demo/AdaptDirBS_IPOLDemo}}} -- GitLab